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https://github.com/Z3Prover/z3
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318 lines
8 KiB
C++
318 lines
8 KiB
C++
/*++
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Copyright (c) 2006 Microsoft Corporation
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Module Name:
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mpq.cpp
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Abstract:
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<abstract>
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Author:
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Leonardo de Moura (leonardo) 2010-06-21.
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Revision History:
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--*/
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#include"mpq.h"
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#include"warning.h"
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#include"z3_exception.h"
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template<bool SYNCH>
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mpq_manager<SYNCH>::mpq_manager() {
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}
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template<bool SYNCH>
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mpq_manager<SYNCH>::~mpq_manager() {
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del(m_n_tmp);
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del(m_add_tmp1);
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del(m_add_tmp2);
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del(m_lt_tmp1);
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del(m_lt_tmp2);
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del(m_addmul_tmp);
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}
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template<bool SYNCH>
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bool mpq_manager<SYNCH>::rat_lt(mpq const & a, mpq const & b) {
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mpz const & na = a.numerator();
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mpz const & nb = b.numerator();
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int sign_a = this->sign(na);
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int sign_b = this->sign(nb);
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if (sign_a < 0) {
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if (sign_b >= 0) return true;
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}
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else if (sign_a == 0) {
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if (sign_b > 0) return true;
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SASSERT(sign_b <= 0); return false;
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}
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else {
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SASSERT(sign_a > 0);
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if (sign_b <= 0) return false;
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}
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SASSERT((sign_a > 0 && sign_b > 0) ||
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(sign_a < 0 && sign_b < 0));
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mpz const & da = a.denominator();
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mpz const & db = b.denominator();
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if (SYNCH) {
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mpq tmp1;
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mpq tmp2;
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mul(na, db, tmp1);
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mul(nb, da, tmp2);
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bool r = lt(tmp1, tmp2);
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del(tmp1);
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del(tmp2);
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return r;
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}
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else {
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mul(na, db, m_lt_tmp1);
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mul(nb, da, m_lt_tmp2);
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return lt(m_lt_tmp1, m_lt_tmp2);
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}
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::floor(mpq const & a, mpz & f) {
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if (is_int(a)) {
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set(f, a.m_num);
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return;
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}
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bool is_neg_num = is_neg(a.m_num);
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machine_div(a.m_num, a.m_den, f);
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if (is_neg_num)
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sub(f, this->mk_z(1), f);
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::ceil(mpq const & a, mpz & c) {
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if (is_int(a)) {
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set(c, a.m_num);
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return;
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}
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bool is_pos_num = is_pos(a.m_num);
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machine_div(a.m_num, a.m_den, c);
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if (is_pos_num)
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add(c, this->mk_z(1), c);
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::gcd(unsigned sz, mpq const * as, mpq & g) {
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switch (sz) {
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case 0:
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reset(g);
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return;
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case 1:
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set(g, as[0]);
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abs(g);
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return;
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default:
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break;
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}
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gcd(as[0], as[1], g);
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for (unsigned i = 2; i < sz; i++) {
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if (is_one(g))
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return;
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gcd(g, as[i], g);
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}
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}
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template<bool SYNCH>
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std::string mpq_manager<SYNCH>::to_string(mpq const & a) const {
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if (is_int(a))
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return to_string(a.m_num);
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return to_string(a.m_num) + "/" + to_string(a.m_den);
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::display(std::ostream & out, mpq const & a) const {
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if (is_int(a)) {
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display(out, a.m_num);
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}
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else {
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display(out, a.m_num);
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out << "/";
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display(out, a.m_den);
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}
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::display_smt2(std::ostream & out, mpq const & a, bool decimal) const {
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if (is_int(a)) {
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display_smt2(out, a.m_num, decimal);
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}
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else {
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out << "(/ ";
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display_smt2(out, a.m_num, decimal);
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out << " ";
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display_smt2(out, a.m_den, decimal);
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out << ")";
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}
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::display_decimal(std::ostream & out, mpq const & a, unsigned prec) {
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mpz n1, d1, v1;
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get_numerator(a, n1);
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get_denominator(a, d1);
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if (is_neg(a)) {
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out << "-";
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neg(n1);
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}
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mpz ten(10);
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div(n1, d1, v1);
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display(out, v1);
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rem(n1, d1, n1);
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if (is_zero(n1))
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goto end; // number is an integer
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out << ".";
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for (unsigned i = 0; i < prec; i++) {
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mul(n1, ten, n1);
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div(n1, d1, v1);
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SASSERT(lt(v1, ten));
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display(out, v1);
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rem(n1, d1, n1);
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if (is_zero(n1))
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goto end; // number is precise
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}
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out << "?";
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end:
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del(ten); del(n1); del(d1); del(v1);
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::set(mpq & a, char const * val) {
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reset(a.m_num);
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mpz ten(10);
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_scoped_numeral<mpz_manager<SYNCH> > tmp(*this);
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char const * str = val;
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bool sign = false;
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while (str[0] == ' ') ++str;
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if (str[0] == '-')
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sign = true;
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while (str[0] && (str[0] != '/') && (str[0] != '.') && (str[0] != 'e') && (str[0] != 'E')) {
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if ('0' <= str[0] && str[0] <= '9') {
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SASSERT(str[0] - '0' <= 9);
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mul(a.m_num, ten, tmp);
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add(tmp, this->mk_z(str[0] - '0'), a.m_num);
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}
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++str;
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}
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TRACE("mpq_set", tout << "[before] a: " << to_string(a) << "\n";);
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if (str[0] == '/' || str[0] == '.' || str[0] == 'e' || str[0] == 'E') {
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bool is_rat = str[0] == '/';
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_scoped_numeral<mpz_manager<SYNCH> > tmp2(*this);
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set(tmp2, 1);
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bool has_den = false;
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if (str[0] == '/' || str[0] == '.') {
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has_den = true;
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++str;
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reset(a.m_den);
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while (str[0] && (str[0] != 'e') && (str[0] != 'E')) {
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if ('0' <= str[0] && str[0] <= '9') {
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mul(a.m_den, ten, tmp);
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add(tmp, this->mk_z(str[0] - '0'), a.m_den);
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if (!is_rat)
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mul(tmp2, ten, tmp2);
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}
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++str;
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}
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}
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unsigned long long exp = 0;
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bool exp_sign = false;
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if (str[0] == 'e' || str[0] == 'E') {
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if (is_rat)
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throw default_exception("mixing rational/scientific notation");
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++str;
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if (str[0] == '-') {
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exp_sign = true;
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++str;
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}
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while (str[0]) {
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if ('0' <= str[0] && str[0] <= '9') {
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SASSERT(str[0] - '0' <= 9);
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exp = (10*exp) + (str[0] - '0');
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}
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TRACE("mpq_set", tout << "[exp]: " << exp << ", str[0]: " << (str[0] - '0') << std::endl;);
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++str;
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}
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}
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if (!is_rat) {
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// a <- a.m_num + a.m_den/tmp2
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if (exp > static_cast<unsigned long long>(UINT_MAX))
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throw default_exception("exponent is too big");
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_scoped_numeral<mpq_manager<SYNCH> > b(*this);
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if (has_den) {
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set(b, a.m_den, tmp2);
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set(a.m_den, 1);
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add(a, b, a);
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}
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if (exp > 0) {
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_scoped_numeral<mpq_manager<SYNCH> > _exp(*this);
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_scoped_numeral<mpq_manager<SYNCH> > _ten(*this);
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set(_ten, 10);
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power(_ten, static_cast<unsigned>(exp), _exp);
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TRACE("mpq_set", tout << "a: " << to_string(a) << ", exp_sign:" << exp_sign << ", exp: " << exp << " " << to_string(_exp) << std::endl;);
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if (exp_sign)
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div(a, _exp, a);
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else
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mul(a, _exp, a);
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}
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}
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else {
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// rational case
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if (is_zero(a.m_den))
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throw default_exception("division by zero");
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}
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}
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else {
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reset_denominator(a);
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}
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if (sign)
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neg(a.m_num);
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normalize(a);
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}
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template<bool SYNCH>
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void mpq_manager<SYNCH>::power(mpq const & a, unsigned p, mpq & b) {
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unsigned mask = 1;
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mpq power;
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set(power, a);
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set(b, 1);
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while (mask <= p) {
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if (mask & p)
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mul(b, power, b);
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mul(power, power, power);
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mask = mask << 1;
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}
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del(power);
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}
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template<bool SYNCH>
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double mpq_manager<SYNCH>::get_double(mpq const & a) const {
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double n;
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double d;
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n = get_double(a.m_num);
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d = get_double(a.m_den);
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SASSERT(d > 0.0);
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return n/d;
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}
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template<bool SYNCH>
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bool mpq_manager<SYNCH>::root(mpq const & a, unsigned n, mpq & r) {
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return root(a.m_num, n, r.m_num) && root(a.m_den, n, r.m_den);
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}
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template<bool SYNCH>
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unsigned mpq_manager<SYNCH>::prev_power_of_two(mpq const & a) {
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_scoped_numeral<mpz_manager<SYNCH> > _tmp(*this);
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floor(a, _tmp);
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return prev_power_of_two(_tmp);
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}
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template class mpq_manager<true>;
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template class mpq_manager<false>;
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