X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fpower.cpp;h=ccbf528122e425fbb004b6c4dbacb2ab8af96fdf;hb=f5b3b828a0c67c1f2c9a8931d980505c3475beef;hp=f0b5c5adb8c566b0b965ac649badcd95b040e510;hpb=6b3768e8c544739ae53321539cb4d1e3112ded1b;p=ginac.git diff --git a/ginac/power.cpp b/ginac/power.cpp index f0b5c5ad..ccbf5281 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -2,11 +2,44 @@ * * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ +/* + * GiNaC Copyright (C) 1999-2000 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 + * the Free Software Foundation; either version 2 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + */ + #include #include #include -#include "ginac.h" +#include "power.h" +#include "expairseq.h" +#include "add.h" +#include "mul.h" +#include "numeric.h" +#include "relational.h" +#include "symbol.h" +#include "archive.h" +#include "debugmsg.h" +#include "utils.h" + +#ifndef NO_GINAC_NAMESPACE +namespace GiNaC { +#endif // ndef NO_GINAC_NAMESPACE + +GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic) typedef vector intvector; @@ -16,7 +49,7 @@ typedef vector intvector; // public -power::power() : basic(TINFO_POWER) +power::power() : basic(TINFO_power) { debugmsg("power default constructor",LOGLEVEL_CONSTRUCT); } @@ -47,14 +80,14 @@ power const & power::operator=(power const & other) void power::copy(power const & other) { - basic::copy(other); + inherited::copy(other); basis=other.basis; exponent=other.exponent; } void power::destroy(bool call_parent) { - if (call_parent) basic::destroy(call_parent); + if (call_parent) inherited::destroy(call_parent); } ////////// @@ -63,16 +96,42 @@ void power::destroy(bool call_parent) // public -power::power(ex const & lh, ex const & rh) : basic(TINFO_POWER), basis(lh), exponent(rh) +power::power(ex const & lh, ex const & rh) : basic(TINFO_power), basis(lh), exponent(rh) { debugmsg("power constructor from ex,ex",LOGLEVEL_CONSTRUCT); - ASSERT(basis.return_type()==return_types::commutative); + GINAC_ASSERT(basis.return_type()==return_types::commutative); } -power::power(ex const & lh, numeric const & rh) : basic(TINFO_POWER), basis(lh), exponent(rh) +power::power(ex const & lh, numeric const & rh) : basic(TINFO_power), basis(lh), exponent(rh) { debugmsg("power constructor from ex,numeric",LOGLEVEL_CONSTRUCT); - ASSERT(basis.return_type()==return_types::commutative); + GINAC_ASSERT(basis.return_type()==return_types::commutative); +} + +////////// +// archiving +////////// + +/** Construct object from archive_node. */ +power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +{ + debugmsg("power constructor from archive_node", LOGLEVEL_CONSTRUCT); + n.find_ex("basis", basis, sym_lst); + n.find_ex("exponent", exponent, sym_lst); +} + +/** Unarchive the object. */ +ex power::unarchive(const archive_node &n, const lst &sym_lst) +{ + return (new power(n, sym_lst))->setflag(status_flags::dynallocated); +} + +/** Archive the object. */ +void power::archive(archive_node &n) const +{ + inherited::archive(n); + n.add_ex("basis", basis); + n.add_ex("exponent", exponent); } ////////// @@ -87,26 +146,131 @@ basic * power::duplicate() const return new power(*this); } +void power::print(ostream & os, unsigned upper_precedence) const +{ + debugmsg("power print",LOGLEVEL_PRINT); + if (exponent.is_equal(_ex1_2())) { + os << "sqrt(" << basis << ")"; + } else { + if (precedence<=upper_precedence) os << "("; + basis.print(os,precedence); + os << "^"; + exponent.print(os,precedence); + if (precedence<=upper_precedence) os << ")"; + } +} + +void power::printraw(ostream & os) const +{ + debugmsg("power printraw",LOGLEVEL_PRINT); + + os << "power("; + basis.printraw(os); + os << ","; + exponent.printraw(os); + os << ",hash=" << hashvalue << ",flags=" << flags << ")"; +} + +void power::printtree(ostream & os, unsigned indent) const +{ + debugmsg("power printtree",LOGLEVEL_PRINT); + + os << string(indent,' ') << "power: " + << "hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")" + << ", flags=" << flags << endl; + basis.printtree(os,indent+delta_indent); + exponent.printtree(os,indent+delta_indent); +} + +static void print_sym_pow(ostream & os, unsigned type, const symbol &x, int exp) +{ + // Optimal output of integer powers of symbols to aid compiler CSE + if (exp == 1) { + x.printcsrc(os, type, 0); + } else if (exp == 2) { + x.printcsrc(os, type, 0); + os << "*"; + x.printcsrc(os, type, 0); + } else if (exp & 1) { + x.printcsrc(os, 0); + os << "*"; + print_sym_pow(os, type, x, exp-1); + } else { + os << "("; + print_sym_pow(os, type, x, exp >> 1); + os << ")*("; + print_sym_pow(os, type, x, exp >> 1); + os << ")"; + } +} + +void power::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const +{ + debugmsg("power print csrc", LOGLEVEL_PRINT); + + // Integer powers of symbols are printed in a special, optimized way + if (exponent.info(info_flags::integer) && + (is_ex_exactly_of_type(basis, symbol) || + is_ex_exactly_of_type(basis, constant))) { + int exp = ex_to_numeric(exponent).to_int(); + if (exp > 0) + os << "("; + else { + exp = -exp; + if (type == csrc_types::ctype_cl_N) + os << "recip("; + else + os << "1.0/("; + } + print_sym_pow(os, type, static_cast(*basis.bp), exp); + os << ")"; + + // ^-1 is printed as "1.0/" or with the recip() function of CLN + } else if (exponent.compare(_num_1()) == 0) { + if (type == csrc_types::ctype_cl_N) + os << "recip("; + else + os << "1.0/("; + basis.bp->printcsrc(os, type, 0); + os << ")"; + + // Otherwise, use the pow() or expt() (CLN) functions + } else { + if (type == csrc_types::ctype_cl_N) + os << "expt("; + else + os << "pow("; + basis.bp->printcsrc(os, type, 0); + os << ","; + exponent.bp->printcsrc(os, type, 0); + os << ")"; + } +} + bool power::info(unsigned inf) const { - if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial) { + if (inf==info_flags::polynomial || + inf==info_flags::integer_polynomial || + inf==info_flags::cinteger_polynomial || + inf==info_flags::rational_polynomial || + inf==info_flags::crational_polynomial) { return exponent.info(info_flags::nonnegint); } else if (inf==info_flags::rational_function) { return exponent.info(info_flags::integer); } else { - return basic::info(inf); + return inherited::info(inf); } } -int power::nops() const +unsigned power::nops() const { return 2; } ex & power::let_op(int const i) { - ASSERT(i>=0); - ASSERT(i<2); + GINAC_ASSERT(i>=0); + GINAC_ASSERT(i<2); return i==0 ? basis : exponent; } @@ -114,7 +278,7 @@ ex & power::let_op(int const i) int power::degree(symbol const & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) + if ((*basis.bp).compare(s)==0) return ex_to_numeric(exponent).to_int(); else return basis.degree(s) * ex_to_numeric(exponent).to_int(); @@ -125,7 +289,7 @@ int power::degree(symbol const & s) const int power::ldegree(symbol const & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) + if ((*basis.bp).compare(s)==0) return ex_to_numeric(exponent).to_int(); else return basis.ldegree(s) * ex_to_numeric(exponent).to_int(); @@ -140,14 +304,14 @@ ex power::coeff(symbol const & s, int const n) const if (n==0) { return *this; } else { - return exZERO(); + return _ex0(); } } else if (is_exactly_of_type(*exponent.bp,numeric)&& (static_cast(*exponent.bp).compare(numeric(n))==0)) { - return exONE(); + return _ex1(); } - return exZERO(); + return _ex0(); } ex power::eval(int level) const @@ -189,10 +353,10 @@ ex power::eval(int level) const // ^(x,0) -> 1 (0^0 also handled here) if (eexponent.is_zero()) - return exONE(); + return _ex1(); // ^(x,1) -> x - if (eexponent.is_equal(exONE())) + if (eexponent.is_equal(_ex1())) return ebasis; // ^(0,x) -> 0 (except if x is real and negative) @@ -200,27 +364,27 @@ ex power::eval(int level) const if (exponent_is_numerical && num_exponent->is_negative()) { throw(std::overflow_error("power::eval(): division by zero")); } else - return exZERO(); + return _ex0(); } // ^(1,x) -> 1 - if (ebasis.is_equal(exONE())) - return exONE(); + if (ebasis.is_equal(_ex1())) + return _ex1(); if (basis_is_numerical && exponent_is_numerical) { // ^(c1,c2) -> c1^c2 (c1, c2 numeric(), // except if c1,c2 are rational, but c1^c2 is not) - bool basis_is_rational = num_basis->is_rational(); - bool exponent_is_rational = num_exponent->is_rational(); + bool basis_is_crational = num_basis->is_crational(); + bool exponent_is_crational = num_exponent->is_crational(); numeric res = (*num_basis).power(*num_exponent); - if ((!basis_is_rational || !exponent_is_rational) - || res.is_rational()) { + if ((!basis_is_crational || !exponent_is_crational) + || res.is_crational()) { return res; } - ASSERT(!num_exponent->is_integer()); // has been handled by now + GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer - if (basis_is_rational && exponent_is_rational + if (basis_is_crational && exponent_is_crational && num_exponent->is_real() && !num_exponent->is_integer()) { numeric r, q, n, m; @@ -229,14 +393,14 @@ ex power::eval(int level) const q = iquo(n, m, r); if (r.is_negative()) { r = r.add(m); - q = q.sub(numONE()); + q = q.sub(_num1()); } if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1 return this->hold(); else { epvector res(2); res.push_back(expair(ebasis,r.div(m))); - res.push_back(expair(ex(num_basis->power(q)),exONE())); + res.push_back(expair(ex(num_basis->power(q)),_ex1())); return (new mul(res))->setflag(status_flags::dynallocated | status_flags::evaluated); /*return mul(num_basis->power(q), power(ex(*num_basis),ex(r.div(m)))).hold(); @@ -257,7 +421,7 @@ ex power::eval(int level) const ex const & sub_exponent=sub_power.exponent; if (is_ex_exactly_of_type(sub_exponent,numeric)) { numeric const & num_sub_exponent=ex_to_numeric(sub_exponent); - ASSERT(num_sub_exponent!=numeric(1)); + GINAC_ASSERT(num_sub_exponent!=numeric(1)); if (num_exponent->is_integer() || abs(num_sub_exponent)<1) { return power(sub_basis,num_sub_exponent.mul(*num_exponent)); } @@ -273,24 +437,24 @@ ex power::eval(int level) const // ^(*(...,x;c1),c2) -> ^(*(...,x;1),c2)*c1^c2 (c1, c2 numeric(), c1>0) // ^(*(...,x,c1),c2) -> ^(*(...,x;-1),c2)*(-c1)^c2 (c1, c2 numeric(), c1<0) if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,mul)) { - ASSERT(!num_exponent->is_integer()); // should have been handled above + GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above mul const & mulref=ex_to_mul(ebasis); - if (!mulref.overall_coeff.is_equal(exONE())) { + if (!mulref.overall_coeff.is_equal(_ex1())) { numeric const & num_coeff=ex_to_numeric(mulref.overall_coeff); if (num_coeff.is_real()) { if (num_coeff.is_positive()>0) { mul * mulp=new mul(mulref); - mulp->overall_coeff=exONE(); + mulp->overall_coeff=_ex1(); mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), power(num_coeff,*num_exponent)))-> setflag(status_flags::dynallocated); } else { - ASSERT(num_coeff.compare(numZERO())<0); - if (num_coeff.compare(numMINUSONE())!=0) { + GINAC_ASSERT(num_coeff.compare(_num0())<0); + if (num_coeff.compare(_num_1())!=0) { mul * mulp=new mul(mulref); - mulp->overall_coeff=exMINUSONE(); + mulp->overall_coeff=_ex_1(); mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), @@ -345,14 +509,14 @@ ex power::subs(lst const & ls, lst const & lr) const ex power::simplify_ncmul(exvector const & v) const { - return basic::simplify_ncmul(v); + return inherited::simplify_ncmul(v); } // protected int power::compare_same_type(basic const & other) const { - ASSERT(is_exactly_of_type(other, power)); + GINAC_ASSERT(is_exactly_of_type(other, power)); power const & o=static_cast(const_cast(other)); int cmpval; @@ -445,8 +609,8 @@ ex power::expand_add(add const & a, int const n) const term.reserve(m+1); for (l=0; lsetflag(status_flags::dynallocated)); // increment k[] @@ -514,41 +678,6 @@ ex power::expand_add(add const & a, int const n) const return (new add(sum))->setflag(status_flags::dynallocated); } -/* -ex power::expand_add_2(add const & a) const -{ - // special case: expand a^2 where a is an add - - epvector sum; - sum.reserve((a.seq.size()*(a.seq.size()+1))/2); - epvector::const_iterator last=a.seq.end(); - - for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) { - ex const & b=a.recombine_pair_to_ex(*cit0); - ASSERT(!is_ex_exactly_of_type(b,add)); - ASSERT(!is_ex_exactly_of_type(b,power)|| - !is_ex_exactly_of_type(ex_to_power(b).exponent,numeric)|| - !ex_to_numeric(ex_to_power(b).exponent).is_pos_integer()); - if (is_ex_exactly_of_type(b,mul)) { - sum.push_back(a.split_ex_to_pair(expand_mul(ex_to_mul(b),numTWO()))); - } else { - sum.push_back(a.split_ex_to_pair((new power(b,exTWO()))-> - setflag(status_flags::dynallocated))); - } - for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { - sum.push_back(a.split_ex_to_pair((new mul(a.recombine_pair_to_ex(*cit0), - a.recombine_pair_to_ex(*cit1)))-> - setflag(status_flags::dynallocated), - exTWO())); - } - } - - ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); - - return (new add(sum))->setflag(status_flags::dynallocated); -} -*/ - ex power::expand_add_2(add const & a) const { // special case: expand a^2 where a is an add @@ -564,28 +693,28 @@ ex power::expand_add_2(add const & a) const ex const & r=(*cit0).rest; ex const & c=(*cit0).coeff; - ASSERT(!is_ex_exactly_of_type(r,add)); - ASSERT(!is_ex_exactly_of_type(r,power)|| + GINAC_ASSERT(!is_ex_exactly_of_type(r,add)); + GINAC_ASSERT(!is_ex_exactly_of_type(r,power)|| !is_ex_exactly_of_type(ex_to_power(r).exponent,numeric)|| !ex_to_numeric(ex_to_power(r).exponent).is_pos_integer()|| !is_ex_exactly_of_type(ex_to_power(r).basis,add)|| !is_ex_exactly_of_type(ex_to_power(r).basis,mul)|| !is_ex_exactly_of_type(ex_to_power(r).basis,power)); - if (are_ex_trivially_equal(c,exONE())) { + if (are_ex_trivially_equal(c,_ex1())) { if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to_mul(r),numTWO()),exONE())); + sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),_ex1())); } else { - sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated), - exONE())); + sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated), + _ex1())); } } else { if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to_mul(r),numTWO()), - ex_to_numeric(c).power_dyn(numTWO()))); + sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()), + ex_to_numeric(c).power_dyn(_num2()))); } else { - sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated), - ex_to_numeric(c).power_dyn(numTWO()))); + sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated), + ex_to_numeric(c).power_dyn(_num2()))); } } @@ -593,21 +722,21 @@ ex power::expand_add_2(add const & a) const ex const & r1=(*cit1).rest; ex const & c1=(*cit1).coeff; sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated), - numTWO().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1)))); + _num2().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1)))); } } - ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); + GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); // second part: add terms coming from overall_factor (if != 0) - if (!a.overall_coeff.is_equal(exZERO())) { + if (!a.overall_coeff.is_equal(_ex0())) { for (epvector::const_iterator cit=a.seq.begin(); cit!=a.seq.end(); ++cit) { - sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to_numeric(a.overall_coeff).mul_dyn(numTWO()))); + sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to_numeric(a.overall_coeff).mul_dyn(_num2()))); } - sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(numTWO()),exONE())); + sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(_num2()),_ex1())); } - ASSERT(sum.size()==(a_nops*(a_nops+1))/2); + GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); return (new add(sum))->setflag(status_flags::dynallocated); } @@ -616,8 +745,8 @@ ex power::expand_mul(mul const & m, numeric const & n) const { // expand m^n where m is a mul and n is and integer - if (n.is_equal(numZERO())) { - return exONE(); + if (n.is_equal(_num0())) { + return _ex1(); } epvector distrseq; @@ -671,7 +800,7 @@ ex power::expand_commutative_3(ex const & basis, numeric const & exponent, ex power::expand_noncommutative(ex const & basis, numeric const & exponent, unsigned options) const { - ex rest_power=ex(power(basis,exponent.add(numMINUSONE()))). + ex rest_power=ex(power(basis,exponent.add(_num_1()))). expand(options | expand_options::internal_do_not_expand_power_operands); return ex(mul(rest_power,basis),0). @@ -693,3 +822,14 @@ unsigned power::precedence=60; const power some_power; type_info const & typeid_power=typeid(some_power); + +// helper function + +ex sqrt(ex const & a) +{ + return power(a,_ex1_2()); +} + +#ifndef NO_GINAC_NAMESPACE +} // namespace GiNaC +#endif // ndef NO_GINAC_NAMESPACE