* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "mul.h"
#include "add.h"
#include "power.h"
+#include "operators.h"
#include "matrix.h"
#include "archive.h"
#include "utils.h"
//////////
// public
-
void mul::print(const print_context & c, unsigned level) const
{
if (is_a<print_tree>(c)) {
while (it != itend) {
// If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
- if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) {
- if (is_a<print_csrc_cl_N>(c))
+ bool needclosingparenthesis = false;
+ if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
+ if (is_a<print_csrc_cl_N>(c)) {
c.s << "recip(";
- else
+ needclosingparenthesis = true;
+ } else
c.s << "1.0/";
}
// If the exponent is 1 or -1, it is left out
- if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0)
+ if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
it->rest.print(c, precedence());
- else {
- // Outer parens around ex needed for broken gcc-2.95 parser:
- (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
- }
+ else if (it->coeff.info(info_flags::negint))
+ // 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 parser:
+ (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
+
+ if (needclosingparenthesis)
+ c.s << ")";
// Separator is "/" for negative integer powers, "*" otherwise
++it;
if (it != itend) {
- if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
+ if (it->coeff.info(info_flags::negint))
c.s << "/";
else
c.s << "*";
} else if (is_a<print_python_repr>(c)) {
c.s << class_name() << '(';
- unsigned end = nops();
- if (end)
- op(0).print(c);
- for (unsigned i=1; i<end; ++i) {
+ op(0).print(c);
+ for (unsigned i=1; i<nops(); ++i) {
c.s << ',';
op(i).print(c);
}
bool first = true;
// 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);
{
// 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 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
{
if (seq.empty()) {
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;
}
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 (is_exactly_a<add>(last_expanded)) {
+#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);
- int n1 = add1.nops();
- int n2 = add2.nops();
+ const int n1 = add1.nops();
+ const int n2 = add2.nops();
+ ex tmp_accu;
exvector distrseq;
- distrseq.reserve(n1*n2);
+ distrseq.reserve(n2);
for (int i1=0; i1<n1; ++i1) {
- for (int i2=0; i2<n2; ++i2) {
- distrseq.push_back(add1.op(i1) * add2.op(i2));
+ 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
+ // 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%!
+
+ const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
+ // add2 is for the inner loop and should be the bigger of the two sums
+ // in the presence of asymptotically good sorting:
+ const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
+ const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
+ const epvector::const_iterator add1begin = add1.seq.begin();
+ const epvector::const_iterator add1end = add1.seq.end();
+ const epvector::const_iterator add2begin = add2.seq.begin();
+ const epvector::const_iterator add2end = add2.seq.end();
+ epvector distrseq;
+ distrseq.reserve(add1.seq.size()+add2.seq.size());
+ // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
+ if (!add1.overall_coeff.is_zero()) {
+ if (add1.overall_coeff.is_equal(_ex1))
+ distrseq.insert(distrseq.end(),add2begin,add2end);
+ else
+ for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
+ distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
+ }
+ // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
+ if (!add2.overall_coeff.is_zero()) {
+ if (add2.overall_coeff.is_equal(_ex1))
+ distrseq.insert(distrseq.end(),add1begin,add1end);
+ else
+ for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
+ distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
+ }
+ // Compute the new overall coefficient and put it together:
+ ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
+ // Multiply explicitly all non-numeric terms of add1 and add2:
+ for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+ // We really have to combine terms here in order to compactify
+ // the result. Otherwise it would become waayy tooo bigg.
+ numeric oc;
+ distrseq.clear();
+ for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+ // 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_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 = (new add(distrseq))->
- setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ 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();
git://www.ginac.de / ginac.git / blobdiff