#include <iostream>
#include <vector>
#include <stdexcept>
+#include <limits>
#include "mul.h"
#include "add.h"
#include "power.h"
+#include "operators.h"
#include "matrix.h"
+#include "lst.h"
#include "archive.h"
#include "utils.h"
GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
//////////
-// default ctor, dtor, copy ctor, assignment operator and helpers
+// default constructor
//////////
mul::mul()
tinfo_key = TINFO_mul;
}
-DEFAULT_COPY(mul)
-DEFAULT_DESTROY(mul)
-
//////////
-// other ctors
+// other constructors
//////////
// public
//////////
// public
-
void mul::print(const print_context & c, unsigned level) const
{
if (is_a<print_tree>(c)) {
if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
it->rest.print(c, precedence());
else if (it->coeff.info(info_flags::negint))
- // Outer parens around ex needed for broken gcc-2.95 parser:
+ // Outer parens around ex needed for broken GCC parser:
(ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
else
- // Outer parens around ex needed for broken gcc-2.95 parser:
+ // Outer parens around ex needed for broken GCC parser:
(ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
if (needclosingparenthesis)
} else if (is_a<print_python_repr>(c)) {
c.s << class_name() << '(';
op(0).print(c);
- for (unsigned i=1; i<nops(); ++i) {
+ for (size_t i=1; i<nops(); ++i) {
c.s << ',';
op(i).print(c);
}
}
// First print the overall numeric coefficient
- numeric coeff = ex_to<numeric>(overall_coeff);
+ const numeric &coeff = ex_to<numeric>(overall_coeff);
if (coeff.csgn() == -1)
c.s << '-';
if (!coeff.is_equal(_num1) &&
GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
(!(ex_to<numeric>(i->coeff).is_integer())));
GINAC_ASSERT(!(i->is_canonical_numeric()));
- if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
+ if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
print(print_tree(std::cerr));
GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
/* for paranoia */
// *(x;1) -> x
return recombine_pair_to_ex(*(seq.begin()));
} else if ((seq_size==1) &&
- is_ex_exactly_of_type((*seq.begin()).rest,add) &&
+ is_exactly_a<add>((*seq.begin()).rest) &&
ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
// *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
const add & addref = ex_to<add>((*seq.begin()).rest);
return mul(s, overall_coeff.evalf(level));
}
-ex mul::evalm(void) const
+ex mul::evalm() const
{
// numeric*matrix
if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
- && is_ex_of_type(seq[0].rest, matrix))
+ && is_a<matrix>(seq[0].rest))
return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
// Evaluate children first, look whether there are any matrices at all
while (i != end) {
const ex &m = recombine_pair_to_ex(*i).evalm();
s->push_back(split_ex_to_pair(m));
- if (is_ex_of_type(m, matrix)) {
+ if (is_a<matrix>(m)) {
have_matrix = true;
the_matrix = s->end() - 1;
}
return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
}
-ex mul::simplify_ncmul(const exvector & v) const
+ex mul::eval_ncmul(const exvector & v) const
{
if (seq.empty())
- return inherited::simplify_ncmul(v);
+ return inherited::eval_ncmul(v);
- // Find first noncommutative element and call its simplify_ncmul()
+ // Find first noncommutative element and call its eval_ncmul()
epvector::const_iterator i = seq.begin(), end = seq.end();
while (i != end) {
if (i->rest.return_type() == return_types::noncommutative)
- return i->rest.simplify_ncmul(v);
+ return i->rest.eval_ncmul(v);
++i;
}
- return inherited::simplify_ncmul(v);
+ return inherited::eval_ncmul(v);
+}
+
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
+{
+ ex origbase;
+ int origexponent;
+ int origexpsign;
+
+ if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
+ origbase = origfactor.op(0);
+ int expon = ex_to<numeric>(origfactor.op(1)).to_int();
+ origexponent = expon > 0 ? expon : -expon;
+ origexpsign = expon > 0 ? 1 : -1;
+ } else {
+ origbase = origfactor;
+ origexponent = 1;
+ origexpsign = 1;
+ }
+
+ ex patternbase;
+ int patternexponent;
+ int patternexpsign;
+
+ if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
+ patternbase = patternfactor.op(0);
+ int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
+ patternexponent = expon > 0 ? expon : -expon;
+ patternexpsign = expon > 0 ? 1 : -1;
+ } else {
+ patternbase = patternfactor;
+ patternexponent = 1;
+ patternexpsign = 1;
+ }
+
+ lst saverepls = repls;
+ if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
+ return false;
+ repls = saverepls;
+
+ int newnummatches = origexponent / patternexponent;
+ if (newnummatches < nummatches)
+ nummatches = newnummatches;
+ return true;
+}
+
+ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
+{
+ std::vector<bool> subsed(seq.size(), false);
+ exvector subsresult(seq.size());
+
+ for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+
+ if (is_exactly_a<mul>(it->first)) {
+
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> currsubsed(seq.size(), false);
+ bool succeed = true;
+ lst repls;
+
+ for (size_t j=0; j<it->first.nops(); j++) {
+ bool found=false;
+ for (size_t k=0; k<nops(); k++) {
+ if (currsubsed[k] || subsed[k])
+ continue;
+ if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
+ currsubsed[k] = true;
+ found = true;
+ break;
+ }
+ }
+ if (!found) {
+ succeed = false;
+ break;
+ }
+ }
+ if (!succeed)
+ continue;
+
+ bool foundfirstsubsedfactor = false;
+ for (size_t j=0; j<subsed.size(); j++) {
+ if (currsubsed[j]) {
+ if (foundfirstsubsedfactor)
+ subsresult[j] = op(j);
+ else {
+ foundfirstsubsedfactor = true;
+ subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches);
+ }
+ subsed[j] = true;
+ }
+ }
+
+ } else {
+
+ int nummatches = std::numeric_limits<int>::max();
+ lst repls;
+
+ for (size_t j=0; j<this->nops(); j++) {
+ if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
+ subsed[j] = true;
+ subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches);
+ }
+ }
+ }
+ }
+
+ bool subsfound = false;
+ for (size_t i=0; i<subsed.size(); i++) {
+ if (subsed[i]) {
+ subsfound = true;
+ break;
+ }
+ }
+ if (!subsfound)
+ return subs_one_level(m, options | subs_options::subs_algebraic);
+
+ exvector ev; ev.reserve(nops());
+ for (size_t i=0; i<nops(); i++) {
+ if (subsed[i])
+ ev.push_back(subsresult[i]);
+ else
+ ev.push_back(op(i));
+ }
+
+ return (new mul(ev))->setflag(status_flags::dynallocated);
}
// protected
* @see ex::diff */
ex mul::derivative(const symbol & s) const
{
- unsigned num = seq.size();
+ size_t num = seq.size();
exvector addseq;
addseq.reserve(num);
return inherited::compare_same_type(other);
}
-bool mul::is_equal_same_type(const basic & other) const
-{
- return inherited::is_equal_same_type(other);
-}
-
-unsigned mul::return_type(void) const
+unsigned mul::return_type() const
{
if (seq.empty()) {
// mul without factors: should not happen, but commutes
return all_commutative ? return_types::commutative : return_types::noncommutative;
}
-unsigned mul::return_type_tinfo(void) const
+unsigned mul::return_type_tinfo() const
{
if (seq.empty())
return tinfo_key; // mul without factors: should not happen
expair mul::split_ex_to_pair(const ex & e) const
{
- if (is_ex_exactly_of_type(e,power)) {
+ if (is_exactly_a<power>(e)) {
const power & powerref = ex_to<power>(e);
- if (is_ex_exactly_of_type(powerref.exponent,numeric))
+ if (is_exactly_a<numeric>(powerref.exponent))
return expair(powerref.basis,powerref.exponent);
}
return expair(e,_ex1);
{
// to avoid duplication of power simplification rules,
// we create a temporary power object
- // otherwise it would be hard to correctly simplify
+ // otherwise it would be hard to correctly evaluate
// expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,_ex1))
+ if (c.is_equal(_ex1))
return split_ex_to_pair(e);
-
+
return split_ex_to_pair(power(e,c));
}
{
// to avoid duplication of power simplification rules,
// we create a temporary power object
- // otherwise it would be hard to correctly simplify
+ // otherwise it would be hard to correctly evaluate
// expression like (4^(1/3))^(3/2)
- if (are_ex_trivially_equal(c,_ex1))
+ if (c.is_equal(_ex1))
return p;
-
+
return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
}
if (ex_to<numeric>(p.coeff).is_equal(_num1))
return p.rest;
else
- return power(p.rest,p.coeff);
+ return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
}
bool mul::expair_needs_further_processing(epp it)
{
- if (is_ex_exactly_of_type((*it).rest,mul) &&
- ex_to<numeric>((*it).coeff).is_integer()) {
+ if (is_exactly_a<mul>(it->rest) &&
+ ex_to<numeric>(it->coeff).is_integer()) {
// combined pair is product with integer power -> expand it
*it = split_ex_to_pair(recombine_pair_to_ex(*it));
return true;
}
- if (is_ex_exactly_of_type((*it).rest,numeric)) {
- expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
+ if (is_exactly_a<numeric>(it->rest)) {
+ expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
if (!ep.is_equal(*it)) {
// combined pair is a numeric power which can be simplified
*it = ep;
return true;
}
- if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
+ if (it->coeff.is_equal(_ex1)) {
// combined pair has coeff 1 and must be moved to the end
return true;
}
return false;
}
-ex mul::default_overall_coeff(void) const
+ex mul::default_overall_coeff() const
{
return _ex1;
}
non_adds.reserve(expanded_seq.size());
epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
while (cit != last) {
- if (is_ex_exactly_of_type(cit->rest, add) &&
+ if (is_exactly_a<add>(cit->rest) &&
(cit->coeff.is_equal(_ex1))) {
++number_of_adds;
- if (is_ex_exactly_of_type(last_expanded, add)) {
-#if 0
- // Expand a product of two sums, simple and robust version.
- const add & add1 = ex_to<add>(last_expanded);
- const add & add2 = ex_to<add>(cit->rest);
- const int n1 = add1.nops();
- const int n2 = add2.nops();
- ex tmp_accu;
- exvector distrseq;
- distrseq.reserve(n2);
- for (int i1=0; i1<n1; ++i1) {
- distrseq.clear();
- // cache the first operand (for efficiency):
- const ex op1 = add1.op(i1);
- for (int i2=0; i2<n2; ++i2)
- distrseq.push_back(op1 * add2.op(i2));
- tmp_accu += (new add(distrseq))->
- setflag(status_flags::dynallocated);
- }
- last_expanded = tmp_accu;
-#else
+ if (is_exactly_a<add>(last_expanded)) {
+
// Expand a product of two sums, aggressive version.
// Caring for the overall coefficients in separate loops can
// sometimes give a performance gain of up to 15%!
// Don't push_back expairs which might have a rest that evaluates to a numeric,
// since that would violate an invariant of expairseq:
const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
- if (is_ex_exactly_of_type(rest, numeric))
+ if (is_exactly_a<numeric>(rest))
oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
else
distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
}
last_expanded = tmp_accu;
-#endif
+
} else {
non_adds.push_back(split_ex_to_pair(last_expanded));
last_expanded = cit->rest;
// Now the only remaining thing to do is to multiply the factors which
// were not sums into the "last_expanded" sum
- if (is_ex_exactly_of_type(last_expanded, add)) {
+ if (is_exactly_a<add>(last_expanded)) {
const add & finaladd = ex_to<add>(last_expanded);
exvector distrseq;
- int n = finaladd.nops();
+ size_t n = finaladd.nops();
distrseq.reserve(n);
- for (int i=0; i<n; ++i) {
+ for (size_t i=0; i<n; ++i) {
epvector factors = non_adds;
factors.push_back(split_ex_to_pair(finaladd.op(i)));
distrseq.push_back((new mul(factors, overall_coeff))->