#define FAST_COMPARE 1
// Set this if you want divide_in_z() to use remembering
-#define USE_REMEMBER 1
+#define USE_REMEMBER 0
+
+// Set this if you want divide_in_z() to use trial division followed by
+// polynomial interpolation (usually slower except for very large problems)
+#define USE_TRIAL_DIVISION 0
+
+// Set this to enable some statistical output for the GCD routines
+#define STATISTICS 0
+
+
+#if STATISTICS
+// Statistics variables
+static int gcd_called = 0;
+static int sr_gcd_called = 0;
+static int heur_gcd_called = 0;
+static int heur_gcd_failed = 0;
+
+// Print statistics at end of program
+static struct _stat_print {
+ _stat_print() {}
+ ~_stat_print() {
+ cout << "gcd() called " << gcd_called << " times\n";
+ cout << "sr_gcd() called " << sr_gcd_called << " times\n";
+ cout << "heur_gcd() called " << heur_gcd_called << " times\n";
+ cout << "heur_gcd() failed " << heur_gcd_failed << " times\n";
+ }
+} stat_print;
+#endif
/** Return pointer to first symbol found in expression. Due to GiNaC´s
if (bdeg > adeg)
return false;
-#if 1
+#if USE_TRIAL_DIVISION
- // Polynomial long division (recursive)
- ex r = a.expand();
- if (r.is_zero())
- return true;
- int rdeg = adeg;
- ex eb = b.expand();
- ex blcoeff = eb.coeff(*x, bdeg);
- while (rdeg >= bdeg) {
- ex term, rcoeff = r.coeff(*x, rdeg);
- if (!divide_in_z(rcoeff, blcoeff, term, var+1))
- break;
- term = (term * power(*x, rdeg - bdeg)).expand();
- q += term;
- r -= (term * eb).expand();
- if (r.is_zero()) {
-#if USE_REMEMBER
- dr_remember[ex2(a, b)] = exbool(q, true);
-#endif
- return true;
- }
- rdeg = r.degree(*x);
- }
-#if USE_REMEMBER
- dr_remember[ex2(a, b)] = exbool(q, false);
-#endif
- return false;
-
-#else
-
- // Trial division using polynomial interpolation
+ // Trial division with polynomial interpolation
int i, k;
// Compute values at evaluation points 0..adeg
// Compute inverses
vector<numeric> rcp; rcp.reserve(adeg + 1);
- rcp.push_back(0);
+ rcp.push_back(_num0());
for (k=1; k<=adeg; k++) {
numeric product = alpha[k] - alpha[0];
for (i=1; i<k; i++)
return true;
} else
return false;
+
+#else
+
+ // Polynomial long division (recursive)
+ ex r = a.expand();
+ if (r.is_zero())
+ return true;
+ int rdeg = adeg;
+ ex eb = b.expand();
+ ex blcoeff = eb.coeff(*x, bdeg);
+ while (rdeg >= bdeg) {
+ ex term, rcoeff = r.coeff(*x, rdeg);
+ if (!divide_in_z(rcoeff, blcoeff, term, var+1))
+ break;
+ term = (term * power(*x, rdeg - bdeg)).expand();
+ q += term;
+ r -= (term * eb).expand();
+ if (r.is_zero()) {
+#if USE_REMEMBER
+ dr_remember[ex2(a, b)] = exbool(q, true);
+#endif
+ return true;
+ }
+ rdeg = r.degree(*x);
+ }
+#if USE_REMEMBER
+ dr_remember[ex2(a, b)] = exbool(q, false);
+#endif
+ return false;
+
#endif
}
static ex sr_gcd(const ex &a, const ex &b, const symbol *x)
{
//clog << "sr_gcd(" << a << "," << b << ")\n";
+#if STATISTICS
+ sr_gcd_called++;
+#endif
// Sort c and d so that c has higher degree
ex c, d;
return gamma;
c = c.primpart(*x, cont_c);
d = d.primpart(*x, cont_d);
+//clog << " content " << gamma << " removed, continuing with sr_gcd(" << c << "," << d << ")\n";
// First element of subresultant sequence
ex r = _ex0(), ri = _ex1(), psi = _ex1();
for (;;) {
// Calculate polynomial pseudo-remainder
+//clog << " start of loop, psi = " << psi << ", calculating pseudo-remainder...\n";
r = prem(c, d, *x, false);
if (r.is_zero())
return gamma * d.primpart(*x);
c = d;
cdeg = ddeg;
+//clog << " dividing...\n";
if (!divide(r, ri * power(psi, delta), d, false))
throw(std::runtime_error("invalid expression in sr_gcd(), division failed"));
ddeg = d.degree(*x);
}
// Next element of subresultant sequence
+//clog << " calculating next subresultant...\n";
ri = c.expand().lcoeff(*x);
if (delta == 1)
psi = ri;
static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
{
//clog << "heur_gcd(" << a << "," << b << ")\n";
+#if STATISTICS
+ heur_gcd_called++;
+#endif
// GCD of two numeric values -> CLN
if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric)) {
xi = mp * _num2() + _num2();
// 6 tries maximum
- for (int t=0; t<6; t++) { // MAGIC
- if (xi.int_length() * maxdeg > 100000) { // MAGIC
-// clog << "giving up heur_gcd, xi.int_length = " << xi.int_length() << ", maxdeg = " << maxdeg << endl;
+ for (int t=0; t<6; t++) {
+ if (xi.int_length() * maxdeg > 100000) {
+//clog << "giving up heur_gcd, xi.int_length = " << xi.int_length() << ", maxdeg = " << maxdeg << endl;
throw gcdheu_failed();
}
ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
{
//clog << "gcd(" << a << "," << b << ")\n";
+#if STATISTICS
+ gcd_called++;
+#endif
+
+ // GCD of numerics -> CLN
+ if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric)) {
+ numeric g = gcd(ex_to_numeric(a), ex_to_numeric(b));
+ if (ca)
+ *ca = ex_to_numeric(a) / g;
+ if (cb)
+ *cb = ex_to_numeric(b) / g;
+ return g;
+ }
+
+ // Check arguments
+ if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) {
+ throw(std::invalid_argument("gcd: arguments must be polynomials over the rationals"));
+ }
// Partially factored cases (to avoid expanding large expressions)
if (is_ex_exactly_of_type(a, mul)) {
return g;
}
+#if FAST_COMPARE
+ // Input polynomials of the form poly^n are sometimes also trivial
+ if (is_ex_exactly_of_type(a, power)) {
+ ex p = a.op(0);
+ if (is_ex_exactly_of_type(b, power)) {
+ if (p.is_equal(b.op(0))) {
+ // a = p^n, b = p^m, gcd = p^min(n, m)
+ ex exp_a = a.op(1), exp_b = b.op(1);
+ if (exp_a < exp_b) {
+ if (ca)
+ *ca = _ex1();
+ if (cb)
+ *cb = power(p, exp_b - exp_a);
+ return power(p, exp_a);
+ } else {
+ if (ca)
+ *ca = power(p, exp_a - exp_b);
+ if (cb)
+ *cb = _ex1();
+ return power(p, exp_b);
+ }
+ }
+ } else {
+ if (p.is_equal(b)) {
+ // a = p^n, b = p, gcd = p
+ if (ca)
+ *ca = power(p, a.op(1) - 1);
+ if (cb)
+ *cb = _ex1();
+ return p;
+ }
+ }
+ } else if (is_ex_exactly_of_type(b, power)) {
+ ex p = b.op(0);
+ if (p.is_equal(a)) {
+ // a = p, b = p^n, gcd = p
+ if (ca)
+ *ca = _ex1();
+ if (cb)
+ *cb = power(p, b.op(1) - 1);
+ return p;
+ }
+ }
+#endif
+
// Some trivial cases
ex aex = a.expand(), bex = b.expand();
if (aex.is_zero()) {
return a;
}
#endif
- if (is_ex_exactly_of_type(aex, numeric) && is_ex_exactly_of_type(bex, numeric)) {
- numeric g = gcd(ex_to_numeric(aex), ex_to_numeric(bex));
- if (ca)
- *ca = ex_to_numeric(aex) / g;
- if (cb)
- *cb = ex_to_numeric(bex) / g;
- return g;
- }
- if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) {
- throw(std::invalid_argument("gcd: arguments must be polynomials over the rationals"));
- }
// Gather symbol statistics
sym_desc_vec sym_stats;
}
if (is_ex_exactly_of_type(g, fail)) {
//clog << "heuristics failed" << endl;
+#if STATISTICS
+ heur_gcd_failed++;
+#endif
g = sr_gcd(aex, bex, x);
- if (ca)
- divide(aex, g, *ca, false);
- if (cb)
- divide(bex, g, *cb, false);
- }
- return g;
+ if (g.is_equal(_ex1())) {
+ // Keep cofactors factored if possible
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ } else {
+ if (ca)
+ divide(aex, g, *ca, false);
+ if (cb)
+ divide(bex, g, *cb, false);
+ }
+ } else {
+ if (g.is_equal(_ex1())) {
+ // Keep cofactors factored if possible
+ if (ca)
+ *ca = a;
+ if (cb)
+ *cb = b;
+ }
+ return g;
+ }
}
git://www.ginac.de / ginac.git / commitdiff