1 ;;; calc-rewr.el --- rewriting functions for Calc
3 ;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; This file is part of GNU Emacs.
9 ;; GNU Emacs is free software: you can redistribute it and/or modify
10 ;; it under the terms of the GNU General Public License as published by
11 ;; the Free Software Foundation, either version 3 of the License, or
12 ;; (at your option) any later version.
14 ;; GNU Emacs is distributed in the hope that it will be useful,
15 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
16 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 ;; GNU General Public License for more details.
19 ;; You should have received a copy of the GNU General Public License
20 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
26 ;; This file is autoloaded from calc-ext.el.
31 (defvar math-rewrite-default-iters 100)
33 ;; The variable calc-rewr-sel is local to calc-rewrite-selection and
34 ;; calc-rewrite, but is used by calc-locate-selection-marker.
35 (defvar calc-rewr-sel)
37 (defun calc-rewrite-selection (rules-str &optional many prefix)
38 (interactive "sRewrite rule(s): \np")
41 (let* ((num (max 1 (calc-locate-cursor-element (point))))
45 (entry (calc-top num 'entry))
47 (calc-rewr-sel (calc-auto-selection entry))
48 (math-rewrite-selections t)
49 (math-rewrite-default-iters 1))
50 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
52 (error "Can't use same stack entry for formula and rules")
53 (setq rules (calc-top-n 1 t)
55 (setq rules (if (stringp rules-str)
56 (math-read-exprs rules-str) rules-str))
57 (if (eq (car-safe rules) 'error)
58 (error "Bad format in expression: %s" (nth 1 rules)))
59 (if (= (length rules) 1)
60 (setq rules (car rules))
61 (setq rules (cons 'vec rules)))
62 (or (memq (car-safe rules) '(vec var calcFunc-assign
64 (let ((rhs (math-read-expr
65 (read-string (concat "Rewrite from: " rules-str
67 (if (eq (car-safe rhs) 'error)
68 (error "Bad format in expression: %s" (nth 1 rhs)))
69 (setq rules (list 'calcFunc-assign rules rhs))))
70 (or (eq (car-safe rules) 'var)
71 (calc-record rules "rule")))
73 (setq many '(var inf var-inf))
74 (if many (setq many (prefix-numeric-value many))))
76 (setq expr (calc-replace-sub-formula (car entry)
78 (list 'calcFunc-select calc-rewr-sel)))
79 (setq expr (car entry)
81 math-rewrite-selections nil))
82 (setq expr (calc-encase-atoms
88 expr (calc-locate-select-marker expr))
89 (or (consp calc-rewr-sel) (setq calc-rewr-sel nil))
90 (if pop-rules (calc-pop-stack 1))
91 (calc-pop-push-record-list 1 (or prefix "rwrt") (list expr)
92 (- num (if pop-rules 1 0))
93 (list (and reselect calc-rewr-sel))))
96 (defun calc-locate-select-marker (expr)
99 (if (and (eq (car expr) 'calcFunc-select)
102 (setq calc-rewr-sel (if calc-rewr-sel t (nth 1 expr)))
105 (mapcar 'calc-locate-select-marker (cdr expr))))))
109 (defun calc-rewrite (rules-str many)
110 (interactive "sRewrite rule(s): \nP")
113 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
114 (setq expr (calc-top-n 2)
115 rules (calc-top-n 1 t)
117 (setq rules (if (stringp rules-str)
118 (math-read-exprs rules-str) rules-str))
119 (if (eq (car-safe rules) 'error)
120 (error "Bad format in expression: %s" (nth 1 rules)))
121 (if (= (length rules) 1)
122 (setq rules (car rules))
123 (setq rules (cons 'vec rules)))
124 (or (memq (car-safe rules) '(vec var calcFunc-assign
126 (let ((rhs (math-read-expr
127 (read-string (concat "Rewrite from: " rules-str
129 (if (eq (car-safe rhs) 'error)
130 (error "Bad format in expression: %s" (nth 1 rhs)))
131 (setq rules (list 'calcFunc-assign rules rhs))))
132 (or (eq (car-safe rules) 'var)
133 (calc-record rules "rule"))
134 (setq expr (calc-top-n 1)
137 (setq many '(var inf var-inf))
138 (if many (setq many (prefix-numeric-value many))))
139 (setq expr (calc-normalize (math-rewrite expr rules many)))
141 (setq expr (calc-locate-select-marker expr)))
142 (calc-pop-push-record-list n "rwrt" (list expr)))
145 (defun calc-match (pat &optional interactive)
146 (interactive "sPattern: \np")
149 (if (or (null pat) (equal pat "") (equal pat "$"))
150 (setq expr (calc-top-n 2)
153 (setq pat (if (stringp pat) (math-read-expr pat) pat))
154 (if (eq (car-safe pat) 'error)
155 (error "Bad format in expression: %s" (nth 1 pat)))
156 (if (not (eq (car-safe pat) 'var))
157 (calc-record pat "pat"))
158 (setq expr (calc-top-n 1)
160 (or (math-vectorp expr) (error "Argument must be a vector"))
161 (if (calc-is-inverse)
162 (calc-enter-result n "mtcn" (math-match-patterns pat expr t))
163 (calc-enter-result n "mtch" (math-match-patterns pat expr nil))))))
166 (defvar math-mt-many)
168 ;; The variable math-rewrite-whole-expr is local to math-rewrite,
169 ;; but is used by math-rewrite-phase
170 (defvar math-rewrite-whole-expr)
171 (defvar math-trace-buffer)
172 (defun math-rewrite (math-rewrite-whole-expr rules &optional math-mt-many)
173 (let* ((crules (math-compile-rewrites rules))
174 (heads (math-rewrite-heads math-rewrite-whole-expr))
175 (math-trace-buffer (get-buffer "*Trace*"))
176 (calc-display-just 'center)
177 (calc-display-origin 39)
178 (calc-line-breaking 78)
179 (calc-line-numbering nil)
180 (calc-show-selections t)
182 (math-mt-func (function
184 (let ((result (math-apply-rewrites x (cdr crules)
188 (if math-trace-buffer
189 (let ((fmt (math-format-stack-value
190 (list result nil nil))))
191 (with-current-buffer math-trace-buffer
192 (insert "\nrewrite to\n" fmt "\n"))))
193 (setq heads (math-rewrite-heads result heads t))))
195 (if math-trace-buffer
196 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
197 (with-current-buffer math-trace-buffer
198 (setq truncate-lines t)
199 (goto-char (point-max))
200 (insert "\n\nBegin rewriting\n" fmt "\n"))))
201 (or math-mt-many (setq math-mt-many (or (nth 1 (car crules))
202 math-rewrite-default-iters)))
203 (if (equal math-mt-many '(var inf var-inf)) (setq math-mt-many 1000000))
204 (if (equal math-mt-many '(neg (var inf var-inf))) (setq math-mt-many -1000000))
205 (math-rewrite-phase (nth 3 (car crules)))
206 (if math-trace-buffer
207 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
208 (with-current-buffer math-trace-buffer
209 (insert "\nDone rewriting"
210 (if (= math-mt-many 0) " (reached iteration limit)" "")
212 math-rewrite-whole-expr))
214 (defun math-rewrite-phase (sched)
215 (while (and sched (/= math-mt-many 0))
216 (if (listp (car sched))
217 (while (let ((save-expr math-rewrite-whole-expr))
218 (math-rewrite-phase (car sched))
219 (not (equal math-rewrite-whole-expr save-expr))))
220 (if (symbolp (car sched))
222 (setq math-rewrite-whole-expr
223 (math-normalize (list (car sched) math-rewrite-whole-expr)))
224 (if math-trace-buffer
225 (let ((fmt (math-format-stack-value
226 (list math-rewrite-whole-expr nil nil))))
227 (with-current-buffer math-trace-buffer
229 (substring (symbol-name (car sched)) 9)
231 (let ((math-rewrite-phase (car sched)))
232 (if math-trace-buffer
233 (with-current-buffer math-trace-buffer
234 (insert (format "\n(Phase %d)\n" math-rewrite-phase))))
235 (while (let ((save-expr math-rewrite-whole-expr))
236 (setq math-rewrite-whole-expr (math-normalize
237 (math-map-tree-rec math-rewrite-whole-expr)))
238 (not (equal math-rewrite-whole-expr save-expr)))))))
239 (setq sched (cdr sched))))
241 (defun calcFunc-rewrite (expr rules &optional many)
242 (or (null many) (integerp many)
243 (equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf)))
244 (math-reject-arg many 'fixnump))
246 (math-rewrite expr rules (or many 1))
247 (error (math-reject-arg rules (nth 1 err)))))
249 (defun calcFunc-match (pat vec)
250 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
252 (math-match-patterns pat vec nil)
253 (error (math-reject-arg pat (nth 1 err)))))
255 (defun calcFunc-matchnot (pat vec)
256 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
258 (math-match-patterns pat vec t)
259 (error (math-reject-arg pat (nth 1 err)))))
261 (defun math-match-patterns (pat vec &optional not-flag)
263 (crules (math-compile-patterns pat)))
264 (while (setq vec (cdr vec))
265 (if (eq (not (math-apply-rewrites (car vec) crules))
267 (setq newvec (cons (car vec) newvec))))
268 (cons 'vec (nreverse newvec))))
270 (defun calcFunc-matches (expr pat)
272 (if (math-apply-rewrites expr (math-compile-patterns pat))
275 (error (math-reject-arg pat (nth 1 err)))))
277 (defun calcFunc-vmatches (expr pat)
279 (or (math-apply-rewrites expr (math-compile-patterns pat))
281 (error (math-reject-arg pat (nth 1 err)))))
285 ;; A compiled rule set is an a-list of entries whose cars are functors,
286 ;; and whose cdrs are lists of rules. If there are rules with no
287 ;; well-defined head functor, they are included on all lists and also
288 ;; on an extra list whose car is nil.
290 ;; The first entry in the a-list is of the form (schedule A B C ...).
292 ;; Rule list entries take the form (regs prog head phases), where:
294 ;; regs is a vector of match registers.
296 ;; prog is a match program (see below).
298 ;; head is a rare function name appearing in the rule body (but not the
299 ;; head of the whole rule), or nil if none.
301 ;; phases is a list of phase numbers for which the rule is enabled.
303 ;; A match program is a list of match instructions.
305 ;; In the following, "part" is a register number that contains the
306 ;; subexpression to be operated on.
308 ;; Register 0 is the whole expression being matched. The others are
309 ;; meta-variables in the pattern, temporaries used for matching and
310 ;; backtracking, and constant expressions.
313 ;; The selected part must be math-equal to the contents of "reg".
315 ;; (same-neg part reg)
316 ;; The selected part must be math-equal to the negative of "reg".
319 ;; The selected part is copied into "reg". (Rarely used.)
321 ;; (copy-neg part reg)
322 ;; The negative of the selected part is copied into "reg".
325 ;; The selected part must be an integer.
328 ;; The selected part must be a real.
331 ;; The selected part must be a constant.
334 ;; The selected part must "look" negative.
337 ;; The selected part must satisfy "part op reg", where "op"
338 ;; is one of the 6 relational ops, and "reg" is a register.
340 ;; (mod part modulo value)
341 ;; The selected part must satisfy "part % modulo = value", where
342 ;; "modulo" and "value" are constants.
344 ;; (func part head reg1 reg2 ... regn)
345 ;; The selected part must be an n-ary call to function "head".
346 ;; The arguments are stored in "reg1" through "regn".
348 ;; (func-def part head defs reg1 reg2 ... regn)
349 ;; The selected part must be an n-ary call to function "head".
350 ;; "Defs" is a list of value/register number pairs for default args.
351 ;; If a match, assign default values to registers and then skip
352 ;; immediately over any following "func-def" instructions and
353 ;; the following "func" instruction. If wrong number of arguments,
354 ;; proceed to the following "func-def" or "func" instruction.
356 ;; (func-opt part head defs reg1)
357 ;; Like func-def with "n=1", except that if the selected part is
358 ;; not a call to "head", then the part itself successfully matches
359 ;; "reg1" (and the defaults are assigned).
361 ;; (try part heads mark reg1 [def])
362 ;; The selected part must be a function of the correct type which is
363 ;; associative and/or commutative. "Heads" is a list of acceptable
364 ;; types. An initial assignment of arguments to "reg1" is tried.
365 ;; If the program later fails, it backtracks to this instruction
366 ;; and tries other assignments of arguments to "reg1".
367 ;; If "def" exists and normal matching fails, backtrack and assign
368 ;; "part" to "reg1", and "def" to "reg2" in the following "try2".
369 ;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized.
370 ;; "mark[0]" points to the argument list; "mark[1]" points to the
371 ;; current argument; "mark[2]" is 0 if there are two arguments,
372 ;; 1 if reg1 is matching single arguments, 2 if reg2 is matching
373 ;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or
374 ;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must
375 ;; have two arguments, 1 if phase-2 can be skipped, 2 if full
376 ;; backtracking is necessary; "mark[4]" is t if the arguments have
377 ;; been switched from the order given in the original pattern.
380 ;; Every "try" will be followed by a "try2" whose "try" field is
381 ;; a pointer to the corresponding "try". The arguments which were
382 ;; not stored in "reg1" by that "try" are now stored in "reg2".
384 ;; (alt instr nil mark)
385 ;; Basic backtracking. Execute the instruction sequence "instr".
386 ;; If this fails, back up and execute following the "alt" instruction.
387 ;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence
388 ;; should execute "end-alt" at the end.
391 ;; Register success of the first alternative of a previous "alt".
392 ;; "Ptr" is a pointer to the next instruction following that "alt".
394 ;; (apply part reg1 reg2)
395 ;; The selected part must be a function call. The functor
396 ;; (as a variable name) is stored in "reg1"; the arguments
397 ;; (as a vector) are stored in "reg2".
399 ;; (cons part reg1 reg2)
400 ;; The selected part must be a nonempty vector. The first element
401 ;; of the vector is stored in "reg1"; the rest of the vector
402 ;; (as another vector) is stored in "reg2".
404 ;; (rcons part reg1 reg2)
405 ;; The selected part must be a nonempty vector. The last element
406 ;; of the vector is stored in "reg2"; the rest of the vector
407 ;; (as another vector) is stored in "reg1".
410 ;; If the selected part is a unary call to function "select", its
411 ;; argument is stored in "reg"; otherwise (provided this is an `a r'
412 ;; and not a `g r' command) the selected part is stored in "reg".
415 ;; The "expr", with registers substituted, must simplify to
419 ;; Evaluate "expr" and store the result in "reg". Always succeeds.
421 ;; (done rhs remember)
422 ;; Rewrite the expression to "rhs", with register substituted.
423 ;; Normalize; if the result is different from the original
424 ;; expression, the match has succeeded. This is the last
425 ;; instruction of every program. If "remember" is non-nil,
426 ;; record the result of the match as a new literal rule.
429 ;; Pseudo-functions related to rewrites:
431 ;; In patterns: quote, plain, condition, opt, apply, cons, select
433 ;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp,
434 ;; apply, cons, select
436 ;; In conditions: let + same as for righthand sides
438 ;; Some optimizations that would be nice to have:
440 ;; * Merge registers with disjoint lifetimes.
441 ;; * Merge constant registers with equivalent values.
443 ;; * If an argument of a commutative op math-depends neither on the
444 ;; rest of the pattern nor on any of the conditions, then no backtracking
445 ;; should be done for that argument. (This won't apply to very many
448 ;; * If top functor is "select", and its argument is a unique function,
449 ;; add the rule to the lists for both "select" and that function.
450 ;; (Currently rules like this go on the "nil" list.)
451 ;; Same for "func-opt" functions. (Though not urgent for these.)
453 ;; * Shouldn't evaluate a "let" condition until the end, or until it
454 ;; would enable another condition to be evaluated.
457 ;; Some additional features to add / things to think about:
459 ;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)".
461 ;;; * Same for interval forms.
463 ;;; * Have a name(v,pat) pattern which matches pat, and gives the
464 ;;; whole match the name v. Beware of circular structures!
467 (defvar math-rewrite-whole nil)
469 (defun math-compile-patterns (pats)
470 (if (and (eq (car-safe pats) 'var)
471 (calc-var-value (nth 2 pats)))
472 (let ((prop (get (nth 2 pats) 'math-pattern-cache)))
474 (put (nth 2 pats) 'math-pattern-cache (setq prop (list nil))))
475 (or (eq (car prop) (symbol-value (nth 2 pats)))
477 (setcdr prop (math-compile-patterns
478 (symbol-value (nth 2 pats))))
479 (setcar prop (symbol-value (nth 2 pats)))))
481 (let ((math-rewrite-whole t))
482 (cdr (math-compile-rewrites (cons
484 (mapcar (function (lambda (x)
486 (if (eq (car-safe pats) 'vec)
490 (defvar math-make-import-list nil)
492 ;; The variable math-import-list is local to part of math-compile-rewrites,
493 ;; but is also used in a different part, and so the local version could
494 ;; be affected by the non-local version when math-compile-rewrites calls itself.
495 (defvar math-import-list nil)
497 ;; The variables math-regs, math-num-regs, math-prog-last, math-bound-vars,
498 ;; math-conds, math-copy-neg, math-rhs, math-pattern, math-remembering and
499 ;; math-aliased-vars are local to math-compile-rewrites,
500 ;; but are used by many functions math-rwcomp-*, which are called by
501 ;; math-compile-rewrites.
503 (defvar math-num-regs)
504 (defvar math-prog-last)
505 (defvar math-bound-vars)
507 (defvar math-copy-neg)
509 (defvar math-pattern)
510 (defvar math-remembering)
511 (defvar math-aliased-vars)
513 (defun math-compile-rewrites (rules &optional name)
514 (if (eq (car-safe rules) 'var)
515 (let ((prop (get (nth 2 rules) 'math-rewrite-cache))
516 (math-import-list nil)
517 (math-make-import-list t)
519 (or (calc-var-value (nth 2 rules))
520 (error "Rules variable %s has no stored value" (nth 1 rules)))
522 (put (nth 2 rules) 'math-rewrite-cache
523 (setq prop (list (list (cons (nth 2 rules) nil))))))
525 (while (and p (eq (symbol-value (car (car p))) (cdr (car p))))
529 (message "Compiling rule set %s..." (nth 1 rules))
530 (setcdr prop (math-compile-rewrites
531 (symbol-value (nth 2 rules))
533 (message "Compiling rule set %s...done" (nth 1 rules))
534 (setcar prop (cons (cons (nth 2 rules)
535 (symbol-value (nth 2 rules)))
538 (if (or (not (eq (car-safe rules) 'vec))
539 (and (memq (length rules) '(3 4))
541 (while (and (setq p (cdr p))
542 (memq (car-safe (car p))
549 calcFunc-iterations))))
551 (setq rules (list rules))
552 (setq rules (cdr rules)))
553 (if (assq 'calcFunc-import rules)
554 (let ((pp (setq rules (copy-sequence rules)))
556 (while (setq p (car (cdr pp)))
557 (if (eq (car-safe p) 'calcFunc-import)
559 (setcdr pp (cdr (cdr pp)))
560 (or (and (eq (car-safe (nth 1 p)) 'var)
561 (setq part (calc-var-value (nth 2 (nth 1 p))))
562 (memq (car-safe part) '(vec
564 calcFunc-condition)))
565 (error "Argument of import() must be a rules variable"))
566 (if math-make-import-list
567 (setq math-import-list
568 (cons (cons (nth 2 (nth 1 p))
569 (symbol-value (nth 2 (nth 1 p))))
571 (while (setq p (cdr (cdr p)))
573 (error "import() must have odd number of arguments"))
574 (setq part (math-rwcomp-substitute part
576 (if (eq (car-safe part) 'vec)
577 (setq part (cdr part))
578 (setq part (list part)))
579 (setcdr pp (append part (cdr pp))))
580 (setq pp (cdr pp))))))
585 (math-iterations nil)
587 (math-all-phases nil)
588 (math-remembering nil)
589 math-pattern math-rhs math-conds)
592 ((and (eq (car-safe (car rules)) 'calcFunc-iterations)
593 (= (length (car rules)) 2))
594 (or (integerp (nth 1 (car rules)))
595 (equal (nth 1 (car rules)) '(var inf var-inf))
596 (equal (nth 1 (car rules)) '(neg (var inf var-inf)))
597 (error "Invalid argument for iterations(n)"))
599 (setq math-iterations (nth 1 (car rules)))))
600 ((eq (car-safe (car rules)) 'calcFunc-schedule)
602 (setq math-schedule (math-parse-schedule (cdr (car rules))))))
603 ((eq (car-safe (car rules)) 'calcFunc-phase)
604 (setq math-phases (cdr (car rules)))
605 (if (equal math-phases '((var all var-all)))
606 (setq math-phases nil))
607 (let ((p math-phases))
609 (or (integerp (car p))
610 (error "Phase numbers must be small integers"))
611 (or (memq (car p) math-all-phases)
612 (setq math-all-phases (cons (car p) math-all-phases)))
614 ((or (and (eq (car-safe (car rules)) 'vec)
615 (cdr (cdr (car rules)))
616 (not (nthcdr 4 (car rules)))
617 (setq math-conds (nth 3 (car rules))
618 math-rhs (nth 2 (car rules))
619 math-pattern (nth 1 (car rules))))
622 math-pattern (car rules))
623 (while (and (eq (car-safe math-pattern) 'calcFunc-condition)
624 (= (length math-pattern) 3))
625 (let ((cond (nth 2 math-pattern)))
626 (setq math-conds (if math-conds
627 (list 'calcFunc-land math-conds cond)
629 math-pattern (nth 1 math-pattern))))
630 (and (eq (car-safe math-pattern) 'calcFunc-assign)
631 (= (length math-pattern) 3)
632 (setq math-rhs (nth 2 math-pattern)
633 math-pattern (nth 1 math-pattern)))))
634 (let* ((math-prog (list nil))
635 (math-prog-last math-prog)
637 (math-regs (list (list nil 0 nil nil)))
638 (math-bound-vars nil)
639 (math-aliased-vars nil)
641 (setq math-conds (and math-conds (math-flatten-lands math-conds)))
642 (math-rwcomp-pattern math-pattern 0)
644 (let ((expr (car math-conds)))
645 (setq math-conds (cdr math-conds))
646 (math-rwcomp-cond-instr expr)))
647 (math-rwcomp-instr 'done
661 (math-rwcomp-register-expr
664 (math-rwcomp-match-vars math-rhs))
666 (setq math-prog (cdr math-prog))
667 (let* ((heads (math-rewrite-heads math-pattern))
670 (mapcar (function (lambda (x) (nth 3 x)))
675 (head (and (not (Math-primp math-pattern))
676 (not (and (eq (car (car math-prog)) 'try)
677 (nth 5 (car math-prog))))
678 (not (memq (car (car math-prog)) '(func-opt
682 (if (memq (car (car math-prog)) '(func
684 (nth 2 (car math-prog))
685 (if (eq (car math-pattern) 'calcFunc-quote)
686 (car-safe (nth 1 math-pattern))
687 (car math-pattern))))))
690 (if (setq found (assq (car heads) all-heads))
691 (setcdr found (1+ (cdr found)))
692 (setq all-heads (cons (cons (car heads) 1) all-heads)))
693 (setq heads (cdr heads))))
694 (if (eq head '-) (setq head '+))
695 (if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec))
698 (nconc (or (assq head rule-set)
699 (car (setq rule-set (cons (cons head
705 (nconc (or (assq '/ rule-set)
706 (car (setq rule-set (cons (cons
712 (setq nil-rules (nconc nil-rules (list rule)))
713 (let ((ptr rule-set))
715 (nconc (car ptr) (list rule))
716 (setq ptr (cdr ptr))))))))
718 (error "Rewrite rule set must be a vector of A := B rules")))
719 (setq rules (cdr rules)))
721 (setq rule-set (cons (cons nil nil-rules) rule-set)))
722 (setq all-heads (mapcar 'car
723 (sort all-heads (function
725 (< (cdr x) (cdr y)))))))
729 (setq rule (cdr (car set)))
731 (if (consp (setq heads (nth 2 (car rule))))
733 (setq heads (delq (car (car set)) heads)
735 (while (and ptr (not (memq (car ptr) heads)))
736 (setq ptr (cdr ptr)))
737 (setcar (nthcdr 2 (car rule)) (car ptr))))
738 (setq rule (cdr rule)))
739 (setq set (cdr set))))
740 (let ((plus (assq '+ rule-set)))
742 (setq rule-set (cons (cons '- (cdr plus)) rule-set))))
743 (cons (list 'schedule math-iterations name
745 (sort math-all-phases '<)
749 (defun math-flatten-lands (expr)
750 (if (eq (car-safe expr) 'calcFunc-land)
751 (append (math-flatten-lands (nth 1 expr))
752 (math-flatten-lands (nth 2 expr)))
755 ;; The variables math-rewrite-heads-heads (i.e.; heads for math-rewrite-heads)
756 ;; math-rewrite-heads-blanks and math-rewrite-heads-skips are local to
757 ;; math-rewrite-heads, but used by math-rewrite-heads-rec, which is called by
758 ;; math-rewrite-heads.
759 (defvar math-rewrite-heads-heads)
760 (defvar math-rewrite-heads-skips)
761 (defvar math-rewrite-heads-blanks)
763 (defun math-rewrite-heads (expr &optional more all)
764 (let ((math-rewrite-heads-heads more)
765 (math-rewrite-heads-skips (and (not all)
766 '(calcFunc-apply calcFunc-condition calcFunc-opt
767 calcFunc-por calcFunc-pnot)))
768 (math-rewrite-heads-blanks (and (not all)
769 '(calcFunc-quote calcFunc-plain calcFunc-select
770 calcFunc-cons calcFunc-rcons
772 (or (Math-primp expr)
773 (math-rewrite-heads-rec expr))
774 math-rewrite-heads-heads))
776 (defun math-rewrite-heads-rec (expr)
777 (or (memq (car expr) math-rewrite-heads-skips)
779 (or (memq (car expr) math-rewrite-heads-heads)
780 (memq (car expr) math-rewrite-heads-blanks)
781 (memq 'algebraic (get (car expr) 'math-rewrite-props))
782 (setq math-rewrite-heads-heads (cons (car expr) math-rewrite-heads-heads)))
783 (while (setq expr (cdr expr))
784 (or (Math-primp (car expr))
785 (math-rewrite-heads-rec (car expr)))))))
787 (defun math-parse-schedule (sched)
793 (math-parse-schedule (cdr s))
794 (if (eq (car-safe s) 'var)
795 (math-var-to-calcFunc s)
796 (error "Improper component in rewrite schedule"))))))
799 (defun math-rwcomp-match-vars (expr)
800 (if (Math-primp expr)
801 (if (eq (car-safe expr) 'var)
802 (let ((entry (assq (nth 2 expr) math-regs)))
804 (math-rwcomp-register-expr (nth 1 entry))
807 (if (and (eq (car expr) 'calcFunc-quote)
809 (math-rwcomp-match-vars (nth 1 expr))
810 (if (and (eq (car expr) 'calcFunc-plain)
812 (not (Math-primp (nth 1 expr))))
814 (cons (car (nth 1 expr))
815 (mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr)))))
817 (mapcar 'math-rwcomp-match-vars (cdr expr)))))))
819 (defun math-rwcomp-register-expr (num)
820 (let ((entry (nth (1- (- math-num-regs num)) math-regs)))
822 (list 'neg (list 'calcFunc-register (nth 1 entry)))
823 (list 'calcFunc-register (nth 1 entry)))))
825 ;; The variables math-rwcomp-subst-old, math-rwcomp-subst-new,
826 ;; math-rwcomp-subst-old-func and math-rwcomp-subst-new-func
827 ;; are local to math-rwcomp-substitute, but are used by
828 ;; math-rwcomp-subst-rec, which is called by math-rwcomp-substitute.
829 (defvar math-rwcomp-subst-new)
830 (defvar math-rwcomp-subst-old)
831 (defvar math-rwcomp-subst-new-func)
832 (defvar math-rwcomp-subst-old-func)
834 (defun math-rwcomp-substitute (expr math-rwcomp-subst-old math-rwcomp-subst-new)
835 (if (and (eq (car-safe math-rwcomp-subst-old) 'var)
836 (memq (car-safe math-rwcomp-subst-new) '(var calcFunc-lambda)))
837 (let ((math-rwcomp-subst-old-func (math-var-to-calcFunc math-rwcomp-subst-old))
838 (math-rwcomp-subst-new-func (math-var-to-calcFunc math-rwcomp-subst-new)))
839 (math-rwcomp-subst-rec expr))
840 (let ((math-rwcomp-subst-old-func nil))
841 (math-rwcomp-subst-rec expr))))
843 (defun math-rwcomp-subst-rec (expr)
844 (cond ((equal expr math-rwcomp-subst-old) math-rwcomp-subst-new)
845 ((Math-primp expr) expr)
846 (t (if (eq (car expr) math-rwcomp-subst-old-func)
847 (math-build-call math-rwcomp-subst-new-func
848 (mapcar 'math-rwcomp-subst-rec
851 (mapcar 'math-rwcomp-subst-rec (cdr expr)))))))
853 (defvar math-rwcomp-tracing nil)
855 (defun math-rwcomp-trace (instr)
856 (when math-rwcomp-tracing
857 (terpri) (princ instr))
860 (defun math-rwcomp-instr (&rest instr)
861 (setcdr math-prog-last
862 (setq math-prog-last (list (math-rwcomp-trace instr)))))
864 (defun math-rwcomp-multi-instr (tail &rest instr)
865 (setcdr math-prog-last
866 (setq math-prog-last (list (math-rwcomp-trace (append instr tail))))))
868 (defun math-rwcomp-bind-var (reg var)
869 (setcar (math-rwcomp-reg-entry reg) (nth 2 var))
870 (setq math-bound-vars (cons (nth 2 var) math-bound-vars))
871 (math-rwcomp-do-conditions))
873 (defun math-rwcomp-unbind-vars (mark)
874 (while (not (eq math-bound-vars mark))
875 (setcar (assq (car math-bound-vars) math-regs) nil)
876 (setq math-bound-vars (cdr math-bound-vars))))
878 (defun math-rwcomp-do-conditions ()
879 (let ((cond math-conds))
881 (if (math-rwcomp-all-regs-done (car cond))
882 (let ((expr (car cond)))
883 (setq math-conds (delq (car cond) math-conds))
885 (math-rwcomp-cond-instr expr)))
886 (setq cond (cdr cond)))))
888 (defun math-rwcomp-cond-instr (expr)
890 (cond ((and (eq (car-safe expr) 'calcFunc-matches)
892 (eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr))))
894 (math-rwcomp-pattern (nth 2 expr) (nth 1 arg)))
895 ((math-numberp (setq expr (math-rwcomp-match-vars expr)))
896 (if (Math-zerop expr)
897 (math-rwcomp-instr 'backtrack)))
898 ((and (eq (car expr) 'calcFunc-let)
900 (let ((reg (math-rwcomp-reg)))
901 (math-rwcomp-instr 'let reg (nth 2 expr))
902 (math-rwcomp-pattern (nth 1 expr) reg)))
903 ((and (eq (car expr) 'calcFunc-let)
905 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
906 (= (length (nth 1 expr)) 3))
907 (let ((reg (math-rwcomp-reg)))
908 (math-rwcomp-instr 'let reg (nth 2 (nth 1 expr)))
909 (math-rwcomp-pattern (nth 1 (nth 1 expr)) reg)))
910 ((and (setq op (cdr (assq (car-safe expr)
911 '( (calcFunc-integer . integer)
912 (calcFunc-real . real)
913 (calcFunc-constant . constant)
914 (calcFunc-negative . negative) ))))
916 (or (and (eq (car-safe (nth 1 expr)) 'neg)
917 (memq op '(integer real constant))
918 (setq arg (nth 1 (nth 1 expr))))
919 (setq arg (nth 1 expr)))
920 (eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register))
921 (math-rwcomp-instr op (nth 1 arg)))
922 ((and (assq (car-safe expr) calc-tweak-eqn-table)
924 (eq (car-safe (nth 1 expr)) 'calcFunc-register))
925 (if (math-constp (nth 2 expr))
926 (let ((reg (math-rwcomp-reg)))
927 (setcar (nthcdr 3 (car math-regs)) (nth 2 expr))
928 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
930 (if (eq (car (nth 2 expr)) 'calcFunc-register)
931 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
932 (car expr) (nth 1 (nth 2 expr)))
933 (math-rwcomp-instr 'cond expr))))
934 ((and (eq (car-safe expr) 'calcFunc-eq)
936 (eq (car-safe (nth 1 expr)) '%)
937 (eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register)
938 (math-constp (nth 2 (nth 1 expr)))
939 (math-constp (nth 2 expr)))
940 (math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr)))
941 (nth 2 (nth 1 expr)) (nth 2 expr)))
942 ((equal expr '(var remember var-remember))
943 (setq math-remembering 1))
944 ((and (eq (car-safe expr) 'calcFunc-remember)
946 (setq math-remembering (if math-remembering
948 math-remembering (nth 1 expr))
950 (t (math-rwcomp-instr 'cond expr)))))
952 (defun math-rwcomp-same-instr (reg1 reg2 neg)
953 (math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
954 (nth 2 (math-rwcomp-reg-entry reg2)))
960 (defun math-rwcomp-copy-instr (reg1 reg2 neg)
961 (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
962 (nth 2 (math-rwcomp-reg-entry reg2)))
964 (math-rwcomp-instr 'copy-neg reg1 reg2)
966 (math-rwcomp-instr 'copy reg1 reg2))))
968 (defun math-rwcomp-reg ()
971 (setq math-regs (cons (list nil math-num-regs nil 0) math-regs)
972 math-num-regs (1+ math-num-regs))))
974 (defun math-rwcomp-reg-entry (num)
975 (nth (1- (- math-num-regs num)) math-regs))
978 (defun math-rwcomp-pattern (expr part &optional not-direct)
979 (cond ((or (math-rwcomp-no-vars expr)
980 (and (eq (car expr) 'calcFunc-quote)
982 (setq expr (nth 1 expr))))
983 (if (eq (car-safe expr) 'calcFunc-register)
984 (math-rwcomp-same-instr part (nth 1 expr) nil)
985 (let ((reg (math-rwcomp-reg)))
986 (setcar (nthcdr 3 (car math-regs)) expr)
987 (math-rwcomp-same-instr part reg nil))))
988 ((eq (car expr) 'var)
989 (let ((entry (assq (nth 2 expr) math-regs)))
991 (math-rwcomp-same-instr part (nth 1 entry) nil)
993 (let ((reg (math-rwcomp-reg)))
994 (math-rwcomp-pattern expr reg)
995 (math-rwcomp-copy-instr part reg nil))
996 (if (setq entry (assq (nth 2 expr) math-aliased-vars))
998 (setcar (math-rwcomp-reg-entry (nth 1 entry))
1001 (math-rwcomp-copy-instr part (nth 1 entry) nil))
1002 (math-rwcomp-bind-var part expr))))))
1003 ((and (eq (car expr) 'calcFunc-select)
1004 (= (length expr) 2))
1005 (let ((reg (math-rwcomp-reg)))
1006 (math-rwcomp-instr 'select part reg)
1007 (math-rwcomp-pattern (nth 1 expr) reg)))
1008 ((and (eq (car expr) 'calcFunc-opt)
1009 (memq (length expr) '(2 3)))
1010 (error "opt( ) occurs in context where it is not allowed"))
1011 ((eq (car expr) 'neg)
1012 (if (eq (car (nth 1 expr)) 'var)
1013 (let ((entry (assq (nth 2 (nth 1 expr)) math-regs)))
1015 (math-rwcomp-same-instr part (nth 1 entry) t)
1017 (let ((reg (math-rwcomp-best-reg (nth 1 expr))))
1018 (math-rwcomp-copy-instr part reg t)
1019 (math-rwcomp-pattern (nth 1 expr) reg))
1020 (setcar (cdr (cdr (math-rwcomp-reg-entry part))) t)
1021 (math-rwcomp-pattern (nth 1 expr) part))))
1022 (if (math-rwcomp-is-algebraic (nth 1 expr))
1023 (math-rwcomp-cond-instr (list 'calcFunc-eq
1024 (math-rwcomp-register-expr part)
1026 (let ((reg (math-rwcomp-reg)))
1027 (math-rwcomp-instr 'func part 'neg reg)
1028 (math-rwcomp-pattern (nth 1 expr) reg)))))
1029 ((and (eq (car expr) 'calcFunc-apply)
1030 (= (length expr) 3))
1031 (let ((reg1 (math-rwcomp-reg))
1032 (reg2 (math-rwcomp-reg)))
1033 (math-rwcomp-instr 'apply part reg1 reg2)
1034 (math-rwcomp-pattern (nth 1 expr) reg1)
1035 (math-rwcomp-pattern (nth 2 expr) reg2)))
1036 ((and (eq (car expr) 'calcFunc-cons)
1037 (= (length expr) 3))
1038 (let ((reg1 (math-rwcomp-reg))
1039 (reg2 (math-rwcomp-reg)))
1040 (math-rwcomp-instr 'cons part reg1 reg2)
1041 (math-rwcomp-pattern (nth 1 expr) reg1)
1042 (math-rwcomp-pattern (nth 2 expr) reg2)))
1043 ((and (eq (car expr) 'calcFunc-rcons)
1044 (= (length expr) 3))
1045 (let ((reg1 (math-rwcomp-reg))
1046 (reg2 (math-rwcomp-reg)))
1047 (math-rwcomp-instr 'rcons part reg1 reg2)
1048 (math-rwcomp-pattern (nth 1 expr) reg1)
1049 (math-rwcomp-pattern (nth 2 expr) reg2)))
1050 ((and (eq (car expr) 'calcFunc-condition)
1051 (>= (length expr) 3))
1052 (math-rwcomp-pattern (nth 1 expr) part)
1053 (setq expr (cdr expr))
1054 (while (setq expr (cdr expr))
1055 (let ((cond (math-flatten-lands (car expr))))
1057 (if (math-rwcomp-all-regs-done (car cond))
1058 (math-rwcomp-cond-instr (car cond))
1059 (setq math-conds (cons (car cond) math-conds)))
1060 (setq cond (cdr cond))))))
1061 ((and (eq (car expr) 'calcFunc-pand)
1062 (= (length expr) 3))
1063 (math-rwcomp-pattern (nth 1 expr) part)
1064 (math-rwcomp-pattern (nth 2 expr) part))
1065 ((and (eq (car expr) 'calcFunc-por)
1066 (= (length expr) 3))
1067 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1068 (let ((math-conds nil)
1069 (head math-prog-last)
1070 (mark math-bound-vars)
1072 (math-rwcomp-pattern (nth 1 expr) part t)
1073 (let ((amark math-aliased-vars)
1074 (math-aliased-vars math-aliased-vars)
1075 (tail math-prog-last)
1078 (while (not (eq p mark))
1079 (setq entry (assq (car p) math-regs)
1080 math-aliased-vars (cons (list (car p) (nth 1 entry) nil)
1083 (setcar (math-rwcomp-reg-entry (nth 1 entry)) nil))
1084 (setcar (cdr (car head)) (cdr head))
1086 (setq math-prog-last head)
1087 (math-rwcomp-pattern (nth 2 expr) part)
1088 (math-rwcomp-instr 'same 0 0)
1089 (setcdr tail math-prog-last)
1090 (setq p math-aliased-vars)
1091 (while (not (eq p amark))
1093 (setcar (math-rwcomp-reg-entry (nth 1 (car p)))
1096 (math-rwcomp-do-conditions))
1097 ((and (eq (car expr) 'calcFunc-pnot)
1098 (= (length expr) 2))
1099 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1100 (let ((head math-prog-last)
1101 (mark math-bound-vars))
1102 (math-rwcomp-pattern (nth 1 expr) part)
1103 (math-rwcomp-unbind-vars mark)
1104 (math-rwcomp-instr 'end-alt head)
1105 (math-rwcomp-instr 'backtrack)
1106 (setcar (cdr (car head)) (cdr head))
1108 (setq math-prog-last head)))
1109 (t (let ((props (get (car expr) 'math-rewrite-props)))
1110 (if (and (eq (car expr) 'calcFunc-plain)
1112 (not (math-primp (nth 1 expr))))
1113 (setq expr (nth 1 expr))) ; but "props" is still nil
1114 (if (and (memq 'algebraic props)
1115 (math-rwcomp-is-algebraic expr))
1116 (math-rwcomp-cond-instr (list 'calcFunc-eq
1117 (math-rwcomp-register-expr part)
1119 (if (and (memq 'commut props)
1120 (= (length expr) 3))
1121 (let ((arg1 (nth 1 expr))
1123 try1 def code head (flip nil))
1124 (if (eq (car expr) '-)
1125 (setq arg2 (math-rwcomp-neg arg2)))
1126 (setq arg1 (cons arg1 (math-rwcomp-best-reg arg1))
1127 arg2 (cons arg2 (math-rwcomp-best-reg arg2)))
1128 (or (math-rwcomp-order arg1 arg2)
1129 (setq def arg1 arg1 arg2 arg2 def flip t))
1130 (if (math-rwcomp-optional-arg (car expr) arg1)
1131 (error "Too many opt( ) arguments in this context"))
1132 (setq def (math-rwcomp-optional-arg (car expr) arg2)
1133 head (if (memq (car expr) '(+ -))
1135 (if (eq (car expr) '*)
1138 code (if (math-rwcomp-is-constrained
1140 (if (math-rwcomp-is-constrained
1144 (math-rwcomp-multi-instr (and def (list def))
1146 (vector nil nil nil code flip)
1148 (setq try1 (car math-prog-last))
1149 (math-rwcomp-pattern (car arg1) (cdr arg1))
1150 (math-rwcomp-instr 'try2 try1 (cdr arg2))
1151 (if (and (= part 0) (not def) (not math-rewrite-whole)
1152 (not (eq math-rhs t))
1153 (setq def (get (car expr)
1154 'math-rewrite-default)))
1155 (let ((reg1 (math-rwcomp-reg))
1156 (reg2 (math-rwcomp-reg)))
1157 (if (= (aref (nth 3 try1) 3) 0)
1158 (aset (nth 3 try1) 3 1))
1159 (math-rwcomp-instr 'try (cdr arg2)
1160 (if (equal head '(* /))
1167 (setq try1 (car math-prog-last))
1168 (math-rwcomp-pattern (car arg2) reg1)
1169 (math-rwcomp-instr 'try2 try1 reg2)
1170 (setq math-rhs (list (if (eq (car expr) '-)
1173 (list 'calcFunc-register
1175 (math-rwcomp-pattern (car arg2) (cdr arg2))))
1176 (let* ((args (mapcar (function
1178 (cons x (math-rwcomp-best-reg x))))
1180 (args2 (copy-sequence args))
1181 (argp (reverse args2))
1185 (let ((def (math-rwcomp-optional-arg (car expr)
1189 (setq args2 (delq (car argp) args2)
1190 defs (cons (cons def (cdr (car argp)))
1192 (math-rwcomp-multi-instr
1194 (if (or (and (memq 'unary1 props)
1195 (= (length args2) 1)
1196 (eq (car args2) (car args)))
1197 (and (memq 'unary2 props)
1199 (eq (car args2) (nth 1 args))))
1204 (setq argp (cdr argp)))
1205 (math-rwcomp-multi-instr (mapcar 'cdr args)
1206 'func part (car expr))
1207 (setq args (sort args 'math-rwcomp-order))
1209 (math-rwcomp-pattern (car (car args)) (cdr (car args)))
1211 args (cdr args))))))))))
1213 (defun math-rwcomp-best-reg (x)
1214 (or (and (eq (car-safe x) 'var)
1215 (let ((entry (assq (nth 2 x) math-aliased-vars)))
1218 (not (nth 2 (math-rwcomp-reg-entry (nth 1 entry))))
1220 (setcar (cdr (cdr entry)) t)
1224 (defun math-rwcomp-all-regs-done (expr)
1225 (if (Math-primp expr)
1226 (or (not (eq (car-safe expr) 'var))
1227 (assq (nth 2 expr) math-regs)
1228 (eq (nth 2 expr) 'var-remember)
1229 (math-const-var expr))
1230 (if (and (eq (car expr) 'calcFunc-let)
1231 (= (length expr) 3))
1232 (math-rwcomp-all-regs-done (nth 2 expr))
1233 (if (and (eq (car expr) 'calcFunc-let)
1235 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
1236 (= (length (nth 1 expr)) 3))
1237 (math-rwcomp-all-regs-done (nth 2 (nth 1 expr)))
1238 (while (and (setq expr (cdr expr))
1239 (math-rwcomp-all-regs-done (car expr))))
1242 (defun math-rwcomp-no-vars (expr)
1243 (if (Math-primp expr)
1244 (or (not (eq (car-safe expr) 'var))
1245 (math-const-var expr))
1246 (and (not (memq (car expr) '(calcFunc-condition
1247 calcFunc-select calcFunc-quote
1248 calcFunc-plain calcFunc-opt
1249 calcFunc-por calcFunc-pand
1250 calcFunc-pnot calcFunc-apply
1251 calcFunc-cons calcFunc-rcons)))
1253 (while (and (setq expr (cdr expr))
1254 (math-rwcomp-no-vars (car expr))))
1257 (defun math-rwcomp-is-algebraic (expr)
1258 (if (Math-primp expr)
1259 (or (not (eq (car-safe expr) 'var))
1260 (math-const-var expr)
1261 (assq (nth 2 expr) math-regs))
1262 (and (memq 'algebraic (get (car expr) 'math-rewrite-props))
1264 (while (and (setq expr (cdr expr))
1265 (math-rwcomp-is-algebraic (car expr))))
1268 (defun math-rwcomp-is-constrained (expr not-these)
1269 (if (Math-primp expr)
1270 (not (eq (car-safe expr) 'var))
1271 (if (eq (car expr) 'calcFunc-plain)
1272 (math-rwcomp-is-constrained (nth 1 expr) not-these)
1273 (not (or (memq (car expr) '(neg calcFunc-select))
1274 (memq (car expr) not-these)
1275 (and (memq 'commut (get (car expr) 'math-rewrite-props))
1276 (or (eq (car-safe (nth 1 expr)) 'calcFunc-opt)
1277 (eq (car-safe (nth 2 expr)) 'calcFunc-opt))))))))
1279 (defun math-rwcomp-optional-arg (head argp)
1280 (let ((arg (car argp)))
1281 (if (eq (car-safe arg) 'calcFunc-opt)
1282 (and (memq (length arg) '(2 3))
1284 (or (eq (car-safe (nth 1 arg)) 'var)
1285 (error "First argument of opt( ) must be a variable"))
1286 (setcar argp (nth 1 arg))
1287 (if (= (length arg) 2)
1288 (or (get head 'math-rewrite-default)
1289 (error "opt( ) must include a default in this context"))
1291 (and (eq (car-safe arg) 'neg)
1292 (let* ((part (list (nth 1 arg)))
1293 (partp (math-rwcomp-optional-arg head part)))
1295 (setcar argp (math-rwcomp-neg (car part)))
1296 (math-neg partp)))))))
1298 (defun math-rwcomp-neg (expr)
1299 (if (memq (car-safe expr) '(* /))
1300 (if (eq (car-safe (nth 1 expr)) 'var)
1301 (list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr))
1302 (if (eq (car-safe (nth 2 expr)) 'var)
1303 (list (car expr) (nth 1 expr) (list 'neg (nth 2 expr)))
1307 (defun math-rwcomp-assoc-args (expr)
1308 (if (and (eq (car-safe (nth 1 expr)) (car expr))
1309 (= (length (nth 1 expr)) 3))
1310 (math-rwcomp-assoc-args (nth 1 expr)))
1311 (if (and (eq (car-safe (nth 2 expr)) (car expr))
1312 (= (length (nth 2 expr)) 3))
1313 (math-rwcomp-assoc-args (nth 2 expr))))
1315 (defun math-rwcomp-addsub-args (expr)
1316 (if (memq (car-safe (nth 1 expr)) '(+ -))
1317 (math-rwcomp-addsub-args (nth 1 expr)))
1318 (if (eq (car expr) '-)
1320 (if (eq (car-safe (nth 2 expr)) '+)
1321 (math-rwcomp-addsub-args (nth 2 expr)))))
1323 (defun math-rwcomp-order (a b)
1324 (< (math-rwcomp-priority (car a))
1325 (math-rwcomp-priority (car b))))
1327 ;; Order of priority: 0 Constants and other exact matches (first)
1328 ;; 10 Functions (except below)
1329 ;; 20 Meta-variables which occur more than once
1330 ;; 30 Algebraic functions
1331 ;; 40 Commutative/associative functions
1332 ;; 50 Meta-variables which occur only once
1333 ;; +100 for every "!!!" (pnot) in the pattern
1334 ;; 10000 Optional arguments (last)
1336 (defun math-rwcomp-priority (expr)
1337 (+ (math-rwcomp-count-pnots expr)
1338 (cond ((eq (car-safe expr) 'calcFunc-opt)
1340 ((math-rwcomp-no-vars expr)
1342 ((eq (car expr) 'calcFunc-quote)
1344 ((eq (car expr) 'var)
1345 (if (assq (nth 2 expr) math-regs)
1347 (if (= (math-rwcomp-count-refs expr) 1)
1350 (t (let ((props (get (car expr) 'math-rewrite-props)))
1351 (if (or (memq 'commut props)
1352 (memq 'assoc props))
1354 (if (memq 'algebraic props)
1358 (defun math-rwcomp-count-refs (var)
1359 (let ((count (or (math-expr-contains-count math-pattern var) 0))
1362 (if (eq (car-safe (car p)) 'calcFunc-let)
1363 (if (= (length (car p)) 3)
1364 (setq count (+ count
1365 (or (math-expr-contains-count (nth 2 (car p)) var)
1367 (if (and (= (length (car p)) 2)
1368 (eq (car-safe (nth 1 (car p))) 'calcFunc-assign)
1369 (= (length (nth 1 (car p))) 3))
1370 (setq count (+ count
1371 (or (math-expr-contains-count
1372 (nth 2 (nth 1 (car p))) var) 0))))))
1376 (defun math-rwcomp-count-pnots (expr)
1377 (if (Math-primp expr)
1379 (if (eq (car expr) 'calcFunc-pnot)
1382 (while (setq expr (cdr expr))
1383 (setq count (+ count (math-rwcomp-count-pnots (car expr)))))
1386 ;; In the current implementation, all associative functions must
1387 ;; also be commutative.
1389 (put '+ 'math-rewrite-props '(algebraic assoc commut))
1390 (put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below
1391 (put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below
1392 (put '/ 'math-rewrite-props '(algebraic unary1))
1393 (put '^ 'math-rewrite-props '(algebraic unary1))
1394 (put '% 'math-rewrite-props '(algebraic))
1395 (put 'neg 'math-rewrite-props '(algebraic))
1396 (put 'calcFunc-idiv 'math-rewrite-props '(algebraic))
1397 (put 'calcFunc-abs 'math-rewrite-props '(algebraic))
1398 (put 'calcFunc-sign 'math-rewrite-props '(algebraic))
1399 (put 'calcFunc-round 'math-rewrite-props '(algebraic))
1400 (put 'calcFunc-rounde 'math-rewrite-props '(algebraic))
1401 (put 'calcFunc-roundu 'math-rewrite-props '(algebraic))
1402 (put 'calcFunc-trunc 'math-rewrite-props '(algebraic))
1403 (put 'calcFunc-floor 'math-rewrite-props '(algebraic))
1404 (put 'calcFunc-ceil 'math-rewrite-props '(algebraic))
1405 (put 'calcFunc-re 'math-rewrite-props '(algebraic))
1406 (put 'calcFunc-im 'math-rewrite-props '(algebraic))
1407 (put 'calcFunc-conj 'math-rewrite-props '(algebraic))
1408 (put 'calcFunc-arg 'math-rewrite-props '(algebraic))
1409 (put 'calcFunc-and 'math-rewrite-props '(assoc commut))
1410 (put 'calcFunc-or 'math-rewrite-props '(assoc commut))
1411 (put 'calcFunc-xor 'math-rewrite-props '(assoc commut))
1412 (put 'calcFunc-eq 'math-rewrite-props '(commut))
1413 (put 'calcFunc-neq 'math-rewrite-props '(commut))
1414 (put 'calcFunc-land 'math-rewrite-props '(assoc commut))
1415 (put 'calcFunc-lor 'math-rewrite-props '(assoc commut))
1416 (put 'calcFunc-beta 'math-rewrite-props '(commut))
1417 (put 'calcFunc-gcd 'math-rewrite-props '(assoc commut))
1418 (put 'calcFunc-lcm 'math-rewrite-props '(assoc commut))
1419 (put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut))
1420 (put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut))
1421 (put 'calcFunc-vunion 'math-rewrite-props '(assoc commut))
1422 (put 'calcFunc-vint 'math-rewrite-props '(assoc commut))
1423 (put 'calcFunc-vxor 'math-rewrite-props '(assoc commut))
1425 ;; Note: "*" is not commutative for matrix args, but we pretend it is.
1426 ;; Also, "-" is not commutative but the code tweaks things so that it is.
1428 (put '+ 'math-rewrite-default 0)
1429 (put '- 'math-rewrite-default 0)
1430 (put '* 'math-rewrite-default 1)
1431 (put '/ 'math-rewrite-default 1)
1432 (put '^ 'math-rewrite-default 1)
1433 (put 'calcFunc-land 'math-rewrite-default 1)
1434 (put 'calcFunc-lor 'math-rewrite-default 0)
1435 (put 'calcFunc-vunion 'math-rewrite-default '(vec))
1436 (put 'calcFunc-vint 'math-rewrite-default '(vec))
1437 (put 'calcFunc-vdiff 'math-rewrite-default '(vec))
1438 (put 'calcFunc-vxor 'math-rewrite-default '(vec))
1440 (defmacro math-rwfail (&optional back)
1441 `(setq pc (and ,(if back
1442 '(setq btrack (cdr btrack))
1446 ;; This monstrosity is necessary because the use of static vectors of
1447 ;; registers makes rewrite rules non-reentrant. Yucko!
1448 (defmacro math-rweval (form)
1449 `(let ((orig (car rules)))
1450 (setcar rules '(nil nil nil no-phase))
1453 (setcar rules orig))))
1455 (defvar math-rewrite-phase 1)
1457 ;; The variable math-apply-rw-regs is local to math-apply-rewrites,
1458 ;; but is used by math-rwapply-replace-regs and math-rwapply-reg-looks-negp
1459 ;; which are called by math-apply-rewrites.
1460 (defvar math-apply-rw-regs)
1462 ;; The variable math-apply-rw-ruleset is local to math-apply-rewrites,
1463 ;; but is used by math-rwapply-remember.
1464 (defvar math-apply-rw-ruleset)
1466 (defun math-apply-rewrites (expr rules &optional heads math-apply-rw-ruleset)
1468 (setq rules (cdr (or (assq (car-safe expr) rules)
1471 op math-apply-rw-regs inst part pc mark btrack
1472 (tracing math-rwcomp-tracing)
1473 (phase math-rewrite-phase))
1476 (and (setq part (nth 2 (car rules)))
1478 (not (memq part heads)))
1479 (and (setq part (nth 3 (car rules)))
1480 (not (memq phase part)))
1482 (setq math-apply-rw-regs (car (car rules))
1483 pc (nth 1 (car rules))
1485 (aset math-apply-rw-regs 0 expr)
1489 (progn (terpri) (princ (car pc))
1490 (if (and (natnump (nth 1 (car pc)))
1491 (< (nth 1 (car pc)) (length math-apply-rw-regs)))
1493 (format "\n part = %s"
1494 (aref math-apply-rw-regs (nth 1 (car pc))))))))
1496 (cond ((eq (setq op (car (setq inst (car pc)))) 'func)
1498 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1500 (car (setq inst (cdr (cdr inst)))))
1502 (while (and (setq inst (cdr inst)
1505 (aset math-apply-rw-regs (car inst) (car part)))
1506 (not (or inst part))))
1511 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1512 (setq mark (aref math-apply-rw-regs (nth 2 inst))))
1513 (Math-equal part mark))
1519 (not (eq calc-matrix-mode 'scalar))
1520 (eq (car (nth 2 inst)) '*)
1521 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1523 (not (math-known-scalarp part)))
1524 (setq mark (nth 3 inst)
1528 (aset math-apply-rw-regs (nth 4 inst) (nth 2 part))
1529 (aset mark 1 (cdr (cdr part))))
1530 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1531 (aset mark 1 (cdr part)))
1532 (aset mark 0 (cdr part))
1536 (if (and (consp (setq part
1537 (aref math-apply-rw-regs (car (cdr inst)))))
1538 (memq (car part) (nth 2 inst))
1540 (or (not (eq (car part) '/))
1541 (Math-objectp (nth 2 part))))
1544 mark (car (cdr (setq inst (cdr (cdr inst))))))
1546 (memq 'assoc (get (car part) 'math-rewrite-props))
1547 (not (= (aref mark 3) 0))
1548 (while (if (and (consp (nth 1 part))
1549 (memq (car (nth 1 part)) (car inst)))
1550 (setq op (cons (if (eq (car part) '-)
1556 (if (and (consp (nth 2 part))
1557 (memq (car (nth 2 part))
1559 (not (eq (car (nth 2 part)) '-)))
1560 (setq op (cons (nth 1 part) op)
1561 part (nth 2 part))))))
1562 (setq op (cons (nth 1 part)
1563 (cons (if (eq (car part) '-)
1566 (if (eq (car part) '/)
1571 btrack (cons pc btrack)
1573 (aset math-apply-rw-regs (nth 2 inst) (car op))
1576 (aset mark 2 (if (cdr (cdr op)) 1 0)))
1578 (if (and (consp part)
1579 (eq (car part) 'neg)
1580 (eq (car (nth 2 inst)) '*)
1581 (eq (nth 5 inst) 1))
1583 (setq mark (nth 3 inst)
1585 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1588 (setq mark (nth 3 inst)
1590 (aset math-apply-rw-regs (nth 4 inst) part)
1595 (setq part (nth 1 inst) ; try instr
1599 (aset math-apply-rw-regs (nth 2 inst)
1602 (if (eq (aref mark 0) (aref mark 1))
1603 (nth 1 (aref mark 0))
1604 (car (aref mark 0))))
1606 (setq mark (delq (car (aref mark 1))
1607 (copy-sequence (aref mark 0)))
1608 op (car (nth 2 part)))
1611 (setq mark (nreverse mark)
1612 part (list '* (nth 1 mark) (car mark))
1614 (while (setq mark (cdr mark))
1615 (setq part (list '* (car mark) part))))
1616 (setq part (car mark)
1618 part (if (and (eq op '+)
1620 (eq (car (car mark)) 'neg))
1623 (list op part (car mark))))
1624 (while (setq mark (cdr mark))
1625 (setq part (if (and (eq op '+)
1627 (eq (car (car mark)) 'neg))
1630 (list op part (car mark))))))
1633 (car (aref mark 1)))
1634 ((eq op 3) (nth 5 part))
1635 (t (aref mark 1)))))
1639 (if (and (consp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1640 (eq (car part) 'calcFunc-select))
1641 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1642 (if math-rewrite-selections
1644 (aset math-apply-rw-regs (nth 2 inst) part))))
1647 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1648 (setq mark (math-neg
1649 (aref math-apply-rw-regs (nth 2 inst)))))
1650 (Math-equal part mark))
1655 (setq inst (car (car btrack)) ; "try" or "alt" instr
1656 pc (cdr (car btrack))
1657 mark (or (nth 3 inst) [nil nil 4])
1660 (if (setq op (cdr (aref mark 1)))
1661 (aset math-apply-rw-regs (nth 4 inst)
1662 (car (aset mark 1 op)))
1666 (aset math-apply-rw-regs (nth 4 inst)
1667 (aref math-apply-rw-regs (nth 1 inst))))
1670 (if (setq op (cdr (aref mark 1)))
1671 (aset math-apply-rw-regs (nth 4 inst)
1672 (car (aset mark 1 op)))
1673 (if (= (aref mark 3) 1)
1677 (aset math-apply-rw-regs (nth 4 inst)
1678 (aref math-apply-rw-regs (nth 1 inst))))
1681 (aset mark 1 (cons nil (aref mark 0)))
1684 (if (setq op (cdr (aref mark 1)))
1686 (setq mark (delq (car (aset mark 1 op))
1689 op (car (nth 2 inst)))
1692 (setq mark (nreverse mark)
1693 part (list '* (nth 1 mark)
1696 (while (setq mark (cdr mark))
1697 (setq part (list '* (car mark)
1699 (setq part (car mark)
1701 part (if (and (eq op '+)
1703 (eq (car (car mark))
1707 (list op part (car mark))))
1708 (while (setq mark (cdr mark))
1709 (setq part (if (and (eq op '+)
1711 (eq (car (car mark))
1715 (list op part (car mark))))))
1716 (aset math-apply-rw-regs (nth 4 inst) part))
1720 (aset math-apply-rw-regs (nth 4 inst)
1721 (aref math-apply-rw-regs (nth 1 inst))))
1724 (setq btrack (cdr btrack)))
1725 (t (math-rwfail t))))
1728 (if (Math-integerp (setq part
1729 (aref math-apply-rw-regs (nth 1 inst))))
1731 (if (Math-primp part)
1733 (setq part (math-rweval (math-simplify part)))
1734 (if (Math-integerp part)
1739 (if (Math-realp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1741 (if (Math-primp part)
1743 (setq part (math-rweval (math-simplify part)))
1744 (if (Math-realp part)
1749 (if (math-constp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1751 (if (Math-primp part)
1753 (setq part (math-rweval (math-simplify part)))
1754 (if (math-constp part)
1759 (if (math-looks-negp (setq part
1760 (aref math-apply-rw-regs (nth 1 inst))))
1762 (if (Math-primp part)
1764 (setq part (math-rweval (math-simplify part)))
1765 (if (math-looks-negp part)
1770 (setq part (math-compare (aref math-apply-rw-regs (nth 1 inst))
1771 (aref math-apply-rw-regs (nth 3 inst)))
1774 (setq part (math-rweval
1778 (aref math-apply-rw-regs (nth 1 inst))
1779 (aref math-apply-rw-regs (nth 3 inst))))))))
1780 (if (cond ((eq op 'calcFunc-eq)
1782 ((eq op 'calcFunc-neq)
1783 (memq part '(-1 1)))
1784 ((eq op 'calcFunc-lt)
1786 ((eq op 'calcFunc-leq)
1787 (memq part '(-1 0)))
1788 ((eq op 'calcFunc-gt)
1790 ((eq op 'calcFunc-geq)
1791 (memq part '(0 1))))
1797 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1799 (car (setq inst (cdr (cdr inst))))))
1801 (setq inst (cdr inst)
1803 (while (and (setq inst (cdr inst)
1806 (aset math-apply-rw-regs (car inst) (car part)))
1809 (while (eq (car (car (setq pc (cdr pc))))
1811 (setq pc (cdr pc)) ; skip over "func"
1813 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1814 (setq mark (cdr mark)))))
1821 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1822 (eq (car part) (nth 2 inst))))
1823 (and (= (length part) 2)
1824 (setq part (nth 1 part))))
1826 (setq mark (nth 3 inst))
1827 (aset math-apply-rw-regs (nth 4 inst) part)
1828 (while (eq (car (car (setq pc (cdr pc)))) 'func-def))
1829 (setq pc (cdr pc)) ; skip over "func"
1831 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1832 (setq mark (cdr mark))))
1833 (setq pc (cdr pc))))
1837 (setq part (aref math-apply-rw-regs (nth 1 inst))))
1838 (Math-zerop (nth 3 inst))
1839 (and (not (Math-zerop (nth 2 inst)))
1841 (setq part (math-mod part (nth 2 inst)))
1842 (or (Math-numberp part)
1843 (setq part (math-rweval
1844 (math-simplify part))))
1845 (Math-equal part (nth 3 inst)))))
1851 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1852 (not (Math-objvecp part))
1853 (not (eq (car part) 'var)))
1855 (aset math-apply-rw-regs (nth 2 inst)
1856 (math-calcFunc-to-var (car part)))
1857 (aset math-apply-rw-regs (nth 3 inst)
1858 (cons 'vec (cdr part)))
1864 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1865 (eq (car part) 'vec)
1868 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1869 (aset math-apply-rw-regs (nth 3 inst)
1870 (cons 'vec (cdr (cdr part))))
1876 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1877 (eq (car part) 'vec)
1880 (aset math-apply-rw-regs (nth 2 inst) (calcFunc-rhead part))
1881 (aset math-apply-rw-regs (nth 3 inst) (calcFunc-rtail part))
1889 (math-rwapply-replace-regs (nth 1 inst)))))
1894 (aset math-apply-rw-regs (nth 1 inst)
1897 (math-rwapply-replace-regs (nth 2 inst)))))
1901 (aset math-apply-rw-regs (nth 2 inst)
1902 (aref math-apply-rw-regs (nth 1 inst)))
1906 (aset math-apply-rw-regs (nth 2 inst)
1907 (math-rwapply-neg (aref math-apply-rw-regs (nth 1 inst))))
1911 (setq btrack (cons pc btrack)
1915 (while (and btrack (not (eq (car btrack) (nth 1 inst))))
1916 (setq btrack (cdr btrack)))
1917 (setq btrack (cdr btrack)
1921 (setq result (math-rwapply-replace-regs (nth 1 inst)))
1922 (if (or (and (eq (car-safe result) '+)
1923 (eq (nth 2 result) 0))
1924 (and (eq (car-safe result) '*)
1925 (eq (nth 2 result) 1)))
1926 (setq result (nth 1 result)))
1927 (setq part (and (nth 2 inst)
1931 (math-rwapply-replace-regs
1933 (if (or (equal result expr)
1934 (equal (setq result (math-normalize result)) expr))
1936 (if part (math-rwapply-remember expr result))
1940 (t (error "%s is not a valid rewrite opcode" op))))))
1941 (setq rules (cdr rules)))
1944 (defun math-rwapply-neg (expr)
1945 (if (and (consp expr)
1946 (memq (car expr) '(* /)))
1947 (if (Math-objectp (nth 2 expr))
1948 (list (car expr) (nth 1 expr) (math-neg (nth 2 expr)))
1950 (if (Math-objectp (nth 1 expr))
1951 (math-neg (nth 1 expr))
1952 (list '* -1 (nth 1 expr)))
1956 (defun math-rwapply-inv (expr)
1957 (if (and (Math-integerp expr)
1959 (math-make-frac 1 expr)
1962 (defun math-rwapply-replace-regs (expr)
1963 (cond ((Math-primp expr)
1965 ((eq (car expr) 'calcFunc-register)
1966 (setq expr (aref math-apply-rw-regs (nth 1 expr)))
1967 (if (eq (car-safe expr) '*)
1968 (if (eq (nth 1 expr) -1)
1969 (math-neg (nth 2 expr))
1970 (if (eq (nth 1 expr) 1)
1974 ((and (eq (car expr) 'calcFunc-eval)
1975 (= (length expr) 2))
1976 (calc-with-default-simplification
1977 (math-normalize (math-rwapply-replace-regs (nth 1 expr)))))
1978 ((and (eq (car expr) 'calcFunc-evalsimp)
1979 (= (length expr) 2))
1980 (math-simplify (math-rwapply-replace-regs (nth 1 expr))))
1981 ((and (eq (car expr) 'calcFunc-evalextsimp)
1982 (= (length expr) 2))
1983 (math-simplify-extended (math-rwapply-replace-regs (nth 1 expr))))
1984 ((and (eq (car expr) 'calcFunc-apply)
1985 (= (length expr) 3))
1986 (let ((func (math-rwapply-replace-regs (nth 1 expr)))
1987 (args (math-rwapply-replace-regs (nth 2 expr)))
1989 (if (and (math-vectorp args)
1990 (not (eq (car-safe (setq call (math-build-call
1991 (math-var-to-calcFunc func)
1995 (list 'calcFunc-apply func args))))
1996 ((and (eq (car expr) 'calcFunc-cons)
1997 (= (length expr) 3))
1998 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
1999 (tail (math-rwapply-replace-regs (nth 2 expr))))
2000 (if (math-vectorp tail)
2001 (cons 'vec (cons head (cdr tail)))
2002 (list 'calcFunc-cons head tail))))
2003 ((and (eq (car expr) 'calcFunc-rcons)
2004 (= (length expr) 3))
2005 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2006 (tail (math-rwapply-replace-regs (nth 2 expr))))
2007 (if (math-vectorp head)
2008 (append head (list tail))
2009 (list 'calcFunc-rcons head tail))))
2010 ((and (eq (car expr) 'neg)
2011 (math-rwapply-reg-looks-negp (nth 1 expr)))
2012 (math-rwapply-reg-neg (nth 1 expr)))
2013 ((and (eq (car expr) 'neg)
2014 (eq (car-safe (nth 1 expr)) 'calcFunc-register)
2015 (math-scalarp (aref math-apply-rw-regs (nth 1 (nth 1 expr)))))
2016 (math-neg (math-rwapply-replace-regs (nth 1 expr))))
2017 ((and (eq (car expr) '+)
2018 (math-rwapply-reg-looks-negp (nth 1 expr)))
2019 (list '- (math-rwapply-replace-regs (nth 2 expr))
2020 (math-rwapply-reg-neg (nth 1 expr))))
2021 ((and (eq (car expr) '+)
2022 (math-rwapply-reg-looks-negp (nth 2 expr)))
2023 (list '- (math-rwapply-replace-regs (nth 1 expr))
2024 (math-rwapply-reg-neg (nth 2 expr))))
2025 ((and (eq (car expr) '-)
2026 (math-rwapply-reg-looks-negp (nth 2 expr)))
2027 (list '+ (math-rwapply-replace-regs (nth 1 expr))
2028 (math-rwapply-reg-neg (nth 2 expr))))
2030 (cond ((eq (nth 1 expr) -1)
2031 (if (math-rwapply-reg-looks-negp (nth 2 expr))
2032 (math-rwapply-reg-neg (nth 2 expr))
2033 (math-neg (math-rwapply-replace-regs (nth 2 expr)))))
2034 ((eq (nth 1 expr) 1)
2035 (math-rwapply-replace-regs (nth 2 expr)))
2036 ((eq (nth 2 expr) -1)
2037 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2038 (math-rwapply-reg-neg (nth 1 expr))
2039 (math-neg (math-rwapply-replace-regs (nth 1 expr)))))
2040 ((eq (nth 2 expr) 1)
2041 (math-rwapply-replace-regs (nth 1 expr)))
2043 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2044 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2045 (cond ((and (eq (car-safe arg1) '/)
2046 (eq (nth 1 arg1) 1))
2047 (list '/ arg2 (nth 2 arg1)))
2048 ((and (eq (car-safe arg2) '/)
2049 (eq (nth 1 arg2) 1))
2050 (list '/ arg1 (nth 2 arg2)))
2051 (t (list '* arg1 arg2)))))))
2053 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2054 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2055 (if (eq (car-safe arg2) '/)
2056 (list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2))
2057 (list '/ arg1 arg2))))
2058 ((and (eq (car expr) 'calcFunc-plain)
2059 (= (length expr) 2))
2060 (if (Math-primp (nth 1 expr))
2062 (if (eq (car (nth 1 expr)) 'calcFunc-register)
2063 (aref math-apply-rw-regs (nth 1 (nth 1 expr)))
2064 (cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs
2065 (cdr (nth 1 expr)))))))
2066 (t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr))))))
2068 (defun math-rwapply-reg-looks-negp (expr)
2069 (if (eq (car-safe expr) 'calcFunc-register)
2070 (math-looks-negp (aref math-apply-rw-regs (nth 1 expr)))
2071 (if (memq (car-safe expr) '(* /))
2072 (or (math-rwapply-reg-looks-negp (nth 1 expr))
2073 (math-rwapply-reg-looks-negp (nth 2 expr))))))
2075 (defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp
2076 (if (eq (car expr) 'calcFunc-register)
2077 (math-neg (math-rwapply-replace-regs expr))
2078 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2079 (math-rwapply-replace-regs (list (car expr)
2080 (math-rwapply-reg-neg (nth 1 expr))
2082 (math-rwapply-replace-regs (list (car expr)
2084 (math-rwapply-reg-neg (nth 2 expr)))))))
2086 (defun math-rwapply-remember (old new)
2087 (let ((varval (symbol-value (nth 2 (car math-apply-rw-ruleset))))
2088 (rules (assq (car-safe old) math-apply-rw-ruleset)))
2089 (if (and (eq (car-safe varval) 'vec)
2090 (not (memq (car-safe old) '(nil schedule + -)))
2093 (setcdr varval (cons (list 'calcFunc-assign
2094 (if (math-rwcomp-no-vars old)
2096 (list 'calcFunc-quote old))
2099 (setcdr rules (cons (list (vector nil old)
2100 (list (list 'same 0 1)
2101 (list 'done new nil))
2105 (provide 'calc-rewr)
2107 ;;; calc-rewr.el ends here