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Extract defining components of algebraic number via C and C++ API (#3321)

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* First steps toward adding Julia bindings

* Simplifications

* Streamlining

* Friends of tactic and probe

* Add missing functions

* Update azure-pipelines.yml for Azure Pipelines

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* Changes for CxxWrap v0.9.0

* Wrap enumeration and tuple sort

* Wrap z3::fixedpoint

* Wrap z3::optimize

* Wrap missing functions

* Fix aux types

* Add some missing functions

* Revert "Update azure-pipelines.yml for Azure Pipelines"

This reverts commit 5aab9f9240.

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* Checkout current version of pipeline

* Build Julia bindings on macOS

* Extract components of algebraic number

* Add type to C API function name

* Remove blank line

* Typo in doc

* Return Z3_ast_vector containing coefficients
This commit is contained in:
ahumenberger 2020-03-17 17:09:02 +01:00 committed by GitHub
parent 1c5283f3a4
commit de9bc930e9
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6 changed files with 160 additions and 72 deletions
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32
src/api/api_algebraic.cpp
View file

@ -418,4 +418,36 @@ extern "C" {
Z3_CATCH_RETURN(0);
}
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a) {
Z3_TRY;
LOG_Z3_algebraic_get_poly(c, a);
RESET_ERROR_CODE();
CHECK_IS_ALGEBRAIC(a, 0);
algebraic_numbers::manager & _am = am(c);
algebraic_numbers::anum const & av = get_irrational(c, a);
scoped_mpz_vector coeffs(_am.qm());
_am.get_polynomial(av, coeffs);
api::context * _c = mk_c(c);
sort * s = _c->m().mk_sort(_c->get_arith_fid(), REAL_SORT);
Z3_ast_vector_ref* result = alloc(Z3_ast_vector_ref, *_c, _c->m());
mk_c(c)->save_object(result);
for (unsigned i = 0; i < coeffs.size(); i++) {
rational r(coeffs[i]);
expr * a = _c->mk_numeral_core(r, s);
result->m_ast_vector.push_back(a);
}
RETURN_Z3(of_ast_vector(result));
Z3_CATCH_RETURN(nullptr);
}
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a) {
Z3_TRY;
LOG_Z3_algebraic_get_i(c, a);
RESET_ERROR_CODE();
CHECK_IS_ALGEBRAIC(a, 0);
algebraic_numbers::manager & _am = am(c);
algebraic_numbers::anum const & av = get_irrational(c, a);
return _am.get_i(av);
Z3_CATCH_RETURN(0);
}
};

160
src/api/c++/z3++.h
View file

@ -66,6 +66,7 @@ namespace z3 {
class func_entry;
class statistics;
class apply_result;
template<typename T> class cast_ast;
template<typename T> class ast_vector_tpl;
typedef ast_vector_tpl<ast> ast_vector;
typedef ast_vector_tpl<expr> expr_vector;
@ -511,6 +512,74 @@ namespace z3 {
inline bool eq(ast const & a, ast const & b) { return Z3_is_eq_ast(a.ctx(), a, b); }
template<typename T>
class ast_vector_tpl : public object {
Z3_ast_vector m_vector;
void init(Z3_ast_vector v) { Z3_ast_vector_inc_ref(ctx(), v); m_vector = v; }
public:
ast_vector_tpl(context & c):object(c) { init(Z3_mk_ast_vector(c)); }
ast_vector_tpl(context & c, Z3_ast_vector v):object(c) { init(v); }
ast_vector_tpl(ast_vector_tpl const & s):object(s), m_vector(s.m_vector) { Z3_ast_vector_inc_ref(ctx(), m_vector); }
ast_vector_tpl(context& c, ast_vector_tpl const& src): object(c) { init(Z3_ast_vector_translate(src.ctx(), src, c)); }
~ast_vector_tpl() { Z3_ast_vector_dec_ref(ctx(), m_vector); }
operator Z3_ast_vector() const { return m_vector; }
unsigned size() const { return Z3_ast_vector_size(ctx(), m_vector); }
T operator[](int i) const { assert(0 <= i); Z3_ast r = Z3_ast_vector_get(ctx(), m_vector, i); check_error(); return cast_ast<T>()(ctx(), r); }
void push_back(T const & e) { Z3_ast_vector_push(ctx(), m_vector, e); check_error(); }
void resize(unsigned sz) { Z3_ast_vector_resize(ctx(), m_vector, sz); check_error(); }
T back() const { return operator[](size() - 1); }
void pop_back() { assert(size() > 0); resize(size() - 1); }
bool empty() const { return size() == 0; }
ast_vector_tpl & operator=(ast_vector_tpl const & s) {
Z3_ast_vector_inc_ref(s.ctx(), s.m_vector);
Z3_ast_vector_dec_ref(ctx(), m_vector);
m_ctx = s.m_ctx;
m_vector = s.m_vector;
return *this;
}
ast_vector_tpl& set(unsigned idx, ast& a) {
Z3_ast_vector_set(ctx(), m_vector, idx, a);
return *this;
}
/*
Disabled pending C++98 build upgrade
bool contains(T const& x) const {
for (T y : *this) if (eq(x, y)) return true;
return false;
}
*/
class iterator {
ast_vector_tpl const* m_vector;
unsigned m_index;
public:
iterator(ast_vector_tpl const* v, unsigned i): m_vector(v), m_index(i) {}
iterator(iterator const& other): m_vector(other.m_vector), m_index(other.m_index) {}
iterator operator=(iterator const& other) { m_vector = other.m_vector; m_index = other.m_index; return *this; }
bool operator==(iterator const& other) const {
return other.m_index == m_index;
};
bool operator!=(iterator const& other) const {
return other.m_index != m_index;
};
iterator& operator++() {
++m_index;
return *this;
}
void set(T& arg) {
Z3_ast_vector_set(m_vector->ctx(), *m_vector, m_index, arg);
}
iterator operator++(int) { iterator tmp = *this; ++m_index; return tmp; }
T * operator->() const { return &(operator*()); }
T operator*() const { return (*m_vector)[m_index]; }
};
iterator begin() const { return iterator(this, 0); }
iterator end() const { return iterator(this, size()); }
friend std::ostream & operator<<(std::ostream & out, ast_vector_tpl const & v) { out << Z3_ast_vector_to_string(v.ctx(), v); return out; }
};
/**
\brief A Z3 sort (aka type). Every expression (i.e., formula or term) in Z3 has a sort.
@ -665,7 +734,6 @@ namespace z3 {
\brief A Z3 expression is used to represent formulas and terms. For Z3, a formula is any expression of sort Boolean.
Every expression has a sort.
*/
class expr : public ast {
public:
expr(context & c):ast(c) {}
@ -815,6 +883,25 @@ namespace z3 {
return expr(ctx(), r);
}
/**
\brief Return coefficients for p of an algebraic number (root-obj p i)
*/
expr_vector algebraic_poly() const {
assert(is_algebraic());
Z3_ast_vector r = Z3_algebraic_get_poly(ctx(), m_ast);
check_error();
return expr_vector(ctx(), r);
}
/**
\brief Return i of an algebraic number (root-obj p i)
*/
unsigned algebraic_i() const {
assert(is_algebraic());
unsigned i = Z3_algebraic_get_i(ctx(), m_ast);
check_error();
return i;
}
/**
\brief retrieve unique identifier for expression.
@ -1848,8 +1935,6 @@ namespace z3 {
return to_func_decl(a.ctx(), Z3_mk_tree_order(a.ctx(), a, index));
}
template<typename T> class cast_ast;
template<> class cast_ast<ast> {
public:
ast operator()(context & c, Z3_ast a) { return ast(c, a); }
@ -1882,75 +1967,6 @@ namespace z3 {
}
};
template<typename T>
class ast_vector_tpl : public object {
Z3_ast_vector m_vector;
void init(Z3_ast_vector v) { Z3_ast_vector_inc_ref(ctx(), v); m_vector = v; }
public:
ast_vector_tpl(context & c):object(c) { init(Z3_mk_ast_vector(c)); }
ast_vector_tpl(context & c, Z3_ast_vector v):object(c) { init(v); }
ast_vector_tpl(ast_vector_tpl const & s):object(s), m_vector(s.m_vector) { Z3_ast_vector_inc_ref(ctx(), m_vector); }
ast_vector_tpl(context& c, ast_vector_tpl const& src): object(c) { init(Z3_ast_vector_translate(src.ctx(), src, c)); }
~ast_vector_tpl() { Z3_ast_vector_dec_ref(ctx(), m_vector); }
operator Z3_ast_vector() const { return m_vector; }
unsigned size() const { return Z3_ast_vector_size(ctx(), m_vector); }
T operator[](int i) const { assert(0 <= i); Z3_ast r = Z3_ast_vector_get(ctx(), m_vector, i); check_error(); return cast_ast<T>()(ctx(), r); }
void push_back(T const & e) { Z3_ast_vector_push(ctx(), m_vector, e); check_error(); }
void resize(unsigned sz) { Z3_ast_vector_resize(ctx(), m_vector, sz); check_error(); }
T back() const { return operator[](size() - 1); }
void pop_back() { assert(size() > 0); resize(size() - 1); }
bool empty() const { return size() == 0; }
ast_vector_tpl & operator=(ast_vector_tpl const & s) {
Z3_ast_vector_inc_ref(s.ctx(), s.m_vector);
Z3_ast_vector_dec_ref(ctx(), m_vector);
m_ctx = s.m_ctx;
m_vector = s.m_vector;
return *this;
}
ast_vector_tpl& set(unsigned idx, ast& a) {
Z3_ast_vector_set(ctx(), m_vector, idx, a);
return *this;
}
/*
Disabled pending C++98 build upgrade
bool contains(T const& x) const {
for (T y : *this) if (eq(x, y)) return true;
return false;
}
*/
class iterator {
ast_vector_tpl const* m_vector;
unsigned m_index;
public:
iterator(ast_vector_tpl const* v, unsigned i): m_vector(v), m_index(i) {}
iterator(iterator const& other): m_vector(other.m_vector), m_index(other.m_index) {}
iterator operator=(iterator const& other) { m_vector = other.m_vector; m_index = other.m_index; return *this; }
bool operator==(iterator const& other) const {
return other.m_index == m_index;
};
bool operator!=(iterator const& other) const {
return other.m_index != m_index;
};
iterator& operator++() {
++m_index;
return *this;
}
void set(T& arg) {
Z3_ast_vector_set(m_vector->ctx(), *m_vector, m_index, arg);
}
iterator operator++(int) { iterator tmp = *this; ++m_index; return tmp; }
T * operator->() const { return &(operator*()); }
T operator*() const { return (*m_vector)[m_index]; }
};
iterator begin() const { return iterator(this, 0); }
iterator end() const { return iterator(this, size()); }
friend std::ostream & operator<<(std::ostream & out, ast_vector_tpl const & v) { out << Z3_ast_vector_to_string(v.ctx(), v); return out; }
};
template<typename T>
template<typename T2>
array<T>::array(ast_vector_tpl<T2> const & v) {

4
src/api/julia/z3jl.cpp
View file

@ -203,6 +203,10 @@ JLCXX_MODULE define_julia_module(jlcxx::Module &m)
.MM(expr, is_well_sorted)
.MM(expr, get_decimal_string)
.MM(expr, id)
.MM(expr, algebraic_lower)
.MM(expr, algebraic_upper)
.MM(expr, algebraic_poly)
.MM(expr, algebraic_i)
.MM(expr, get_numeral_int)
.MM(expr, get_numeral_uint)
.MM(expr, get_numeral_int64)

18
src/api/z3_algebraic.h
View file

@ -223,6 +223,24 @@ extern "C" {
*/
int Z3_API Z3_algebraic_eval(Z3_context c, Z3_ast p, unsigned n, Z3_ast a[]);
/**
\brief Return the coefficients of the defining polynomial.
\pre Z3_algebraic_is_value(c, a)
def_API('Z3_algebraic_get_poly', AST_VECTOR, (_in(CONTEXT), _in(AST)))
*/
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a);
/**
\brief Return which root of the polynomial the algebraic number represents.
\pre Z3_algebraic_is_value(c, a)
def_API('Z3_algebraic_get_i', UINT, (_in(CONTEXT), _in(AST)))
*/
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a);
/*@}*/
/*@}*/

17
src/math/polynomial/algebraic_numbers.cpp
View file

@ -1951,6 +1951,19 @@ namespace algebraic_numbers {
}
}
unsigned get_i(numeral const & a) {
if (a.is_basic()) {
if (is_zero(a)) {
return 0;
}
return 1;
}
else {
algebraic_cell * c = a.to_algebraic();
return c->m_i;
}
}
/**
\brief "Optimistic" mapping: it assumes all variables are mapped to
basic_values (rationals). Throws an exception if that is not the case.
@ -3000,6 +3013,10 @@ namespace algebraic_numbers {
m_imp->get_polynomial(a, r);
}
unsigned manager::get_i(numeral const & a) {
return m_imp->get_i(a);
}
void manager::get_lower(numeral const & a, mpbq & l) {
SASSERT(!is_rational(a));
bqm().set(l, a.to_algebraic()->m_interval.lower());

1
src/math/polynomial/algebraic_numbers.h
View file

@ -307,6 +307,7 @@ namespace algebraic_numbers {
sign eval_sign_at(polynomial_ref const & p, polynomial::var2anum const & x2v);
void get_polynomial(numeral const & a, svector<mpz> & r);
unsigned get_i(numeral const & a);
// Procedures for getting lower and upper bounds for irrational numbers
void get_lower(numeral const & a, mpbq & l);