mirror of
https://github.com/Z3Prover/z3
synced 2025-11-04 13:29:11 +00:00
Simplify RCF C API. Add Z3_rcf_mk_roots (C API) and MkRoots (Python API). Implement basic root isolation support.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
3c1f1a3b65
commit
09b5724d82
6 changed files with 216 additions and 118 deletions
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@ -23,29 +23,10 @@ Notes:
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#include"z3.h"
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#include"api_log_macros.h"
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#include"api_context.h"
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#include"api_rcf.h"
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#include"realclosure.h"
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extern "C" {
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void Z3_API Z3_rcf_inc_ref(Z3_context c, Z3_rcf_num a) {
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Z3_TRY;
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LOG_Z3_rcf_inc_ref(c, a);
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RESET_ERROR_CODE();
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to_rcf_num(a)->inc_ref();
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Z3_CATCH;
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}
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void Z3_API Z3_rcf_dec_ref(Z3_context c, Z3_rcf_num a) {
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Z3_TRY;
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LOG_Z3_rcf_dec_ref(c, a);
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RESET_ERROR_CODE();
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if (to_rcf_num(a)->ref_count() == 1) {
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mk_c(c)->rcfm().del(to_rcnumeral(a));
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}
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to_rcf_num(a)->dec_ref();
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Z3_CATCH;
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}
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static rcmanager & rcfm(Z3_context c) {
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return mk_c(c)->rcfm();
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}
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@ -53,14 +34,24 @@ extern "C" {
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static void reset_rcf_cancel(Z3_context c) {
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rcfm(c).reset_cancel();
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}
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static Z3_rcf_num mk_rcf_num(Z3_context c, rcnumeral & a) {
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Z3_rcf_num_ref * r = alloc(Z3_rcf_num_ref);
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rcfm(c).swap(r->m_num, a);
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mk_c(c)->save_object(r);
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return of_rcf_num(r);
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static rcnumeral to_rcnumeral(Z3_rcf_num a) {
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return rcnumeral::mk(a);
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}
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static Z3_rcf_num from_rcnumeral(rcnumeral a) {
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return reinterpret_cast<Z3_rcf_num>(a.c_ptr());
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}
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void Z3_API Z3_rcf_del(Z3_context c, Z3_rcf_num a) {
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Z3_TRY;
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LOG_Z3_rcf_del(c, a);
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RESET_ERROR_CODE();
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rcnumeral _a = to_rcnumeral(a);
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rcfm(c).del(_a);
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Z3_CATCH;
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}
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Z3_rcf_num Z3_API Z3_rcf_mk_rational(Z3_context c, Z3_string val) {
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Z3_TRY;
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LOG_Z3_rcf_mk_rational(c, val);
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@ -68,9 +59,9 @@ extern "C" {
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reset_rcf_cancel(c);
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scoped_mpq q(rcfm(c).qm());
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rcfm(c).qm().set(q, val);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).set(r, q);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -79,9 +70,9 @@ extern "C" {
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LOG_Z3_rcf_mk_small_int(c, val);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).set(r, val);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -90,9 +81,9 @@ extern "C" {
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LOG_Z3_rcf_mk_pi(c);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).mk_pi(r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -101,9 +92,9 @@ extern "C" {
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LOG_Z3_rcf_mk_e(c);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).mk_e(r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -112,9 +103,37 @@ extern "C" {
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LOG_Z3_rcf_mk_infinitesimal(c, name);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).mk_infinitesimal(name, r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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unsigned Z3_API Z3_rcf_mk_roots(Z3_context c, unsigned n, Z3_rcf_num const a[], Z3_rcf_num roots[]) {
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Z3_TRY;
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LOG_Z3_rcf_mk_roots(c, n, a, roots);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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rcnumeral_vector av;
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unsigned rz = 0;
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for (unsigned i = 0; i < n; i++) {
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if (!rcfm(c).is_zero(to_rcnumeral(a[i])))
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rz = i + 1;
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av.push_back(to_rcnumeral(a[i]));
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}
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if (rz == 0) {
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// it is the zero polynomial
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SET_ERROR_CODE(Z3_INVALID_ARG);
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return 0;
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}
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av.shrink(rz);
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rcnumeral_vector rs;
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rcfm(c).isolate_roots(av.size(), av.c_ptr(), rs);
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unsigned num_roots = rs.size();
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for (unsigned i = 0; i < num_roots; i++) {
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roots[i] = from_rcnumeral(rs[i]);
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}
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return num_roots;
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Z3_CATCH_RETURN(0);
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}
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@ -123,9 +142,9 @@ extern "C" {
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LOG_Z3_rcf_add(c, a, b);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).add(to_rcnumeral(a), to_rcnumeral(b), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -134,9 +153,9 @@ extern "C" {
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LOG_Z3_rcf_sub(c, a, b);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).sub(to_rcnumeral(a), to_rcnumeral(b), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -145,9 +164,9 @@ extern "C" {
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LOG_Z3_rcf_mul(c, a, b);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).mul(to_rcnumeral(a), to_rcnumeral(b), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -156,9 +175,9 @@ extern "C" {
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LOG_Z3_rcf_div(c, a, b);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).div(to_rcnumeral(a), to_rcnumeral(b), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -167,9 +186,9 @@ extern "C" {
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LOG_Z3_rcf_neg(c, a);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).neg(to_rcnumeral(a), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -178,9 +197,9 @@ extern "C" {
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LOG_Z3_rcf_inv(c, a);
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RESET_ERROR_CODE();
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reset_rcf_cancel(c);
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scoped_rcnumeral r(rcfm(c));
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rcnumeral r;
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rcfm(c).inv(to_rcnumeral(a), r);
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RETURN_Z3(mk_rcf_num(c, r));
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RETURN_Z3(from_rcnumeral(r));
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Z3_CATCH_RETURN(0);
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}
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@ -1,38 +0,0 @@
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/*++
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Copyright (c) 2013 Microsoft Corporation
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Module Name:
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api_rcf.h
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Abstract:
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Additional APIs for handling elements of the Z3 real closed field that contains:
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- transcendental extensions
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- infinitesimal extensions
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- algebraic extensions
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Author:
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Leonardo de Moura (leonardo) 2012-01-05
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Notes:
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--*/
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#ifndef _API_RCF_H_
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#define _API_RCF_H_
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#include"api_util.h"
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#include"realclosure.h"
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struct Z3_rcf_num_ref : public api::object {
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rcnumeral m_num;
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virtual ~Z3_rcf_num_ref() {}
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};
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inline Z3_rcf_num_ref * to_rcf_num(Z3_rcf_num n) { return reinterpret_cast<Z3_rcf_num_ref *>(n); }
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inline Z3_rcf_num of_rcf_num(Z3_rcf_num_ref * n) { return reinterpret_cast<Z3_rcf_num>(n); }
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inline rcnumeral & to_rcnumeral(Z3_rcf_num n) { SASSERT(n != 0); return to_rcf_num(n)->m_num; }
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#endif
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@ -32,6 +32,22 @@ def MkInfinitesimal(name="eps", ctx=None):
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ctx = z3._get_ctx(ctx)
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return RCFNum(Z3_rcf_mk_infinitesimal(ctx.ref(), name), ctx)
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def MkRoots(p, ctx=None):
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ctx = z3._get_ctx(ctx)
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num = len(p)
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_tmp = []
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_as = (RCFNumObj * num)()
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_rs = (RCFNumObj * num)()
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for i in range(num):
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_a = _to_rcfnum(p[i], ctx)
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_tmp.append(_a) # prevent GC
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_as[i] = _a.num
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nr = Z3_rcf_mk_roots(ctx.ref(), num, _as, _rs)
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r = []
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for i in range(nr):
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r.append(RCFNum(_rs[i], ctx))
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return r
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class RCFNum:
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def __init__(self, num, ctx=None):
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# TODO: add support for converting AST numeral values into RCFNum
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@ -41,10 +57,9 @@ class RCFNum:
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else:
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self.ctx = z3._get_ctx(ctx)
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self.num = Z3_rcf_mk_rational(self.ctx_ref(), str(num))
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Z3_rcf_inc_ref(self.ctx_ref(), self.num)
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def __del__(self):
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Z3_rcf_dec_ref(self.ctx_ref(), self.num)
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Z3_rcf_del(self.ctx_ref(), self.num)
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def ctx_ref(self):
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return self.ctx.ref()
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@ -53,28 +68,36 @@ class RCFNum:
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return Z3_rcf_num_to_string(self.ctx_ref(), self.num)
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def __add__(self, other):
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return RCFNum(Z3_rcf_add(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_add(self.ctx_ref(), self.num, v.num), self.ctx)
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def __radd__(self, other):
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return RCFNum(Z3_rcf_add(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_add(self.ctx_ref(), v.num, self.num), self.ctx)
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def __mul__(self, other):
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return RCFNum(Z3_rcf_mul(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_mul(self.ctx_ref(), self.num, v.num), self.ctx)
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def __rmul__(self, other):
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return RCFNum(Z3_rcf_mul(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_mul(self.ctx_ref(), v.num, self.num), self.ctx)
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def __sub__(self, other):
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return RCFNum(Z3_rcf_sub(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_sub(self.ctx_ref(), self.num, v.num), self.ctx)
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def __rsub__(self, other):
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return RCFNum(Z3_rcf_sub(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_sub(self.ctx_ref(), v.num, self.num), self.ctx)
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def __div__(self, other):
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return RCFNum(Z3_rcf_div(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_div(self.ctx_ref(), self.num, v.num), self.ctx)
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def __rdiv__(self, other):
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return RCFNum(Z3_rcf_div(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num), self.ctx)
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v = _to_rcfnum(other, self.ctx)
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return RCFNum(Z3_rcf_div(self.ctx_ref(), v.num, self.num), self.ctx)
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def __neg__(self):
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return self.__rsub__(0)
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@ -83,32 +106,42 @@ class RCFNum:
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return Z3_rcf_num_to_decimal_string(self.ctx_ref(), self.num, prec)
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def __lt__(self, other):
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return Z3_rcf_lt(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_lt(self.ctx_ref(), self.num, v.num)
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def __rlt__(self, other):
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return Z3_rcf_lt(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_lt(self.ctx_ref(), v.num, self.num)
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def __gt__(self, other):
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return Z3_rcf_gt(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_gt(self.ctx_ref(), self.num, v.num)
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def __rgt__(self, other):
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return Z3_rcf_gt(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_gt(self.ctx_ref(), v.num, self.num)
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def __le__(self, other):
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return Z3_rcf_le(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_le(self.ctx_ref(), self.num, v.num)
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def __rle__(self, other):
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return Z3_rcf_le(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_le(self.ctx_ref(), v.num, self.num)
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def __ge__(self, other):
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return Z3_rcf_ge(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_ge(self.ctx_ref(), self.num, v.num)
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def __rge__(self, other):
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return Z3_rcf_ge(self.ctx_ref(), _to_rcfnum(other, self.ctx).num, self.num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_ge(self.ctx_ref(), v.num, self.num)
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def __eq__(self, other):
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return Z3_rcf_eq(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
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v = _to_rcfnum(other, self.ctx)
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return Z3_rcf_eq(self.ctx_ref(), self.num, v.num)
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def __ne__(self, other):
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return Z3_rcf_neq(self.ctx_ref(), self.num, _to_rcfnum(other, self.ctx).num)
|
||||
v = _to_rcfnum(other, self.ctx)
|
||||
return Z3_rcf_neq(self.ctx_ref(), self.num, v.num)
|
||||
|
||||
|
|
|
|||
|
|
@ -27,18 +27,11 @@ extern "C" {
|
|||
#endif // __cplusplus
|
||||
|
||||
/**
|
||||
\brief Increment the reference counter of a RCF numeral.
|
||||
|
||||
def_API('Z3_rcf_inc_ref', VOID, (_in(CONTEXT), _in(RCF_NUM)))
|
||||
*/
|
||||
void Z3_API Z3_rcf_inc_ref(__in Z3_context c, __in Z3_rcf_num a);
|
||||
\brief Delete a RCF numeral created using the RCF API.
|
||||
|
||||
/**
|
||||
\brief Decrement the reference counter of a RCF numeral.
|
||||
|
||||
def_API('Z3_rcf_dec_ref', VOID, (_in(CONTEXT), _in(RCF_NUM)))
|
||||
def_API('Z3_rcf_del', VOID, (_in(CONTEXT), _in(RCF_NUM)))
|
||||
*/
|
||||
void Z3_API Z3_rcf_dec_ref(__in Z3_context c, __in Z3_rcf_num a);
|
||||
void Z3_API Z3_rcf_del(__in Z3_context c, __in Z3_rcf_num a);
|
||||
|
||||
/**
|
||||
\brief Return a RCF rational using the given string.
|
||||
|
|
@ -75,6 +68,17 @@ extern "C" {
|
|||
*/
|
||||
Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(__in Z3_context c, __in Z3_string name);
|
||||
|
||||
/**
|
||||
\brief Store in roots the roots of the polynomial <tt>a[n-1]*x^{n-1} + ... + a[0]</tt>.
|
||||
The output vector \c roots must have size \c n.
|
||||
It returns the number of roots of the polynomial.
|
||||
|
||||
\pre The input polynomial is not the zero polynomial.
|
||||
|
||||
def_API('Z3_rcf_mk_roots', UINT, (_in(CONTEXT), _in(UINT), _in_array(1, RCF_NUM), _out_array(1, RCF_NUM)))
|
||||
*/
|
||||
unsigned Z3_API Z3_rcf_mk_roots(__in Z3_context c, __in unsigned n, __in_ecount(n) Z3_rcf_num const a[], __out_ecount(n) Z3_rcf_num roots[]);
|
||||
|
||||
/**
|
||||
\brief Return the value a + b.
|
||||
|
||||
|
|
|
|||
|
|
@ -1082,10 +1082,86 @@ namespace realclosure {
|
|||
}
|
||||
}
|
||||
|
||||
void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots) {
|
||||
/**
|
||||
\brief Root isolation for polynomials that are
|
||||
- nonlinear (degree > 2)
|
||||
- zero is not a root
|
||||
- square free
|
||||
- nonconstant
|
||||
*/
|
||||
void nl_nz_sqf_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
|
||||
SASSERT(n > 2);
|
||||
SASSERT(!is_zero(as[0]));
|
||||
SASSERT(!is_zero(as[n-1]));
|
||||
// TODO
|
||||
}
|
||||
|
||||
/**
|
||||
\brief Root isolation for polynomials that are
|
||||
- zero is not a root
|
||||
- square free
|
||||
- nonconstant
|
||||
*/
|
||||
void nz_sqf_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
|
||||
SASSERT(n > 1);
|
||||
SASSERT(!is_zero(as[0]));
|
||||
SASSERT(!is_zero(as[n-1]));
|
||||
if (n == 2) {
|
||||
// we don't need a field extension for linear polynomials.
|
||||
numeral r;
|
||||
value_ref neg_as_0(*this);
|
||||
neg_as_0 = neg(as[0]);
|
||||
set(r, div(neg_as_0, as[1]));
|
||||
roots.push_back(r);
|
||||
}
|
||||
else {
|
||||
nl_nz_sqf_isolate_roots(n, as, roots);
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
\brief Root isolation for polynomials where 0 is not a root.
|
||||
*/
|
||||
void nz_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
|
||||
SASSERT(n > 0);
|
||||
SASSERT(!is_zero(as[0]));
|
||||
SASSERT(!is_zero(as[n-1]));
|
||||
if (n == 1) {
|
||||
// constant polynomial
|
||||
return;
|
||||
}
|
||||
value_ref_buffer sqf(*this);
|
||||
square_free(n, as, sqf);
|
||||
nz_sqf_isolate_roots(sqf.size(), sqf.c_ptr(), roots);
|
||||
}
|
||||
|
||||
/**
|
||||
\brief Root isolation entry point.
|
||||
*/
|
||||
void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots) {
|
||||
SASSERT(n > 0);
|
||||
SASSERT(!is_zero(as[n-1]));
|
||||
if (n == 1) {
|
||||
// constant polynomial
|
||||
return;
|
||||
}
|
||||
unsigned i = 0;
|
||||
for (; i < n; i++) {
|
||||
if (!is_zero(as[i]))
|
||||
break;
|
||||
}
|
||||
SASSERT(i < n);
|
||||
SASSERT(!is_zero(as[i]));
|
||||
ptr_buffer<value> as_values;
|
||||
for (; i < n; i++)
|
||||
as_values.push_back(as[i].m_value);
|
||||
nz_isolate_roots(as_values.size(), as_values.c_ptr(), roots);
|
||||
if (as_values.size() < n) {
|
||||
// zero is a root
|
||||
roots.push_back(numeral());
|
||||
}
|
||||
}
|
||||
|
||||
void reset(numeral & a) {
|
||||
del(a);
|
||||
SASSERT(is_zero(a));
|
||||
|
|
|
|||
|
|
@ -278,6 +278,10 @@ namespace realclosure {
|
|||
value * m_value;
|
||||
public:
|
||||
num():m_value(0) {}
|
||||
|
||||
// Low level functions for implementing the C API
|
||||
void * c_ptr() { return m_value; }
|
||||
static num mk(void * ptr) { num r; r.m_value = reinterpret_cast<value*>(ptr); return r; }
|
||||
};
|
||||
};
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue