/** @file basic.cpp
*
- * Implementation of GiNaC's ABC.
- *
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * Implementation of GiNaC's ABC. */
+
+/*
+ * 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 <typeinfo>
#include <stdexcept>
+#ifdef DO_GINAC_ASSERT
+# include <typeinfo>
+#endif
-#include "ginac.h"
+#include "basic.h"
+#include "ex.h"
+#include "numeric.h"
+#include "power.h"
+#include "symbol.h"
+#include "lst.h"
+#include "ncmul.h"
+#include "relational.h"
+#include "operators.h"
+#include "wildcard.h"
+#include "archive.h"
#include "utils.h"
+namespace GiNaC {
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(basic, void,
+ print_func<print_context>(&basic::do_print).
+ print_func<print_tree>(&basic::do_print_tree).
+ print_func<print_python_repr>(&basic::do_print_python_repr))
+
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor, destructor, copy constructor and assignment operator
//////////
// public
-#ifndef INLINE_BASIC_CONSTRUCTORS
-basic::basic() : flags(0), refcount(0), tinfo_key(TINFO_BASIC)
+/** basic copy constructor: implicitly assumes that the other class is of
+ * the exact same type (as it's used by duplicate()), so it can copy the
+ * tinfo_key and the hash value. */
+basic::basic(const basic & other) : tinfo_key(other.tinfo_key), flags(other.flags & ~status_flags::dynallocated), hashvalue(other.hashvalue), refcount(0)
{
- debugmsg("basic default constructor",LOGLEVEL_CONSTRUCT);
- // nothing to do
+ GINAC_ASSERT(typeid(*this) == typeid(other));
}
-basic::~basic()
+/** basic assignment operator: the other object might be of a derived class. */
+const basic & basic::operator=(const basic & other)
{
- debugmsg("basic destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
- ASSERT((!(flags & status_flags::dynallocated))||(refcount==0));
-}
-
-basic::basic(basic const & other) : flags(0), refcount(0), tinfo_key(TINFO_BASIC)
-{
- debugmsg("basic copy constructor",LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-#endif
-
-basic const & basic::operator=(basic const & other)
-{
- debugmsg("basic operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ unsigned fl = other.flags & ~status_flags::dynallocated;
+ if (tinfo_key != other.tinfo_key) {
+ // The other object is of a derived class, so clear the flags as they
+ // might no longer apply (especially hash_calculated). Oh, and don't
+ // copy the tinfo_key: it is already set correctly for this object.
+ fl &= ~(status_flags::evaluated | status_flags::expanded | status_flags::hash_calculated);
+ } else {
+ // The objects are of the exact same class, so copy the hash value.
+ hashvalue = other.hashvalue;
+ }
+ flags = fl;
+ refcount = 0;
+ return *this;
}
// protected
-#if 0
-void basic::copy(basic const & other)
-{
- flags=other.flags & ~ status_flags::dynallocated;
- hashvalue=other.hashvalue;
- tinfo_key=other.tinfo_key;
-}
-#endif
+// none (all inlined)
//////////
// other constructors
//////////
-#ifndef INLINE_BASIC_CONSTRUCTORS
-basic::basic(unsigned ti) : flags(0), refcount(0), tinfo_key(ti)
-{
- debugmsg("basic constructor with tinfo_key",LOGLEVEL_CONSTRUCT);
- // nothing to do
-}
-#endif
+// none (all inlined)
//////////
-// functions overriding virtual functions from bases classes
+// archiving
//////////
-// none
+/** Construct object from archive_node. */
+basic::basic(const archive_node &n, lst &sym_lst) : flags(0), refcount(0)
+{
+ // Reconstruct tinfo_key from class name
+ std::string class_name;
+ if (n.find_string("class", class_name))
+ tinfo_key = find_tinfo_key(class_name);
+ else
+ throw (std::runtime_error("archive node contains no class name"));
+}
+
+/** Unarchive the object. */
+DEFAULT_UNARCHIVE(basic)
+
+/** Archive the object. */
+void basic::archive(archive_node &n) const
+{
+ n.add_string("class", class_name());
+}
//////////
// new virtual functions which can be overridden by derived classes
// public
-basic * basic::duplicate() const
+/** Output to stream. This performs double dispatch on the dynamic type of
+ * *this and the dynamic type of the supplied print context.
+ * @param c print context object that describes the output formatting
+ * @param level value that is used to identify the precedence or indentation
+ * level for placing parentheses and formatting */
+void basic::print(const print_context & c, unsigned level) const
{
- debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
- return new basic(*this);
+ print_dispatch(get_class_info(), c, level);
}
-bool basic::info(unsigned inf) const
+/** Like print(), but dispatch to the specified class. Can be used by
+ * implementations of print methods to dispatch to the method of the
+ * superclass.
+ *
+ * @see basic::print */
+void basic::print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const
{
- return false; // all possible properties are false for basic objects
+ // Double dispatch on object type and print_context type
+ const registered_class_info * reg_info = &ri;
+ const print_context_class_info * pc_info = &c.get_class_info();
+
+next_class:
+ const std::vector<print_functor> & pdt = reg_info->options.get_print_dispatch_table();
+
+next_context:
+ unsigned id = pc_info->options.get_id();
+ if (id >= pdt.size() || !(pdt[id].is_valid())) {
+
+ // Method not found, try parent print_context class
+ const print_context_class_info * parent_pc_info = pc_info->get_parent();
+ if (parent_pc_info) {
+ pc_info = parent_pc_info;
+ goto next_context;
+ }
+
+ // Method still not found, try parent class
+ const registered_class_info * parent_reg_info = reg_info->get_parent();
+ if (parent_reg_info) {
+ reg_info = parent_reg_info;
+ pc_info = &c.get_class_info();
+ goto next_class;
+ }
+
+ // Method still not found. This shouldn't happen because basic (the
+ // base class of the algebraic hierarchy) registers a method for
+ // print_context (the base class of the print context hierarchy),
+ // so if we end up here, there's something wrong with the class
+ // registry.
+ throw (std::runtime_error(std::string("basic::print(): method for ") + class_name() + "/" + c.class_name() + " not found"));
+
+ } else {
+
+ // Call method
+ pdt[id](*this, c, level);
+ }
}
-int basic::nops() const
+/** Default output to stream. */
+void basic::do_print(const print_context & c, unsigned level) const
{
- return 0;
+ c.s << "[" << class_name() << " object]";
}
-ex basic::op(int const i) const
+/** Tree output to stream. */
+void basic::do_print_tree(const print_tree & c, unsigned level) const
{
- return (const_cast<basic *>(this))->let_op(i);
+ c.s << std::string(level, ' ') << class_name()
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec;
+ if (nops())
+ c.s << ", nops=" << nops();
+ c.s << std::endl;
+ for (size_t i=0; i<nops(); ++i)
+ op(i).print(c, level + c.delta_indent);
}
-ex & basic::let_op(int const i)
+/** Python parsable output to stream. */
+void basic::do_print_python_repr(const print_python_repr & c, unsigned level) const
{
- throw(std::out_of_range("op() out of range"));
+ c.s << class_name() << "()";
}
-ex basic::operator[](ex const & index) const
+/** Little wrapper around print to be called within a debugger.
+ * This is needed because you cannot call foo.print(cout) from within the
+ * debugger because it might not know what cout is. This method can be
+ * invoked with no argument and it will simply print to stdout.
+ *
+ * @see basic::print
+ * @see basic::dbgprinttree */
+void basic::dbgprint() const
{
- if (is_exactly_of_type(*index.bp,numeric)) {
- return op(static_cast<numeric const &>(*index.bp).to_int());
- }
- throw(std::invalid_argument("non-numeric indices not supported by this type"));
+ this->print(std::cerr);
+ std::cerr << std::endl;
}
-ex basic::operator[](int const i) const
+/** Little wrapper around printtree to be called within a debugger.
+ *
+ * @see basic::dbgprint */
+void basic::dbgprinttree() const
{
- return op(i);
+ this->print(print_tree(std::cerr));
}
-bool basic::has(ex const & other) const
+/** Return relative operator precedence (for parenthezing output). */
+unsigned basic::precedence() const
{
- ASSERT(other.bp!=0);
- if (is_equal(*other.bp)) return true;
- if (nops()>0) {
- for (int i=0; i<nops(); i++) {
- if (op(i).has(other)) return true;
- }
- }
- return false;
+ return 70;
}
-int basic::degree(symbol const & s) const
+/** Information about the object.
+ *
+ * @see class info_flags */
+bool basic::info(unsigned inf) const
{
- return 0;
+ // all possible properties are false for basic objects
+ return false;
}
-int basic::ldegree(symbol const & s) const
+/** Number of operands/members. */
+size_t basic::nops() const
{
- return 0;
+ // iterating from 0 to nops() on atomic objects should be an empty loop,
+ // and accessing their elements is a range error. Container objects should
+ // override this.
+ return 0;
}
-ex basic::coeff(symbol const & s, int const n) const
+/** Return operand/member at position i. */
+ex basic::op(size_t i) const
{
- return n==0 ? *this : exZERO();
+ throw(std::range_error(std::string("basic::op(): ") + class_name() + std::string(" has no operands")));
}
-ex basic::collect(symbol const & s) const
+/** Return modifyable operand/member at position i. */
+ex & basic::let_op(size_t i)
{
- ex x;
- int ldeg=ldegree(s);
- int deg=degree(s);
- for (int n=ldeg; n<=deg; n++) {
- x += coeff(s,n)*power(s,n);
- }
- return x;
+ ensure_if_modifiable();
+ throw(std::range_error(std::string("basic::let_op(): ") + class_name() + std::string(" has no operands")));
}
-ex basic::eval(int level) const
+ex basic::operator[](const ex & index) const
{
- return this->hold();
+ if (is_exactly_a<numeric>(index))
+ return op(static_cast<size_t>(ex_to<numeric>(index).to_int()));
+
+ throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
}
-ex basic::evalf(int level) const
+ex basic::operator[](size_t i) const
{
- return *this;
+ return op(i);
}
-ex basic::subs(lst const & ls, lst const & lr) const
+ex & basic::operator[](const ex & index)
{
- return *this;
+ if (is_exactly_a<numeric>(index))
+ return let_op(ex_to<numeric>(index).to_int());
+
+ throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
}
-exvector basic::get_indices(void) const
+ex & basic::operator[](size_t i)
{
- return exvector(); // return an empty exvector
+ return let_op(i);
}
-ex basic::simplify_ncmul(exvector const & v) const
+/** Test for occurrence of a pattern. An object 'has' a pattern if it matches
+ * the pattern itself or one of the children 'has' it. As a consequence
+ * (according to the definition of children) given e=x+y+z, e.has(x) is true
+ * but e.has(x+y) is false. */
+bool basic::has(const ex & pattern) const
{
- return simplified_ncmul(v);
+ lst repl_lst;
+ if (match(pattern, repl_lst))
+ return true;
+ for (size_t i=0; i<nops(); i++)
+ if (op(i).has(pattern))
+ return true;
+
+ return false;
}
-// protected
+/** Construct new expression by applying the specified function to all
+ * sub-expressions (one level only, not recursively). */
+ex basic::map(map_function & f) const
+{
+ size_t num = nops();
+ if (num == 0)
+ return *this;
+
+ basic *copy = duplicate();
+ copy->setflag(status_flags::dynallocated);
+ copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
+ for (size_t i=0; i<num; i++)
+ copy->let_op(i) = f(copy->op(i));
+ return *copy;
+}
-int basic::compare_same_type(basic const & other) const
+/** Return degree of highest power in object s. */
+int basic::degree(const ex & s) const
{
- return compare_pointers(this, &other);
+ return is_equal(ex_to<basic>(s)) ? 1 : 0;
}
-bool basic::is_equal_same_type(basic const & other) const
+/** Return degree of lowest power in object s. */
+int basic::ldegree(const ex & s) const
{
- return compare_same_type(other)==0;
+ return is_equal(ex_to<basic>(s)) ? 1 : 0;
}
-unsigned basic::return_type(void) const
+/** Return coefficient of degree n in object s. */
+ex basic::coeff(const ex & s, int n) const
{
- return return_types::commutative;
+ if (is_equal(ex_to<basic>(s)))
+ return n==1 ? _ex1 : _ex0;
+ else
+ return n==0 ? *this : _ex0;
}
-unsigned basic::return_type_tinfo(void) const
+/** Sort expanded expression in terms of powers of some object(s).
+ * @param s object(s) to sort in
+ * @param distributed recursive or distributed form (only used when s is a list) */
+ex basic::collect(const ex & s, bool distributed) const
{
- return tinfo();
+ ex x;
+ if (is_a<lst>(s)) {
+
+ // List of objects specified
+ if (s.nops() == 0)
+ return *this;
+ if (s.nops() == 1)
+ return collect(s.op(0));
+
+ else if (distributed) {
+
+ // Get lower/upper degree of all symbols in list
+ size_t num = s.nops();
+ struct sym_info {
+ ex sym;
+ int ldeg, deg;
+ int cnt; // current degree, 'counter'
+ ex coeff; // coefficient for degree 'cnt'
+ };
+ sym_info *si = new sym_info[num];
+ ex c = *this;
+ for (size_t i=0; i<num; i++) {
+ si[i].sym = s.op(i);
+ si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
+ si[i].deg = this->degree(si[i].sym);
+ c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+ }
+
+ while (true) {
+
+ // Calculate coeff*x1^c1*...*xn^cn
+ ex y = _ex1;
+ for (size_t i=0; i<num; i++) {
+ int cnt = si[i].cnt;
+ y *= power(si[i].sym, cnt);
+ }
+ x += y * si[num - 1].coeff;
+
+ // Increment counters
+ size_t n = num - 1;
+ while (true) {
+ ++si[n].cnt;
+ if (si[n].cnt <= si[n].deg) {
+ // Update coefficients
+ ex c;
+ if (n == 0)
+ c = *this;
+ else
+ c = si[n - 1].coeff;
+ for (size_t i=n; i<num; i++)
+ c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+ break;
+ }
+ if (n == 0)
+ goto done;
+ si[n].cnt = si[n].ldeg;
+ n--;
+ }
+ }
+
+done: delete[] si;
+
+ } else {
+
+ // Recursive form
+ x = *this;
+ size_t n = s.nops() - 1;
+ while (true) {
+ x = x.collect(s[n]);
+ if (n == 0)
+ break;
+ n--;
+ }
+ }
+
+ } else {
+
+ // Only one object specified
+ for (int n=this->ldegree(s); n<=this->degree(s); ++n)
+ x += this->coeff(s,n)*power(s,n);
+ }
+
+ // correct for lost fractional arguments and return
+ return x + (*this - x).expand();
+}
+
+/** Perform automatic non-interruptive term rewriting rules. */
+ex basic::eval(int level) const
+{
+ // There is nothing to do for basic objects:
+ return hold();
}
-unsigned basic::calchash(void) const
+/** Function object to be applied by basic::evalf(). */
+struct evalf_map_function : public map_function {
+ int level;
+ evalf_map_function(int l) : level(l) {}
+ ex operator()(const ex & e) { return evalf(e, level); }
+};
+
+/** Evaluate object numerically. */
+ex basic::evalf(int level) const
{
- unsigned v=golden_ratio_hash(tinfo());
- for (int i=0; i<nops(); i++) {
- v=rotate_left_31(v);
- v ^= (const_cast<basic *>(this))->let_op(i).gethash();
- }
+ if (nops() == 0)
+ return *this;
+ else {
+ if (level == 1)
+ return *this;
+ else if (level == -max_recursion_level)
+ throw(std::runtime_error("max recursion level reached"));
+ else {
+ evalf_map_function map_evalf(level - 1);
+ return map(map_evalf);
+ }
+ }
+}
- v = v & 0x7FFFFFFFU;
-
- // store calculated hash value only if object is already evaluated
- if (flags & status_flags::evaluated) {
- setflag(status_flags::hash_calculated);
- hashvalue=v;
- }
+/** Function object to be applied by basic::evalm(). */
+struct evalm_map_function : public map_function {
+ ex operator()(const ex & e) { return evalm(e); }
+} map_evalm;
- return v;
+/** Evaluate sums, products and integer powers of matrices. */
+ex basic::evalm() const
+{
+ if (nops() == 0)
+ return *this;
+ else
+ return map(map_evalm);
}
-ex basic::expand(unsigned options) const
+/** Perform automatic symbolic evaluations on indexed expression that
+ * contains this object as the base expression. */
+ex basic::eval_indexed(const basic & i) const
+ // this function can't take a "const ex & i" because that would result
+ // in an infinite eval() loop
{
- return this->setflag(status_flags::expanded);
+ // There is nothing to do for basic objects
+ return i.hold();
}
-//////////
-// non-virtual functions in this class
-//////////
+/** Add two indexed expressions. They are guaranteed to be of class indexed
+ * (or a subclass) and their indices are compatible. This function is used
+ * internally by simplify_indexed().
+ *
+ * @param self First indexed expression; it's base object is *this
+ * @param other Second indexed expression
+ * @return sum of self and other
+ * @see ex::simplify_indexed() */
+ex basic::add_indexed(const ex & self, const ex & other) const
+{
+ return self + other;
+}
-// public
+/** Multiply an indexed expression with a scalar. This function is used
+ * internally by simplify_indexed().
+ *
+ * @param self Indexed expression; it's base object is *this
+ * @param other Numeric value
+ * @return product of self and other
+ * @see ex::simplify_indexed() */
+ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
+{
+ return self * other;
+}
-ex basic::subs(ex const & e) const
-{
- // accept 2 types of replacement expressions:
- // - symbol==ex
- // - lst(symbol1==ex1,symbol2==ex2,...)
- // convert to subs(lst(symbol1,symbol2,...),lst(ex1,ex2,...))
- // additionally, idx can be used instead of symbol
- if (e.info(info_flags::relation_equal)) {
- return subs(lst(e));
- }
- if (!e.info(info_flags::list)) {
- throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
- }
- lst ls;
- lst lr;
- for (int i=0; i<e.nops(); i++) {
- if (!e.op(i).info(info_flags::relation_equal)) {
- throw(std::invalid_argument("basic::subs(ex): argument must be a list or equations"));
- }
- if (!e.op(i).op(0).info(info_flags::symbol)) {
- if (!e.op(i).op(0).info(info_flags::idx)) {
- throw(std::invalid_argument("basic::subs(ex): lhs must be a symbol or an idx"));
- }
- }
- ls.append(e.op(i).op(0));
- lr.append(e.op(i).op(1));
- }
- return subs(ls,lr);
-}
-
-// compare functions to sort expressions canonically
-// all compare functions return: -1 for *this less than other, 0 equal, 1 greater
+/** Try to contract two indexed expressions that appear in the same product.
+ * If a contraction exists, the function overwrites one or both of the
+ * expressions and returns true. Otherwise it returns false. It is
+ * guaranteed that both expressions are of class indexed (or a subclass)
+ * and that at least one dummy index has been found. This functions is
+ * used internally by simplify_indexed().
+ *
+ * @param self Pointer to first indexed expression; it's base object is *this
+ * @param other Pointer to second indexed expression
+ * @param v The complete vector of factors
+ * @return true if the contraction was successful, false otherwise
+ * @see ex::simplify_indexed() */
+bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ // Do nothing
+ return false;
+}
-/*
-int basic::compare(basic const & other) const
+/** Check whether the expression matches a given pattern. For every wildcard
+ * object in the pattern, an expression of the form "wildcard == matching_expression"
+ * is added to repl_lst. */
+bool basic::match(const ex & pattern, lst & repl_lst) const
{
- const type_info & typeid_this = typeid(*this);
- const type_info & typeid_other = typeid(other);
+/*
+ Sweet sweet shapes, sweet sweet shapes,
+ That's the key thing, right right.
+ Feed feed face, feed feed shapes,
+ But who is the king tonight?
+ Who is the king tonight?
+ Pattern is the thing, the key thing-a-ling,
+ But who is the king of Pattern?
+ But who is the king, the king thing-a-ling,
+ Who is the king of Pattern?
+ Bog is the king, the king thing-a-ling,
+ Bog is the king of Pattern.
+ Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
+ Bog is the king of Pattern.
+*/
+
+ if (is_exactly_a<wildcard>(pattern)) {
+
+ // Wildcard matches anything, but check whether we already have found
+ // a match for that wildcard first (if so, it the earlier match must
+ // be the same expression)
+ for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
+ if (it->op(0).is_equal(pattern))
+ return is_equal(ex_to<basic>(it->op(1)));
+ }
+ repl_lst.append(pattern == *this);
+ return true;
+
+ } else {
- if (typeid_this==typeid_other) {
- return compare_same_type(other);
- }
+ // Expression must be of the same type as the pattern
+ if (tinfo() != ex_to<basic>(pattern).tinfo())
+ return false;
- // special rule: sort numeric() to end
- if (typeid_this==typeid_numeric) return 1;
- if (typeid_other==typeid_numeric) return -1;
+ // Number of subexpressions must match
+ if (nops() != pattern.nops())
+ return false;
- // otherwise: sort according to type_info order (arbitrary, but well defined)
- return typeid_this.before(typeid_other) ? -1 : 1;
+ // No subexpressions? Then just compare the objects (there can't be
+ // wildcards in the pattern)
+ if (nops() == 0)
+ return is_equal_same_type(ex_to<basic>(pattern));
+
+ // Check whether attributes that are not subexpressions match
+ if (!match_same_type(ex_to<basic>(pattern)))
+ return false;
+
+ // Otherwise the subexpressions must match one-to-one
+ for (size_t i=0; i<nops(); i++)
+ if (!op(i).match(pattern.op(i), repl_lst))
+ return false;
+
+ // Looks similar enough, match found
+ return true;
+ }
}
-*/
-int basic::compare(basic const & other) const
+/** Helper function for subs(). Does not recurse into subexpressions. */
+ex basic::subs_one_level(const exmap & m, unsigned options) const
{
- unsigned hash_this = gethash();
- unsigned hash_other = other.gethash();
+ exmap::const_iterator it;
- if (hash_this<hash_other) return -1;
- if (hash_this>hash_other) return 1;
+ if (options & subs_options::no_pattern) {
+ it = m.find(*this);
+ if (it != m.end())
+ return it->second;
+ } else {
+ for (it = m.begin(); it != m.end(); ++it) {
+ lst repl_lst;
+ if (match(ex_to<basic>(it->first), repl_lst))
+ return it->second.subs(repl_lst, options | subs_options::no_pattern); // avoid infinite recursion when re-substituting the wildcards
+ }
+ }
+
+ return *this;
+}
+
+/** Substitute a set of objects by arbitrary expressions. The ex returned
+ * will already be evaluated. */
+ex basic::subs(const exmap & m, unsigned options) const
+{
+ size_t num = nops();
+ if (num) {
- unsigned typeid_this = tinfo();
- unsigned typeid_other = other.tinfo();
+ // Substitute in subexpressions
+ for (size_t i=0; i<num; i++) {
+ const ex & orig_op = op(i);
+ const ex & subsed_op = orig_op.subs(m, options);
+ if (!are_ex_trivially_equal(orig_op, subsed_op)) {
- if (typeid_this<typeid_other) {
- /*
- cout << "hash collision, different types: "
- << *this << " and " << other << endl;
- this->printraw(cout);
- cout << " and ";
- other.printraw(cout);
- cout << endl;
- */
- return -1;
- }
- if (typeid_this>typeid_other) {
- /*
- cout << "hash collision, different types: "
- << *this << " and " << other << endl;
- this->printraw(cout);
- cout << " and ";
- other.printraw(cout);
- cout << endl;
- */
- return 1;
- }
+ // Something changed, clone the object
+ basic *copy = duplicate();
+ copy->setflag(status_flags::dynallocated);
+ copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
- ASSERT(typeid(*this)==typeid(other));
+ // Substitute the changed operand
+ copy->let_op(i++) = subsed_op;
- int cmpval=compare_same_type(other);
- if ((cmpval!=0)&&(hash_this<0x80000000U)) {
- /*
- cout << "hash collision, same type: "
- << *this << " and " << other << endl;
- this->printraw(cout);
- cout << " and ";
- other.printraw(cout);
- cout << endl;
- */
- }
- return cmpval;
+ // Substitute the other operands
+ for (; i<num; i++)
+ copy->let_op(i) = op(i).subs(m, options);
+
+ // Perform substitutions on the new object as a whole
+ return copy->subs_one_level(m, options);
+ }
+ }
+ }
+
+ // Nothing changed or no subexpressions
+ return subs_one_level(m, options);
}
-bool basic::is_equal(basic const & other) const
+/** Default interface of nth derivative ex::diff(s, n). It should be called
+ * instead of ::derivative(s) for first derivatives and for nth derivatives it
+ * just recurses down.
+ *
+ * @param s symbol to differentiate in
+ * @param nth order of differentiation
+ * @see ex::diff */
+ex basic::diff(const symbol & s, unsigned nth) const
{
- unsigned hash_this = gethash();
- unsigned hash_other = other.gethash();
+ // trivial: zeroth derivative
+ if (nth==0)
+ return ex(*this);
+
+ // evaluate unevaluated *this before differentiating
+ if (!(flags & status_flags::evaluated))
+ return ex(*this).diff(s, nth);
+
+ ex ndiff = this->derivative(s);
+ while (!ndiff.is_zero() && // stop differentiating zeros
+ nth>1) {
+ ndiff = ndiff.diff(s);
+ --nth;
+ }
+ return ndiff;
+}
- if (hash_this!=hash_other) return false;
+/** Return a vector containing the free indices of an expression. */
+exvector basic::get_free_indices() const
+{
+ return exvector(); // return an empty exvector
+}
- unsigned typeid_this = tinfo();
- unsigned typeid_other = other.tinfo();
+ex basic::eval_ncmul(const exvector & v) const
+{
+ return hold_ncmul(v);
+}
- if (typeid_this!=typeid_other) return false;
+// protected
- ASSERT(typeid(*this)==typeid(other));
+/** Function object to be applied by basic::derivative(). */
+struct derivative_map_function : public map_function {
+ const symbol &s;
+ derivative_map_function(const symbol &sym) : s(sym) {}
+ ex operator()(const ex & e) { return diff(e, s); }
+};
- return is_equal_same_type(other);
+/** Default implementation of ex::diff(). It maps the operation on the
+ * operands (or returns 0 when the object has no operands).
+ *
+ * @see ex::diff */
+ex basic::derivative(const symbol & s) const
+{
+ if (nops() == 0)
+ return _ex0;
+ else {
+ derivative_map_function map_derivative(s);
+ return map(map_derivative);
+ }
}
-// protected
+/** Returns order relation between two objects of same type. This needs to be
+ * implemented by each class. It may never return anything else than 0,
+ * signalling equality, or +1 and -1 signalling inequality and determining
+ * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
+ * the spaceship operator <=> for denoting just this.) */
+int basic::compare_same_type(const basic & other) const
+{
+ return compare_pointers(this, &other);
+}
-basic const & basic::hold(void) const
+/** Returns true if two objects of same type are equal. Normally needs
+ * not be reimplemented as long as it wasn't overwritten by some parent
+ * class, since it just calls compare_same_type(). The reason why this
+ * function exists is that sometimes it is easier to determine equality
+ * than an order relation and then it can be overridden. */
+bool basic::is_equal_same_type(const basic & other) const
{
- return setflag(status_flags::evaluated);
+ return compare_same_type(other)==0;
}
-void basic::ensure_if_modifiable(void) const
+/** Returns true if the attributes of two objects are similar enough for
+ * a match. This function must not match subexpressions (this is already
+ * done by basic::match()). Only attributes not accessible by op() should
+ * be compared. This is also the reason why this function doesn't take the
+ * wildcard replacement list from match() as an argument: only subexpressions
+ * are subject to wildcard matches. Also, this function only needs to be
+ * implemented for container classes because is_equal_same_type() is
+ * automatically used instead of match_same_type() if nops() == 0.
+ *
+ * @see basic::match */
+bool basic::match_same_type(const basic & other) const
{
- if (refcount>1) {
- throw(std::runtime_error("cannot modify multiply referenced object"));
- }
+ // The default is to only consider subexpressions, but not any other
+ // attributes
+ return true;
}
-//////////
-// static member variables
-//////////
+unsigned basic::return_type() const
+{
+ return return_types::commutative;
+}
-// protected
+unsigned basic::return_type_tinfo() const
+{
+ return tinfo();
+}
+
+/** Compute the hash value of an object and if it makes sense to store it in
+ * the objects status_flags, do so. The method inherited from class basic
+ * computes a hash value based on the type and hash values of possible
+ * members. For this reason it is well suited for container classes but
+ * atomic classes should override this implementation because otherwise they
+ * would all end up with the same hashvalue. */
+unsigned basic::calchash() const
+{
+ unsigned v = golden_ratio_hash(tinfo());
+ for (size_t i=0; i<nops(); i++) {
+ v = rotate_left(v);
+ v ^= this->op(i).gethash();
+ }
+
+ // store calculated hash value only if object is already evaluated
+ if (flags & status_flags::evaluated) {
+ setflag(status_flags::hash_calculated);
+ hashvalue = v;
+ }
+
+ return v;
+}
+
+/** Function object to be applied by basic::expand(). */
+struct expand_map_function : public map_function {
+ unsigned options;
+ expand_map_function(unsigned o) : options(o) {}
+ ex operator()(const ex & e) { return expand(e, options); }
+};
+
+/** Expand expression, i.e. multiply it out and return the result as a new
+ * expression. */
+ex basic::expand(unsigned options) const
+{
+ if (nops() == 0)
+ return (options == 0) ? setflag(status_flags::expanded) : *this;
+ else {
+ expand_map_function map_expand(options);
+ return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
+ }
+}
-unsigned basic::precedence=70;
-unsigned basic::delta_indent=4;
//////////
-// global constants
+// non-virtual functions in this class
//////////
-const basic some_basic;
-type_info const & typeid_basic=typeid(some_basic);
+// public
+
+/** Compare objects syntactically to establish canonical ordering.
+ * All compare functions return: -1 for *this less than other, 0 equal,
+ * 1 greater. */
+int basic::compare(const basic & other) const
+{
+ const unsigned hash_this = gethash();
+ const unsigned hash_other = other.gethash();
+ if (hash_this<hash_other) return -1;
+ if (hash_this>hash_other) return 1;
+
+ const unsigned typeid_this = tinfo();
+ const unsigned typeid_other = other.tinfo();
+ if (typeid_this==typeid_other) {
+ GINAC_ASSERT(typeid(*this)==typeid(other));
+// int cmpval = compare_same_type(other);
+// if (cmpval!=0) {
+// std::cout << "hash collision, same type: "
+// << *this << " and " << other << std::endl;
+// this->print(print_tree(std::cout));
+// std::cout << " and ";
+// other.print(print_tree(std::cout));
+// std::cout << std::endl;
+// }
+// return cmpval;
+ return compare_same_type(other);
+ } else {
+// std::cout << "hash collision, different types: "
+// << *this << " and " << other << std::endl;
+// this->print(print_tree(std::cout));
+// std::cout << " and ";
+// other.print(print_tree(std::cout));
+// std::cout << std::endl;
+ return (typeid_this<typeid_other ? -1 : 1);
+ }
+}
+
+/** Test for syntactic equality.
+ * This is only a quick test, meaning objects should be in the same domain.
+ * You might have to .expand(), .normal() objects first, depending on the
+ * domain of your computation, to get a more reliable answer.
+ *
+ * @see is_equal_same_type */
+bool basic::is_equal(const basic & other) const
+{
+ if (this->gethash()!=other.gethash())
+ return false;
+ if (this->tinfo()!=other.tinfo())
+ return false;
+
+ GINAC_ASSERT(typeid(*this)==typeid(other));
+
+ return is_equal_same_type(other);
+}
+
+// protected
+
+/** Stop further evaluation.
+ *
+ * @see basic::eval */
+const basic & basic::hold() const
+{
+ return setflag(status_flags::evaluated);
+}
+
+/** Ensure the object may be modified without hurting others, throws if this
+ * is not the case. */
+void basic::ensure_if_modifiable() const
+{
+ if (refcount > 1)
+ throw(std::runtime_error("cannot modify multiply referenced object"));
+ clearflag(status_flags::hash_calculated | status_flags::evaluated);
+}
//////////
// global variables
//////////
-int max_recursion_level=1024;
+int max_recursion_level = 1024;
+
+} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff