subs() and normal() use maps instead of lists, resulting in a huge performance
[ginac.git] / ginac / mul.cpp
index 47f74f6..2c84565 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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 <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"
 
@@ -36,7 +39,7 @@ namespace GiNaC {
 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
 
 //////////
-// default ctor, dtor, copy ctor, assignment operator and helpers
+// default constructor
 //////////
 
 mul::mul()
@@ -44,11 +47,8 @@ mul::mul()
        tinfo_key = TINFO_mul;
 }
 
-DEFAULT_COPY(mul)
-DEFAULT_DESTROY(mul)
-
 //////////
-// other ctors
+// other constructors
 //////////
 
 // public
@@ -119,7 +119,6 @@ DEFAULT_ARCHIVING(mul)
 //////////
 
 // public
-
 void mul::print(const print_context & c, unsigned level) const
 {
        if (is_a<print_tree>(c)) {
@@ -141,25 +140,32 @@ void mul::print(const print_context & c, unsigned level) const
                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 << "*";
@@ -171,10 +177,8 @@ void mul::print(const print_context & c, unsigned level) const
 
        } 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 (size_t i=1; i<nops(); ++i) {
                        c.s << ',';
                        op(i).print(c);
                }
@@ -188,10 +192,8 @@ void mul::print(const print_context & c, unsigned level) const
                                c.s << "(";
                }
 
-               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) &&
@@ -215,17 +217,51 @@ void mul::print(const print_context & c, unsigned level) const
 
                // Then proceed with the remaining factors
                epvector::const_iterator it = seq.begin(), itend = seq.end();
-               while (it != itend) {
-                       if (!first) {
-                               if (is_a<print_latex>(c))
-                                       c.s << ' ';
+               if (is_a<print_latex>(c)) {
+
+                       // Separate factors into those with negative numeric exponent
+                       // and all others
+                       exvector neg_powers, others;
+                       while (it != itend) {
+                               GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
+                               if (ex_to<numeric>(it->coeff).is_negative())
+                                       neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
                                else
-                                       c.s << '*';
+                                       others.push_back(recombine_pair_to_ex(*it));
+                               ++it;
+                       }
+
+                       if (!neg_powers.empty()) {
+
+                               // Factors with negative exponent are printed as a fraction
+                               c.s << "\\frac{";
+                               mul(others).eval().print(c);
+                               c.s << "}{";
+                               mul(neg_powers).eval().print(c);
+                               c.s << "}";
+
                        } else {
-                               first = false;
+
+                               // All other factors are printed in the ordinary way
+                               exvector::const_iterator vit = others.begin(), vitend = others.end();
+                               while (vit != vitend) {
+                                       c.s << ' ';
+                                       vit->print(c, precedence());
+                                       ++vit;
+                               }
+                       }
+
+               } else {
+
+                       bool first = true;
+                       while (it != itend) {
+                               if (!first)
+                                       c.s << '*';
+                               else
+                                       first = false;
+                               recombine_pair_to_ex(*it).print(c, precedence());
+                               ++it;
                        }
-                       recombine_pair_to_ex(*it).print(c, precedence());
-                       ++it;
                }
 
                if (precedence() <= level) {
@@ -355,7 +391,7 @@ ex mul::eval(int level) const
                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 */
@@ -384,7 +420,7 @@ ex mul::eval(int level) const
                // *(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);
@@ -424,11 +460,11 @@ ex mul::evalf(int level) const
        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
@@ -444,7 +480,7 @@ ex mul::evalm(void) const
        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;
                }
@@ -464,19 +500,143 @@ ex mul::evalm(void) const
                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
@@ -485,7 +645,7 @@ ex mul::simplify_ncmul(const exvector & v) const
  *  @see ex::diff */
 ex mul::derivative(const symbol & s) const
 {
-       unsigned num = seq.size();
+       size_t num = seq.size();
        exvector addseq;
        addseq.reserve(num);
        
@@ -509,12 +669,7 @@ int mul::compare_same_type(const basic & other) const
        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
@@ -547,7 +702,7 @@ unsigned mul::return_type(void) const
        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
@@ -575,9 +730,9 @@ ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 
 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);
@@ -588,11 +743,11 @@ expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 {
        // 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));
 }
        
@@ -601,11 +756,11 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 {
        // 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));
 }
        
@@ -614,25 +769,25 @@ ex mul::recombine_pair_to_ex(const expair & p) const
        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;
                }
@@ -640,7 +795,7 @@ bool mul::expair_needs_further_processing(epp it)
        return false;
 }       
 
-ex mul::default_overall_coeff(void) const
+ex mul::default_overall_coeff() const
 {
        return _ex1;
 }
@@ -684,23 +839,63 @@ ex mul::expand(unsigned options) const
        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)) {
-                               const add & add1 = ex_to<add>(last_expanded);
-                               const add & add2 = ex_to<add>(cit->rest);
-                               int n1 = add1.nops();
-                               int n2 = add2.nops();
-                               exvector distrseq;
-                               distrseq.reserve(n1*n2);
-                               for (int i1=0; i1<n1; ++i1) {
-                                       for (int i2=0; i2<n2; ++i2) {
-                                               distrseq.push_back(add1.op(i1) * add2.op(i2));
+                       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%!
+
+                               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;
+
                        } else {
                                non_adds.push_back(split_ex_to_pair(last_expanded));
                                last_expanded = cit->rest;
@@ -715,12 +910,12 @@ ex mul::expand(unsigned options) const
        
        // 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))->