/** @file power.cpp
*
- * Implementation of GiNaC's symbolic exponentiation (basis^exponent).
- *
+ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
+
+/*
* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
#include "numeric.h"
#include "relational.h"
#include "symbol.h"
+#include "debugmsg.h"
+#include "utils.h"
+
+#ifndef NO_GINAC_NAMESPACE
+namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
typedef vector<int> intvector;
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)
{
debugmsg("power constructor from ex,numeric",LOGLEVEL_CONSTRUCT);
- ASSERT(basis.return_type()==return_types::commutative);
+ GINAC_ASSERT(basis.return_type()==return_types::commutative);
}
//////////
return new power(*this);
}
+void power::print(ostream & os, unsigned upper_precedence) const
+{
+ debugmsg("power print",LOGLEVEL_PRINT);
+ 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<const symbol &>(*basis.bp), exp);
+ os << ")";
+
+ // <expr>^-1 is printed as "1.0/<expr>" 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);
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;
}
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();
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();
if (n==0) {
return *this;
} else {
- return exZERO();
+ return _ex0();
}
} else if (is_exactly_of_type(*exponent.bp,numeric)&&
(static_cast<numeric const &>(*exponent.bp).compare(numeric(n))==0)) {
- return exONE();
+ return _ex1();
}
- return exZERO();
+ return _ex0();
}
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)
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;
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();
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));
}
// ^(*(...,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),
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<power const &>(const_cast<basic &>(other));
int cmpval;
term.reserve(m+1);
for (l=0; l<m-1; l++) {
ex const & b=a.op(l);
- ASSERT(!is_ex_exactly_of_type(b,add));
- ASSERT(!is_ex_exactly_of_type(b,power)||
+ GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
+ GINAC_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)) {
}
ex const & b=a.op(l);
- ASSERT(!is_ex_exactly_of_type(b,add));
- ASSERT(!is_ex_exactly_of_type(b,power)||
+ GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
+ GINAC_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)) {
cout << "end term" << endl;
*/
- // TODO: optimize!!!!!!!!
+ // TODO: optimize this
sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
// increment k[]
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
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())));
}
}
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);
}
{
// 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;
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).
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
git://www.ginac.de / ginac.git / blobdiff