X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=c899ee11f25248cc0edd547f8149bd1a556c512f;hp=3385bcae2b072a65bf56db5aca883205bf294875;hb=9593ce33c14b7ff535d113f8a825f4c42ca81912;hpb=5a8b8e3c4d882249db35b679ce3144a59a7012e8 diff --git a/ginac/mul.cpp b/ginac/mul.cpp index 3385bcae..c899ee11 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's products of expressions. */ /* - * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2015 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 @@ -20,15 +20,8 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include -#include -#include -#include - #include "mul.h" #include "add.h" -#include "color.h" -#include "clifford.h" #include "power.h" #include "operators.h" #include "matrix.h" @@ -36,6 +29,13 @@ #include "lst.h" #include "archive.h" #include "utils.h" +#include "symbol.h" +#include "compiler.h" + +#include +#include +#include +#include namespace GiNaC { @@ -53,7 +53,6 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq, mul::mul() { - tinfo_key = &mul::tinfo_static; } ////////// @@ -64,7 +63,6 @@ mul::mul() mul::mul(const ex & lh, const ex & rh) { - tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_2_ex(lh,rh); GINAC_ASSERT(is_canonical()); @@ -72,7 +70,6 @@ mul::mul(const ex & lh, const ex & rh) mul::mul(const exvector & v) { - tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_exvector(v); GINAC_ASSERT(is_canonical()); @@ -80,32 +77,27 @@ mul::mul(const exvector & v) mul::mul(const epvector & v) { - tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_epvector(v); GINAC_ASSERT(is_canonical()); } -mul::mul(const epvector & v, const ex & oc) +mul::mul(const epvector & v, const ex & oc, bool do_index_renaming) { - tinfo_key = &mul::tinfo_static; overall_coeff = oc; - construct_from_epvector(v); + construct_from_epvector(v, do_index_renaming); GINAC_ASSERT(is_canonical()); } -mul::mul(std::auto_ptr vp, const ex & oc) +mul::mul(epvector && vp, const ex & oc, bool do_index_renaming) { - tinfo_key = &mul::tinfo_static; - GINAC_ASSERT(vp.get()!=0); overall_coeff = oc; - construct_from_epvector(*vp); + construct_from_epvector(std::move(vp), do_index_renaming); GINAC_ASSERT(is_canonical()); } mul::mul(const ex & lh, const ex & mh, const ex & rh) { - tinfo_key = &mul::tinfo_static; exvector factors; factors.reserve(3); factors.push_back(lh); @@ -120,8 +112,6 @@ mul::mul(const ex & lh, const ex & mh, const ex & rh) // archiving ////////// -DEFAULT_ARCHIVING(mul) - ////////// // functions overriding virtual functions from base classes ////////// @@ -155,15 +145,13 @@ void mul::do_print(const print_context & c, unsigned level) const print_overall_coeff(c, "*"); - epvector::const_iterator it = seq.begin(), itend = seq.end(); bool first = true; - while (it != itend) { + for (auto & it : seq) { if (!first) c.s << '*'; else first = false; - recombine_pair_to_ex(*it).print(c, precedence()); - ++it; + recombine_pair_to_ex(it).print(c, precedence()); } if (precedence() <= level) @@ -179,15 +167,13 @@ void mul::do_print_latex(const print_latex & c, unsigned level) const // Separate factors into those with negative numeric exponent // and all others - epvector::const_iterator it = seq.begin(), itend = seq.end(); exvector neg_powers, others; - while (it != itend) { - GINAC_ASSERT(is_exactly_a(it->coeff)); - if (ex_to(it->coeff).is_negative()) - neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff)))); + for (auto & it : seq) { + GINAC_ASSERT(is_exactly_a(it.coeff)); + if (ex_to(it.coeff).is_negative()) + neg_powers.push_back(recombine_pair_to_ex(expair(it.rest, -it.coeff))); else - others.push_back(recombine_pair_to_ex(*it)); - ++it; + others.push_back(recombine_pair_to_ex(it)); } if (!neg_powers.empty()) { @@ -202,11 +188,9 @@ void mul::do_print_latex(const print_latex & c, unsigned level) const } else { // All other factors are printed in the ordinary way - exvector::const_iterator vit = others.begin(), vitend = others.end(); - while (vit != vitend) { + for (auto & vit : others) { c.s << ' '; - vit->print(c, precedence()); - ++vit; + vit.print(c, precedence()); } } @@ -220,12 +204,16 @@ void mul::do_print_csrc(const print_csrc & c, unsigned level) const c.s << "("; if (!overall_coeff.is_equal(_ex1)) { - overall_coeff.print(c, precedence()); - c.s << "*"; + if (overall_coeff.is_equal(_ex_1)) + c.s << "-"; + else { + overall_coeff.print(c, precedence()); + c.s << "*"; + } } // Print arguments, separated by "*" or "/" - epvector::const_iterator it = seq.begin(), itend = seq.end(); + auto it = seq.begin(), itend = seq.end(); while (it != itend) { // If the first argument is a negative integer power, it gets printed as "1.0/" @@ -242,11 +230,9 @@ void mul::do_print_csrc(const print_csrc & c, unsigned level) const 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 parser: - (ex(power(it->rest, -ex_to(it->coeff)))).print(c, level); + ex(power(it->rest, -ex_to(it->coeff))).print(c, level); else - // Outer parens around ex needed for broken GCC parser: - (ex(power(it->rest, ex_to(it->coeff)))).print(c, level); + ex(power(it->rest, ex_to(it->coeff))).print(c, level); if (needclosingparenthesis) c.s << ")"; @@ -283,38 +269,142 @@ bool mul::info(unsigned inf) const case info_flags::integer_polynomial: case info_flags::cinteger_polynomial: case info_flags::rational_polynomial: + case info_flags::real: + case info_flags::rational: + case info_flags::integer: + case info_flags::crational: + case info_flags::cinteger: + case info_flags::even: case info_flags::crational_polynomial: case info_flags::rational_function: { - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - if (!(recombine_pair_to_ex(*i).info(inf))) + for (auto & it : seq) { + if (!recombine_pair_to_ex(it).info(inf)) return false; - ++i; } + if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even) + return true; return overall_coeff.info(inf); } case info_flags::algebraic: { - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - if ((recombine_pair_to_ex(*i).info(inf))) + for (auto & it : seq) { + if (recombine_pair_to_ex(it).info(inf)) return true; - ++i; } return false; } + case info_flags::positive: + case info_flags::negative: { + if ((inf==info_flags::positive) && (flags & status_flags::is_positive)) + return true; + else if ((inf==info_flags::negative) && (flags & status_flags::is_negative)) + return true; + if (flags & status_flags::purely_indefinite) + return false; + + bool pos = true; + for (auto & it : seq) { + const ex& factor = recombine_pair_to_ex(it); + if (factor.info(info_flags::positive)) + continue; + else if (factor.info(info_flags::negative)) + pos = !pos; + else + return false; + } + if (overall_coeff.info(info_flags::negative)) + pos = !pos; + setflag(pos ? status_flags::is_positive : status_flags::is_negative); + return (inf == info_flags::positive? pos : !pos); + } + case info_flags::nonnegative: { + if (flags & status_flags::is_positive) + return true; + bool pos = true; + for (auto & it : seq) { + const ex& factor = recombine_pair_to_ex(it); + if (factor.info(info_flags::nonnegative) || factor.info(info_flags::positive)) + continue; + else if (factor.info(info_flags::negative)) + pos = !pos; + else + return false; + } + return (overall_coeff.info(info_flags::negative)? !pos : pos); + } + case info_flags::posint: + case info_flags::negint: { + bool pos = true; + for (auto & it : seq) { + const ex& factor = recombine_pair_to_ex(it); + if (factor.info(info_flags::posint)) + continue; + else if (factor.info(info_flags::negint)) + pos = !pos; + else + return false; + } + if (overall_coeff.info(info_flags::negint)) + pos = !pos; + else if (!overall_coeff.info(info_flags::posint)) + return false; + return (inf ==info_flags::posint? pos : !pos); + } + case info_flags::nonnegint: { + bool pos = true; + for (auto & it : seq) { + const ex& factor = recombine_pair_to_ex(it); + if (factor.info(info_flags::nonnegint) || factor.info(info_flags::posint)) + continue; + else if (factor.info(info_flags::negint)) + pos = !pos; + else + return false; + } + if (overall_coeff.info(info_flags::negint)) + pos = !pos; + else if (!overall_coeff.info(info_flags::posint)) + return false; + return pos; + } + case info_flags::indefinite: { + if (flags & status_flags::purely_indefinite) + return true; + if (flags & (status_flags::is_positive | status_flags::is_negative)) + return false; + for (auto & it : seq) { + const ex& term = recombine_pair_to_ex(it); + if (term.info(info_flags::positive) || term.info(info_flags::negative)) + return false; + } + setflag(status_flags::purely_indefinite); + return true; + } } return inherited::info(inf); } +bool mul::is_polynomial(const ex & var) const +{ + for (auto & it : seq) { + if (!it.rest.is_polynomial(var) || + (it.rest.has(var) && !it.coeff.info(info_flags::nonnegint))) { + return false; + } + } + return true; +} + int mul::degree(const ex & s) const { // Sum up degrees of factors int deg_sum = 0; - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - if (ex_to(i->coeff).is_integer()) - deg_sum += i->rest.degree(s) * ex_to(i->coeff).to_int(); - ++i; + for (auto & it : seq) { + if (ex_to(it.coeff).is_integer()) + deg_sum += recombine_pair_to_ex(it).degree(s); + else { + if (it.rest.has(s)) + throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent"); + } } return deg_sum; } @@ -323,11 +413,13 @@ int mul::ldegree(const ex & s) const { // Sum up degrees of factors int deg_sum = 0; - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - if (ex_to(i->coeff).is_integer()) - deg_sum += i->rest.ldegree(s) * ex_to(i->coeff).to_int(); - ++i; + for (auto & it : seq) { + if (ex_to(it.coeff).is_integer()) + deg_sum += recombine_pair_to_ex(it).ldegree(s); + else { + if (it.rest.has(s)) + throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent"); + } } return deg_sum; } @@ -340,19 +432,15 @@ ex mul::coeff(const ex & s, int n) const if (n==0) { // product of individual coeffs // if a non-zero power of s is found, the resulting product will be 0 - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n)); - ++i; - } + for (auto & it : seq) + coeffseq.push_back(recombine_pair_to_ex(it).coeff(s,n)); coeffseq.push_back(overall_coeff); return (new mul(coeffseq))->setflag(status_flags::dynallocated); } - epvector::const_iterator i = seq.begin(), end = seq.end(); bool coeff_found = false; - while (i != end) { - ex t = recombine_pair_to_ex(*i); + for (auto & it : seq) { + ex t = recombine_pair_to_ex(it); ex c = t.coeff(s, n); if (!c.is_zero()) { coeffseq.push_back(c); @@ -360,7 +448,6 @@ ex mul::coeff(const ex & s, int n) const } else { coeffseq.push_back(t); } - ++i; } if (coeff_found) { coeffseq.push_back(overall_coeff); @@ -381,38 +468,20 @@ ex mul::coeff(const ex & s, int n) const * @param level cut-off in recursive evaluation */ ex mul::eval(int level) const { - std::auto_ptr evaled_seqp = evalchildren(level); - if (evaled_seqp.get()) { + epvector evaled = evalchildren(level); + if (unlikely(!evaled.empty())) { // do more evaluation later - return (new mul(evaled_seqp, overall_coeff))-> - setflag(status_flags::dynallocated); - } - -#ifdef DO_GINAC_ASSERT - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - GINAC_ASSERT((!is_exactly_a(i->rest)) || - (!(ex_to(i->coeff).is_integer()))); - GINAC_ASSERT(!(i->is_canonical_numeric())); - if (is_exactly_a(recombine_pair_to_ex(*i))) - print(print_tree(std::cerr)); - GINAC_ASSERT(!is_exactly_a(recombine_pair_to_ex(*i))); - /* for paranoia */ - expair p = split_ex_to_pair(recombine_pair_to_ex(*i)); - GINAC_ASSERT(p.rest.is_equal(i->rest)); - GINAC_ASSERT(p.coeff.is_equal(i->coeff)); - /* end paranoia */ - ++i; + return (new mul(std::move(evaled), overall_coeff))-> + setflag(status_flags::dynallocated); } -#endif // def DO_GINAC_ASSERT - + if (flags & status_flags::evaluated) { GINAC_ASSERT(seq.size()>0); GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1)); return *this; } - int seq_size = seq.size(); + size_t seq_size = seq.size(); if (overall_coeff.is_zero()) { // *(...,x;0) -> 0 return _ex0; @@ -427,18 +496,86 @@ ex mul::eval(int level) const ex_to((*seq.begin()).coeff).is_equal(*_num1_p)) { // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +()) const add & addref = ex_to((*seq.begin()).rest); - std::auto_ptr distrseq(new epvector); - distrseq->reserve(addref.seq.size()); - epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end(); - while (i != end) { - distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff)); - ++i; + epvector distrseq; + distrseq.reserve(addref.seq.size()); + for (auto & it : addref.seq) { + distrseq.push_back(addref.combine_pair_with_coeff_to_pair(it, overall_coeff)); } - return (new add(distrseq, + return (new add(std::move(distrseq), ex_to(addref.overall_coeff). - mul_dyn(ex_to(overall_coeff)))) - ->setflag(status_flags::dynallocated | status_flags::evaluated); + mul_dyn(ex_to(overall_coeff))) + )->setflag(status_flags::dynallocated | status_flags::evaluated); + } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) { + // Strip the content and the unit part from each term. Thus + // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2 + + auto i = seq.begin(), last = seq.end(); + auto j = seq.begin(); + epvector s; + numeric oc = *_num1_p; + bool something_changed = false; + while (i!=last) { + if (likely(! (is_a(i->rest) && i->coeff.is_equal(_ex1)))) { + // power::eval has such a rule, no need to handle powers here + ++i; + continue; + } + + // XXX: What is the best way to check if the polynomial is a primitive? + numeric c = i->rest.integer_content(); + const numeric lead_coeff = + ex_to(ex_to(i->rest).seq.begin()->coeff).div(c); + const bool canonicalizable = lead_coeff.is_integer(); + + // XXX: The main variable is chosen in a random way, so this code + // does NOT transform the term into the canonical form (thus, in some + // very unlucky event it can even loop forever). Hopefully the main + // variable will be the same for all terms in *this + const bool unit_normal = lead_coeff.is_pos_integer(); + if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) { + ++i; + continue; + } + + if (! something_changed) { + s.reserve(seq_size); + something_changed = true; + } + + while ((j!=i) && (j!=last)) { + s.push_back(*j); + ++j; + } + + if (! unit_normal) + c = c.mul(*_num_1_p); + + oc = oc.mul(c); + + // divide add by the number in place to save at least 2 .eval() calls + const add& addref = ex_to(i->rest); + add* primitive = new add(addref); + primitive->setflag(status_flags::dynallocated); + primitive->clearflag(status_flags::hash_calculated); + primitive->overall_coeff = ex_to(primitive->overall_coeff).div_dyn(c); + for (epvector::iterator ai = primitive->seq.begin(); ai != primitive->seq.end(); ++ai) + ai->coeff = ex_to(ai->coeff).div_dyn(c); + + s.push_back(expair(*primitive, _ex1)); + + ++i; + ++j; + } + if (something_changed) { + while (j!=last) { + s.push_back(*j); + ++j; + } + return (new mul(std::move(s), ex_to(overall_coeff).mul_dyn(oc)) + )->setflag(status_flags::dynallocated); + } } + return this->hold(); } @@ -450,17 +587,50 @@ ex mul::evalf(int level) const if (level==-max_recursion_level) throw(std::runtime_error("max recursion level reached")); - std::auto_ptr s(new epvector); - s->reserve(seq.size()); + epvector s; + s.reserve(seq.size()); --level; - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level), - i->coeff)); - ++i; + for (auto & it : seq) { + s.push_back(combine_ex_with_coeff_to_pair(it.rest.evalf(level), + it.coeff)); + } + return mul(std::move(s), overall_coeff.evalf(level)); +} + +void mul::find_real_imag(ex & rp, ex & ip) const +{ + rp = overall_coeff.real_part(); + ip = overall_coeff.imag_part(); + for (auto & it : seq) { + ex factor = recombine_pair_to_ex(it); + ex new_rp = factor.real_part(); + ex new_ip = factor.imag_part(); + if (new_ip.is_zero()) { + rp *= new_rp; + ip *= new_rp; + } else { + ex temp = rp*new_rp - ip*new_ip; + ip = ip*new_rp + rp*new_ip; + rp = temp; + } } - return mul(s, overall_coeff.evalf(level)); + rp = rp.expand(); + ip = ip.expand(); +} + +ex mul::real_part() const +{ + ex rp, ip; + find_real_imag(rp, ip); + return rp; +} + +ex mul::imag_part() const +{ + ex rp, ip; + find_real_imag(rp, ip); + return ip; } ex mul::evalm() const @@ -473,21 +643,19 @@ ex mul::evalm() const // Evaluate children first, look whether there are any matrices at all // (there can be either no matrices or one matrix; if there were more // than one matrix, it would be a non-commutative product) - std::auto_ptr s(new epvector); - s->reserve(seq.size()); + epvector s; + s.reserve(seq.size()); bool have_matrix = false; epvector::iterator the_matrix; - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - const ex &m = recombine_pair_to_ex(*i).evalm(); - s->push_back(split_ex_to_pair(m)); + for (auto & it : seq) { + const ex &m = recombine_pair_to_ex(it).evalm(); + s.push_back(split_ex_to_pair(m)); if (is_a(m)) { have_matrix = true; - the_matrix = s->end() - 1; + the_matrix = s.end() - 1; } - ++i; } if (have_matrix) { @@ -495,12 +663,12 @@ ex mul::evalm() const // The product contained a matrix. We will multiply all other factors // into that matrix. matrix m = ex_to(the_matrix->rest); - s->erase(the_matrix); - ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated); + s.erase(the_matrix); + ex scalar = (new mul(std::move(s), overall_coeff))->setflag(status_flags::dynallocated); return m.mul_scalar(scalar); } else - return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated); + return (new mul(std::move(s), overall_coeff))->setflag(status_flags::dynallocated); } ex mul::eval_ncmul(const exvector & v) const @@ -509,16 +677,13 @@ ex mul::eval_ncmul(const exvector & v) const return inherited::eval_ncmul(v); // 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.eval_ncmul(v); - ++i; - } + for (auto & it : seq) + if (it.rest.return_type() == return_types::noncommutative) + return it.rest.eval_ncmul(v); return inherited::eval_ncmul(v); } -bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls) +bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls) { ex origbase; int origexponent; @@ -550,7 +715,7 @@ bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatch patternexpsign = 1; } - lst saverepls = repls; + exmap saverepls = repls; if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls)) return false; repls = saverepls; @@ -561,7 +726,7 @@ bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatch return true; } -/** Checks wheter e matches to the pattern pat and the (possibly to be updated +/** Checks whether e matches to the pattern pat and the (possibly to be updated) * list of replacements repls. This matching is in the sense of algebraic * substitutions. Matching starts with pat.op(factor) of the pattern because * the factors before this one have already been matched. The (possibly @@ -569,17 +734,20 @@ bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatch * that already have been replaced by previous substitutions and matched[i] * is true for factors that have been matched by the current match. */ -bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, lst &repls, - int factor, int &nummatches, const std::vector &subsed, - std::vector &matched) +bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls, + int factor, int &nummatches, const std::vector &subsed, + std::vector &matched) { - if (factor == pat.nops()) + GINAC_ASSERT(subsed.size() == e.nops()); + GINAC_ASSERT(matched.size() == e.nops()); + + if (factor == (int)pat.nops()) return true; for (size_t i=0; i(pattern)) { - lst repls; + exmap repls; int nummatches = std::numeric_limits::max(); - std::vector subsed(seq.size(), false); - std::vector matched(seq.size(), false); + std::vector subsed(nops(), false); + std::vector matched(nops(), false); if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches, subsed, matched)) return true; @@ -615,45 +783,45 @@ bool mul::has(const ex & pattern, unsigned options) const ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const { - std::vector subsed(seq.size(), false); - exvector subsresult(seq.size()); + std::vector subsed(nops(), false); + ex divide_by = 1; + ex multiply_by = 1; - for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) { + for (auto & it : m) { - if (is_exactly_a(it->first)) { + if (is_exactly_a(it.first)) { retry1: int nummatches = std::numeric_limits::max(); - std::vector currsubsed(seq.size(), false); - bool succeed = true; - lst repls; + std::vector currsubsed(nops(), false); + exmap repls; - if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed)) + if (!algebraic_match_mul_with_mul(*this, it.first, repls, 0, nummatches, subsed, currsubsed)) continue; - bool foundfirstsubsedfactor = false; - for (size_t j=0; jsecond.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches); - } + for (size_t j=0; j::max(); - lst repls; for (size_t j=0; jnops(); j++) { - if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) { + int nummatches = std::numeric_limits::max(); + exmap repls; + 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::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches); - goto retry2; + ex subsed_pattern + = it.first.subs(repls, subs_options::no_pattern); + divide_by *= power(subsed_pattern, nummatches); + ex subsed_result + = it.second.subs(repls, subs_options::no_pattern); + multiply_by *= power(subsed_result, nummatches); } } } @@ -669,17 +837,39 @@ retry2: if (!subsfound) return subs_one_level(m, options | subs_options::algebraic); - exvector ev; ev.reserve(nops()); - for (size_t i=0; isetflag(status_flags::dynallocated); +ex mul::conjugate() const +{ + // The base class' method is wrong here because we have to be careful at + // branch cuts. power::conjugate takes care of that already, so use it. + std::unique_ptr newepv(nullptr); + for (auto i=seq.begin(); i!=seq.end(); ++i) { + if (newepv) { + newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate())); + continue; + } + ex x = recombine_pair_to_ex(*i); + ex c = x.conjugate(); + if (c.is_equal(x)) { + continue; + } + newepv.reset(new epvector); + newepv->reserve(seq.size()); + for (auto j=seq.begin(); j!=i; ++j) { + newepv->push_back(*j); + } + newepv->push_back(split_ex_to_pair(c)); + } + ex x = overall_coeff.conjugate(); + if (!newepv && are_ex_trivially_equal(x, overall_coeff)) { + return *this; + } + return thisexpairseq(newepv ? std::move(*newepv) : seq, x); } + // protected /** Implementation of ex::diff() for a product. It applies the product rule. @@ -692,8 +882,8 @@ ex mul::derivative(const symbol & s) const // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c) epvector mulseq = seq; - epvector::const_iterator i = seq.begin(), end = seq.end(); - epvector::iterator i2 = mulseq.begin(); + auto i = seq.begin(), end = seq.end(); + auto i2 = mulseq.begin(); while (i != end) { expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) * i->rest.diff(s)); @@ -732,21 +922,8 @@ unsigned mul::return_type() const } if ((rt == return_types::noncommutative) && (!all_commutative)) { // another nc element found, compare type_infos - if (noncommutative_element->rest.return_type_tinfo()->tinfo() == &clifford::tinfo_static) { - if (i->rest.return_type_tinfo()->tinfo() != &clifford::tinfo_static || - ((clifford*)(noncommutative_element->rest.return_type_tinfo()))->get_representation_label() != - ((clifford*)(i->rest.return_type_tinfo()))->get_representation_label()) { - // diffent types -> mul is ncc - return return_types::noncommutative_composite; - } - } else if (noncommutative_element->rest.return_type_tinfo()->tinfo() == &color::tinfo_static) { - if (i->rest.return_type_tinfo()->tinfo() != &color::tinfo_static || - ((color*)(noncommutative_element->rest.return_type_tinfo()))->get_representation_label() != - ((color*)(i->rest.return_type_tinfo()))->get_representation_label()) { - // diffent types -> mul is ncc - return return_types::noncommutative_composite; - } - } else if (noncommutative_element->rest.return_type_tinfo()->tinfo() != i->rest.return_type_tinfo()->tinfo()) { + if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) { + // different types -> mul is ncc return return_types::noncommutative_composite; } } @@ -755,31 +932,29 @@ unsigned mul::return_type() const // all factors checked return all_commutative ? return_types::commutative : return_types::noncommutative; } - -const basic* mul::return_type_tinfo() const + +return_type_t mul::return_type_tinfo() const { if (seq.empty()) - return this; // mul without factors: should not happen + return make_return_type_t(); // mul without factors: should not happen // return type_info of first noncommutative element - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - if (i->rest.return_type() == return_types::noncommutative) - return i->rest.return_type_tinfo(); - ++i; - } + for (auto & it : seq) + if (it.rest.return_type() == return_types::noncommutative) + return it.rest.return_type_tinfo(); + // no noncommutative element found, should not happen - return this; + return make_return_type_t(); } -ex mul::thisexpairseq(const epvector & v, const ex & oc) const +ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const { - return (new mul(v, oc))->setflag(status_flags::dynallocated); + return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated); } -ex mul::thisexpairseq(std::auto_ptr vp, const ex & oc) const +ex mul::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const { - return (new mul(vp, oc))->setflag(status_flags::dynallocated); + return (new mul(std::move(vp), oc, do_index_renaming))->setflag(status_flags::dynallocated); } expair mul::split_ex_to_pair(const ex & e) const @@ -791,7 +966,7 @@ expair mul::split_ex_to_pair(const ex & e) const } return expair(e,_ex1); } - + expair mul::combine_ex_with_coeff_to_pair(const ex & e, const ex & c) const { @@ -804,7 +979,7 @@ expair mul::combine_ex_with_coeff_to_pair(const ex & e, return split_ex_to_pair(power(e,c)); } - + expair mul::combine_pair_with_coeff_to_pair(const expair & p, const ex & c) const { @@ -817,7 +992,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p, return split_ex_to_pair(power(recombine_pair_to_ex(p),c)); } - + ex mul::recombine_pair_to_ex(const expair & p) const { if (ex_to(p.coeff).is_equal(*_num1_p)) @@ -829,22 +1004,22 @@ ex mul::recombine_pair_to_ex(const expair & p) const bool mul::expair_needs_further_processing(epp it) { if (is_exactly_a(it->rest) && - ex_to(it->coeff).is_integer()) { + ex_to(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_exactly_a(it->rest)) { + if (it->coeff.is_equal(_ex1)) { + // pair has coeff 1 and must be moved to the end + return true; + } 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 (it->coeff.is_equal(_ex1)) { - // combined pair has coeff 1 and must be moved to the end - return true; - } } return false; } @@ -872,17 +1047,16 @@ void mul::combine_overall_coeff(const ex & c1, const ex & c2) bool mul::can_make_flat(const expair & p) const { GINAC_ASSERT(is_exactly_a(p.coeff)); - // this assertion will probably fail somewhere - // it would require a more careful make_flat, obeying the power laws - // probably should return true only if p.coeff is integer - return ex_to(p.coeff).is_equal(*_num1_p); + + // (x*y)^c == x^c*y^c if c ∈ ℤ + return p.coeff.info(info_flags::integer); } bool mul::can_be_further_expanded(const ex & e) { if (is_exactly_a(e)) { - for (epvector::const_iterator cit = ex_to(e).seq.begin(); cit != ex_to(e).seq.end(); ++cit) { - if (is_exactly_a(cit->rest) && cit->coeff.info(info_flags::posint)) + for (auto & it : ex_to(e).seq) { + if (is_exactly_a(it.rest) && it.coeff.info(info_flags::posint)) return true; } } else if (is_exactly_a(e)) { @@ -894,9 +1068,27 @@ bool mul::can_be_further_expanded(const ex & e) ex mul::expand(unsigned options) const { + { + // trivial case: expanding the monomial (~ 30% of all calls) + epvector::const_iterator i = seq.begin(), seq_end = seq.end(); + while ((i != seq.end()) && is_a(i->rest) && i->coeff.info(info_flags::integer)) + ++i; + if (i == seq_end) { + setflag(status_flags::expanded); + return *this; + } + } + + // do not rename indices if the object has no indices at all + if ((!(options & expand_options::expand_rename_idx)) && + this->info(info_flags::has_indices)) + options |= expand_options::expand_rename_idx; + + const bool skip_idx_rename = !(options & expand_options::expand_rename_idx); + // First, expand the children - std::auto_ptr expanded_seqp = expandchildren(options); - const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq); + epvector expanded = expandchildren(options); + const epvector & expanded_seq = (expanded.empty() ? seq : expanded); // Now, look for all the factors that are sums and multiply each one out // with the next one that is found while collecting the factors which are @@ -906,93 +1098,94 @@ ex mul::expand(unsigned options) const epvector non_adds; non_adds.reserve(expanded_seq.size()); - for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) { - if (is_exactly_a(cit->rest) && - (cit->coeff.is_equal(_ex1))) { + for (const auto & cit : expanded_seq) { + if (is_exactly_a(cit.rest) && + (cit.coeff.is_equal(_ex1))) { if (is_exactly_a(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(last_expanded).seq.size()-ex_to(cit->rest).seq.size(); + const int sizedifference = ex_to(last_expanded).seq.size()-ex_to(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(last_expanded) : ex_to(cit->rest)); - const add& add2 = (sizedifference<0 ? ex_to(cit->rest) : ex_to(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(); + const add& add1 = (sizedifference<0 ? ex_to(last_expanded) : ex_to(cit.rest)); + const add& add2 = (sizedifference<0 ? ex_to(cit.rest) : ex_to(last_expanded)); 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); + distrseq.insert(distrseq.end(), add2.seq.begin(), add2.seq.end()); else - for (epvector::const_iterator i=add2begin; i!=add2end; ++i) - distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add1.overall_coeff)))); + for (const auto & i : add2.seq) + distrseq.push_back(expair(i.rest, ex_to(i.coeff).mul_dyn(ex_to(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); + distrseq.insert(distrseq.end(), add1.seq.begin(), add1.seq.end()); else - for (epvector::const_iterator i=add1begin; i!=add1end; ++i) - distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add2.overall_coeff)))); + for (const auto & i : add1.seq) + distrseq.push_back(expair(i.rest, ex_to(i.coeff).mul_dyn(ex_to(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); exvector add1_dummy_indices, add2_dummy_indices, add_indices; + lst dummy_subs; - for (epvector::const_iterator i=add1begin; i!=add1end; ++i) { - add_indices = get_all_dummy_indices(i->rest); - add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end()); - } - for (epvector::const_iterator i=add2begin; i!=add2end; ++i) { - add_indices = get_all_dummy_indices(i->rest); - add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end()); - } + if (!skip_idx_rename) { + for (const auto & i : add1.seq) { + add_indices = get_all_dummy_indices_safely(i.rest); + add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end()); + } + for (const auto & i : add2.seq) { + add_indices = get_all_dummy_indices_safely(i.rest); + add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end()); + } - sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less()); - sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less()); - lst dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices); + sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less()); + sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less()); + dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices); + } // Multiply explicitly all non-numeric terms of add1 and add2: - for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) { + for (const auto & i2 : add2.seq) { // We really have to combine terms here in order to compactify // the result. Otherwise it would become waayy tooo bigg. - numeric oc; - distrseq.clear(); - ex i2_new = (dummy_subs.op(0).nops()>0? - i2->rest.subs((lst)dummy_subs.op(0), (lst)dummy_subs.op(1), subs_options::no_pattern) : i2->rest); - for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) { + numeric oc(*_num0_p); + epvector distrseq2; + distrseq2.reserve(add1.seq.size()); + const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ? + i2.rest : + i2.rest.subs(ex_to(dummy_subs.op(0)), + ex_to(dummy_subs.op(1)), subs_options::no_pattern)); + for (const auto & i1 : add1.seq) { // 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_new))->setflag(status_flags::dynallocated); + const ex rest = (new mul(i1.rest, i2_new))->setflag(status_flags::dynallocated); if (is_exactly_a(rest)) { - oc += ex_to(rest).mul(ex_to(i1->coeff).mul(ex_to(i2->coeff))); + oc += ex_to(rest).mul(ex_to(i1.coeff).mul(ex_to(i2.coeff))); } else { - distrseq.push_back(expair(rest, ex_to(i1->coeff).mul_dyn(ex_to(i2->coeff)))); + distrseq2.push_back(expair(rest, ex_to(i1.coeff).mul_dyn(ex_to(i2.coeff)))); } } - tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated); + tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated); } last_expanded = tmp_accu; - } else { if (!last_expanded.is_equal(_ex1)) non_adds.push_back(split_ex_to_pair(last_expanded)); - last_expanded = cit->rest; + last_expanded = cit.rest; } } else { - non_adds.push_back(*cit); + non_adds.push_back(cit); } } @@ -1002,12 +1195,18 @@ ex mul::expand(unsigned options) const size_t n = last_expanded.nops(); exvector distrseq; distrseq.reserve(n); - exvector va = get_all_dummy_indices(mul(non_adds)); - sort(va.begin(), va.end(), ex_is_less()); + exvector va; + if (! skip_idx_rename) { + va = get_all_dummy_indices_safely(mul(non_adds)); + sort(va.begin(), va.end(), ex_is_less()); + } for (size_t i=0; isetflag(status_flags::dynallocated); if (can_be_further_expanded(term)) { distrseq.push_back(term.expand()); @@ -1047,46 +1246,47 @@ ex mul::expand(unsigned options) const /** Member-wise expand the expairs representing this sequence. This must be * overridden from expairseq::expandchildren() and done iteratively in order - * to allow for early cancallations and thus safe memory. + * to allow for early cancellations and thus safe memory. * * @see mul::expand() - * @return pointer to epvector containing expanded representation or zero - * pointer, if sequence is unchanged. */ -std::auto_ptr mul::expandchildren(unsigned options) const + * @return epvector containing expanded pairs, empty if no members + * had to be changed. */ +epvector mul::expandchildren(unsigned options) const { - const epvector::const_iterator last = seq.end(); - epvector::const_iterator cit = seq.begin(); + auto cit = seq.begin(), last = seq.end(); while (cit!=last) { const ex & factor = recombine_pair_to_ex(*cit); const ex & expanded_factor = factor.expand(options); if (!are_ex_trivially_equal(factor,expanded_factor)) { // something changed, copy seq, eval and return it - std::auto_ptr s(new epvector); - s->reserve(seq.size()); + epvector s; + s.reserve(seq.size()); // copy parts of seq which are known not to have changed - epvector::const_iterator cit2 = seq.begin(); + auto cit2 = seq.begin(); while (cit2!=cit) { - s->push_back(*cit2); + s.push_back(*cit2); ++cit2; } // copy first changed element - s->push_back(split_ex_to_pair(expanded_factor)); + s.push_back(split_ex_to_pair(expanded_factor)); ++cit2; // copy rest while (cit2!=last) { - s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options))); + s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options))); ++cit2; } return s; } ++cit; } - - return std::auto_ptr(0); // nothing has changed + + return epvector(); // nothing has changed } +GINAC_BIND_UNARCHIVER(mul); + } // namespace GiNaC