3 * Implementation of GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
31 #include "relational.h"
46 // non-virtual functions in this class
51 /** Print expression to stream. The formatting of the output is determined
52 * by the kind of print_context object that is passed. Possible formattings
53 * include ginsh-parsable output (the default), tree-like output for
54 * debugging, and C++ source.
55 * @see print_context */
56 void ex::print(const print_context & c, unsigned level) const
61 /** Little wrapper arount print to be called within a debugger. */
62 void ex::dbgprint() const
67 /** Little wrapper arount printtree to be called within a debugger. */
68 void ex::dbgprinttree() const
73 ex ex::expand(unsigned options) const
75 if (options == 0 && (bp->flags & status_flags::expanded)) // The "expanded" flag only covers the standard options; someone might want to re-expand with different options
78 return bp->expand(options);
81 /** Compute partial derivative of an expression.
83 * @param s symbol by which the expression is derived
84 * @param nth order of derivative (default 1)
85 * @return partial derivative as a new expression */
86 ex ex::diff(const symbol & s, unsigned nth) const
91 return bp->diff(s, nth);
94 /** Check whether expression matches a specified pattern. */
95 bool ex::match(const ex & pattern) const
98 return bp->match(pattern, repl_lst);
101 /** Find all occurrences of a pattern. The found matches are appended to
102 * the "found" list. If the expression itself matches the pattern, the
103 * children are not further examined. This function returns true when any
104 * matches were found. */
105 bool ex::find(const ex & pattern, exset& found) const
107 if (match(pattern)) {
111 bool any_found = false;
112 for (size_t i=0; i<nops(); i++)
113 if (op(i).find(pattern, found))
118 /** Substitute objects in an expression (syntactic substitution) and return
119 * the result as a new expression. */
120 ex ex::subs(const lst & ls, const lst & lr, unsigned options) const
122 GINAC_ASSERT(ls.nops() == lr.nops());
124 // Convert the lists to a map
126 for (auto its = ls.begin(), itr = lr.begin(); its != ls.end(); ++its, ++itr) {
127 m.insert(std::make_pair(*its, *itr));
129 // Search for products and powers in the expressions to be substituted
130 // (for an optimization in expairseq::subs())
131 if (is_exactly_a<mul>(*its) || is_exactly_a<power>(*its))
132 options |= subs_options::pattern_is_product;
134 if (!(options & subs_options::pattern_is_product))
135 options |= subs_options::pattern_is_not_product;
137 return bp->subs(m, options);
140 /** Substitute objects in an expression (syntactic substitution) and return
141 * the result as a new expression. There are two valid types of
142 * replacement arguments: 1) a relational like object==ex and 2) a list of
143 * relationals lst{object1==ex1,object2==ex2,...}. */
144 ex ex::subs(const ex & e, unsigned options) const
146 if (e.info(info_flags::relation_equal)) {
148 // Argument is a relation: convert it to a map
150 const ex & s = e.op(0);
151 m.insert(std::make_pair(s, e.op(1)));
153 if (is_exactly_a<mul>(s) || is_exactly_a<power>(s))
154 options |= subs_options::pattern_is_product;
156 options |= subs_options::pattern_is_not_product;
158 return bp->subs(m, options);
160 } else if (e.info(info_flags::list)) {
162 // Argument is a list: convert it to a map
164 GINAC_ASSERT(is_a<lst>(e));
165 for (auto & r : ex_to<lst>(e)) {
166 if (!r.info(info_flags::relation_equal))
167 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
168 const ex & s = r.op(0);
169 m.insert(std::make_pair(s, r.op(1)));
171 // Search for products and powers in the expressions to be substituted
172 // (for an optimization in expairseq::subs())
173 if (is_exactly_a<mul>(s) || is_exactly_a<power>(s))
174 options |= subs_options::pattern_is_product;
176 if (!(options & subs_options::pattern_is_product))
177 options |= subs_options::pattern_is_not_product;
179 return bp->subs(m, options);
182 throw(std::invalid_argument("ex::subs(ex): argument must be a relation_equal or a list"));
185 /** Traverse expression tree with given visitor, preorder traversal. */
186 void ex::traverse_preorder(visitor & v) const
191 for (size_t i = 0; i < n; ++i)
192 op(i).traverse_preorder(v);
195 /** Traverse expression tree with given visitor, postorder traversal. */
196 void ex::traverse_postorder(visitor & v) const
199 for (size_t i = 0; i < n; ++i)
200 op(i).traverse_postorder(v);
205 /** Return modifiable operand/member at position i. */
206 ex & ex::let_op(size_t i)
209 return bp->let_op(i);
212 ex & ex::operator[](const ex & index)
218 ex & ex::operator[](size_t i)
224 /** Left hand side of relational expression. */
227 if (!is_a<relational>(*this))
228 throw std::runtime_error("ex::lhs(): not a relation");
232 /** Right hand side of relational expression. */
235 if (!is_a<relational>(*this))
236 throw std::runtime_error("ex::rhs(): not a relation");
240 /** Check whether expression is a polynomial. */
241 bool ex::is_polynomial(const ex & vars) const
243 if (is_a<lst>(vars)) {
244 const lst & varlst = ex_to<lst>(vars);
245 for (auto & it : varlst)
246 if (!bp->is_polynomial(it))
251 return bp->is_polynomial(vars);
254 /** Check whether expression is zero or zero matrix. */
255 bool ex::is_zero_matrix() const
261 return is_a<matrix>(e) && ex_to<matrix>(e).is_zero_matrix();
267 /** Make this ex writable (if more than one ex handle the same basic) by
268 * unlinking the object and creating an unshared copy of it. */
269 void ex::makewriteable()
271 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
273 GINAC_ASSERT(bp->get_refcount() == 1);
276 /** Share equal objects between expressions.
277 * @see ex::compare(const ex &) */
278 void ex::share(const ex & other) const
280 if ((bp->flags | other.bp->flags) & status_flags::not_shareable)
283 if (bp->get_refcount() <= other.bp->get_refcount())
289 /** Helper function for the ex-from-basic constructor. This is where GiNaC's
290 * automatic evaluator and memory management are implemented.
291 * @see ex::ex(const basic &) */
292 ptr<basic> ex::construct_from_basic(const basic & other)
294 if (!(other.flags & status_flags::evaluated)) {
296 // The object is not yet evaluated, so call eval() to evaluate
297 // the top level. This will return either
298 // a) the original object with status_flags::evaluated set (when the
299 // eval() implementation calls hold())
301 // b) a different expression.
303 // eval() returns an ex, not a basic&, so this will go through
304 // construct_from_basic() a second time. In case a) we end up in
305 // the "else" branch below. In case b) we end up here again and
306 // apply eval() once more. The recursion stops when eval() calls
307 // hold() or returns an object that already has its "evaluated"
308 // flag set, such as a symbol or a numeric.
309 const ex & tmpex = other.eval();
311 // Eventually, the eval() recursion goes through the "else" branch
312 // below, which assures that the object pointed to by tmpex.bp is
313 // allocated on the heap (either it was already on the heap or it
314 // is a heap-allocated duplicate of another object).
315 GINAC_ASSERT(tmpex.bp->flags & status_flags::dynallocated);
317 // If the original object is not referenced but heap-allocated,
318 // it means that eval() hit case b) above. The original object is
319 // no longer needed (it evaluated into something different), so we
320 // delete it (because nobody else will).
321 if ((other.get_refcount() == 0) && (other.flags & status_flags::dynallocated))
322 delete &other; // yes, you can apply delete to a const pointer
324 // We can't return a basic& here because the tmpex is destroyed as
325 // soon as we leave the function, which would deallocate the
331 // The easy case: making an "ex" out of an evaluated object.
332 if (other.flags & status_flags::dynallocated) {
334 // The object is already heap-allocated, so we can just make
335 // another reference to it.
336 return ptr<basic>(const_cast<basic &>(other));
340 // The object is not heap-allocated, so we create a duplicate
342 basic *bp = other.duplicate();
343 bp->setflag(status_flags::dynallocated);
344 GINAC_ASSERT(bp->get_refcount() == 0);
350 basic & ex::construct_from_int(int i)
352 switch (i) { // prefer flyweights over new objects
354 return *const_cast<numeric *>(_num_12_p);
356 return *const_cast<numeric *>(_num_11_p);
358 return *const_cast<numeric *>(_num_10_p);
360 return *const_cast<numeric *>(_num_9_p);
362 return *const_cast<numeric *>(_num_8_p);
364 return *const_cast<numeric *>(_num_7_p);
366 return *const_cast<numeric *>(_num_6_p);
368 return *const_cast<numeric *>(_num_5_p);
370 return *const_cast<numeric *>(_num_4_p);
372 return *const_cast<numeric *>(_num_3_p);
374 return *const_cast<numeric *>(_num_2_p);
376 return *const_cast<numeric *>(_num_1_p);
378 return *const_cast<numeric *>(_num0_p);
380 return *const_cast<numeric *>(_num1_p);
382 return *const_cast<numeric *>(_num2_p);
384 return *const_cast<numeric *>(_num3_p);
386 return *const_cast<numeric *>(_num4_p);
388 return *const_cast<numeric *>(_num5_p);
390 return *const_cast<numeric *>(_num6_p);
392 return *const_cast<numeric *>(_num7_p);
394 return *const_cast<numeric *>(_num8_p);
396 return *const_cast<numeric *>(_num9_p);
398 return *const_cast<numeric *>(_num10_p);
400 return *const_cast<numeric *>(_num11_p);
402 return *const_cast<numeric *>(_num12_p);
404 return dynallocate<numeric>(i);
408 basic & ex::construct_from_uint(unsigned int i)
410 switch (i) { // prefer flyweights over new objects
412 return *const_cast<numeric *>(_num0_p);
414 return *const_cast<numeric *>(_num1_p);
416 return *const_cast<numeric *>(_num2_p);
418 return *const_cast<numeric *>(_num3_p);
420 return *const_cast<numeric *>(_num4_p);
422 return *const_cast<numeric *>(_num5_p);
424 return *const_cast<numeric *>(_num6_p);
426 return *const_cast<numeric *>(_num7_p);
428 return *const_cast<numeric *>(_num8_p);
430 return *const_cast<numeric *>(_num9_p);
432 return *const_cast<numeric *>(_num10_p);
434 return *const_cast<numeric *>(_num11_p);
436 return *const_cast<numeric *>(_num12_p);
438 return dynallocate<numeric>(i);
442 basic & ex::construct_from_long(long i)
444 switch (i) { // prefer flyweights over new objects
446 return *const_cast<numeric *>(_num_12_p);
448 return *const_cast<numeric *>(_num_11_p);
450 return *const_cast<numeric *>(_num_10_p);
452 return *const_cast<numeric *>(_num_9_p);
454 return *const_cast<numeric *>(_num_8_p);
456 return *const_cast<numeric *>(_num_7_p);
458 return *const_cast<numeric *>(_num_6_p);
460 return *const_cast<numeric *>(_num_5_p);
462 return *const_cast<numeric *>(_num_4_p);
464 return *const_cast<numeric *>(_num_3_p);
466 return *const_cast<numeric *>(_num_2_p);
468 return *const_cast<numeric *>(_num_1_p);
470 return *const_cast<numeric *>(_num0_p);
472 return *const_cast<numeric *>(_num1_p);
474 return *const_cast<numeric *>(_num2_p);
476 return *const_cast<numeric *>(_num3_p);
478 return *const_cast<numeric *>(_num4_p);
480 return *const_cast<numeric *>(_num5_p);
482 return *const_cast<numeric *>(_num6_p);
484 return *const_cast<numeric *>(_num7_p);
486 return *const_cast<numeric *>(_num8_p);
488 return *const_cast<numeric *>(_num9_p);
490 return *const_cast<numeric *>(_num10_p);
492 return *const_cast<numeric *>(_num11_p);
494 return *const_cast<numeric *>(_num12_p);
496 return dynallocate<numeric>(i);
500 basic & ex::construct_from_ulong(unsigned long i)
502 switch (i) { // prefer flyweights over new objects
504 return *const_cast<numeric *>(_num0_p);
506 return *const_cast<numeric *>(_num1_p);
508 return *const_cast<numeric *>(_num2_p);
510 return *const_cast<numeric *>(_num3_p);
512 return *const_cast<numeric *>(_num4_p);
514 return *const_cast<numeric *>(_num5_p);
516 return *const_cast<numeric *>(_num6_p);
518 return *const_cast<numeric *>(_num7_p);
520 return *const_cast<numeric *>(_num8_p);
522 return *const_cast<numeric *>(_num9_p);
524 return *const_cast<numeric *>(_num10_p);
526 return *const_cast<numeric *>(_num11_p);
528 return *const_cast<numeric *>(_num12_p);
530 return dynallocate<numeric>(i);
534 basic & ex::construct_from_longlong(long long i)
536 if (i >= -12 && i <= 12) {
537 return construct_from_int(static_cast<int>(i));
539 return dynallocate<numeric>(i);
543 basic & ex::construct_from_ulonglong(unsigned long long i)
546 return construct_from_uint(static_cast<unsigned>(i));
548 return dynallocate<numeric>(i);
552 basic & ex::construct_from_double(double d)
554 return dynallocate<numeric>(d);
558 // static member variables
564 // functions which are not member functions