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fix #2613 fix #2612

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2019-10-05 16:57:51 -07:00
parent 016732aa59
commit 39edf73e78
16 changed files with 222 additions and 162 deletions
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40
src/math/polynomial/upolynomial.cpp
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@ -1327,25 +1327,25 @@ namespace upolynomial {
div(sz, p, 2, two_x_1, buffer);
}
int manager::sign_of(numeral const & c) {
polynomial::sign manager::sign_of(numeral const & c) {
if (m().is_zero(c))
return 0;
return polynomial::sign_zero;
if (m().is_pos(c))
return 1;
return polynomial::sign_pos;
else
return -1;
return polynomial::sign_neg;
}
// Return the number of sign changes in the coefficients of p
unsigned manager::sign_changes(unsigned sz, numeral const * p) {
unsigned r = 0;
int prev_sign = 0;
auto prev_sign = polynomial::sign_zero;
unsigned i = 0;
for (; i < sz; i++) {
int sign = sign_of(p[i]);
if (sign == 0)
auto sign = sign_of(p[i]);
if (sign == polynomial::sign_zero)
continue;
if (sign != prev_sign && prev_sign != 0)
if (sign != prev_sign && prev_sign != polynomial::sign_zero)
r++;
prev_sign = sign;
}
@ -1729,14 +1729,14 @@ namespace upolynomial {
}
// Evaluate the sign of p(b)
int manager::eval_sign_at(unsigned sz, numeral const * p, mpbq const & b) {
polynomial::sign manager::eval_sign_at(unsigned sz, numeral const * p, mpbq const & b) {
// Actually, given b = c/2^k, we compute the sign of (2^k)^n*p(b)
// Original Horner Sequence
// ((a_n * b + a_{n-1})*b + a_{n-2})*b + a_{n-3} ...
// Variation of the Horner Sequence for (2^k)^n*p(b)
// ((a_n * c + a_{n-1}*2_k)*c + a_{n-2}*(2_k)^2)*c + a_{n-3}*(2_k)^3 ... + a_0*(2_k)^n
if (sz == 0)
return 0;
return polynomial::sign_zero;
if (sz == 1)
return sign_of(p[0]);
numeral const & c = b.numerator();
@ -1762,14 +1762,14 @@ namespace upolynomial {
}
// Evaluate the sign of p(b)
int manager::eval_sign_at(unsigned sz, numeral const * p, mpq const & b) {
polynomial::sign manager::eval_sign_at(unsigned sz, numeral const * p, mpq const & b) {
// Actually, given b = c/d, we compute the sign of (d^n)*p(b)
// Original Horner Sequence
// ((a_n * b + a_{n-1})*b + a_{n-2})*b + a_{n-3} ...
// Variation of the Horner Sequence for (d^n)*p(b)
// ((a_n * c + a_{n-1}*d)*c + a_{n-2}*d^2)*c + a_{n-3}*d^3 ... + a_0*d^n
if (sz == 0)
return 0;
return polynomial::sign_zero;
if (sz == 1)
return sign_of(p[0]);
numeral const & c = b.numerator();
@ -1796,11 +1796,11 @@ namespace upolynomial {
}
// Evaluate the sign of p(b)
int manager::eval_sign_at(unsigned sz, numeral const * p, mpz const & b) {
polynomial::sign manager::eval_sign_at(unsigned sz, numeral const * p, mpz const & b) {
// Using Horner Sequence
// ((a_n * b + a_{n-1})*b + a_{n-2})*b + a_{n-3} ...
if (sz == 0)
return 0;
return polynomial::sign_zero;
if (sz == 1)
return sign_of(p[0]);
scoped_numeral r(m());
@ -1817,21 +1817,21 @@ namespace upolynomial {
return sign_of(r);
}
int manager::eval_sign_at_zero(unsigned sz, numeral const * p) {
polynomial::sign manager::eval_sign_at_zero(unsigned sz, numeral const * p) {
if (sz == 0)
return 0;
return polynomial::sign_zero;
return sign_of(p[0]);
}
int manager::eval_sign_at_plus_inf(unsigned sz, numeral const * p) {
polynomial::sign manager::eval_sign_at_plus_inf(unsigned sz, numeral const * p) {
if (sz == 0)
return 0;
return polynomial::sign_zero;
return sign_of(p[sz-1]);
}
int manager::eval_sign_at_minus_inf(unsigned sz, numeral const * p) {
polynomial::sign manager::eval_sign_at_minus_inf(unsigned sz, numeral const * p) {
if (sz == 0)
return 0;
return polynomial::sign_zero;
unsigned degree = sz - 1;
if (degree % 2 == 0)
return sign_of(p[sz-1]);