1 ;;; calc-rewr.el --- rewriting functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005 Free Software Foundation, Inc.
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <belanger@truman.edu>
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is distributed in the hope that it will be useful,
12 ;; but WITHOUT ANY WARRANTY. No author or distributor
13 ;; accepts responsibility to anyone for the consequences of using it
14 ;; or for whether it serves any particular purpose or works at all,
15 ;; unless he says so in writing. Refer to the GNU Emacs General Public
16 ;; License for full details.
18 ;; Everyone is granted permission to copy, modify and redistribute
19 ;; GNU Emacs, but only under the conditions described in the
20 ;; GNU Emacs General Public License. A copy of this license is
21 ;; supposed to have been given to you along with GNU Emacs so you
22 ;; can know your rights and responsibilities. It should be in a
23 ;; file named COPYING. Among other things, the copyright notice
24 ;; and this notice must be preserved on all copies.
30 ;; This file is autoloaded from calc-ext.el.
35 (defvar math-rewrite-default-iters 100)
37 ;; The variable calc-rewr-sel is local to calc-rewrite-selection and
38 ;; calc-rewrite, but is used by calc-locate-selection-marker.
39 (defvar calc-rewr-sel)
41 (defun calc-rewrite-selection (rules-str &optional many prefix)
42 (interactive "sRewrite rule(s): \np")
45 (let* ((num (max 1 (calc-locate-cursor-element (point))))
49 (entry (calc-top num 'entry))
51 (calc-rewr-sel (calc-auto-selection entry))
52 (math-rewrite-selections t)
53 (math-rewrite-default-iters 1))
54 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
56 (error "Can't use same stack entry for formula and rules")
57 (setq rules (calc-top-n 1 t)
59 (setq rules (if (stringp rules-str)
60 (math-read-exprs rules-str) rules-str))
61 (if (eq (car-safe rules) 'error)
62 (error "Bad format in expression: %s" (nth 1 rules)))
63 (if (= (length rules) 1)
64 (setq rules (car rules))
65 (setq rules (cons 'vec rules)))
66 (or (memq (car-safe rules) '(vec var calcFunc-assign
68 (let ((rhs (math-read-expr
69 (read-string (concat "Rewrite from: " rules-str
71 (if (eq (car-safe rhs) 'error)
72 (error "Bad format in expression: %s" (nth 1 rhs)))
73 (setq rules (list 'calcFunc-assign rules rhs))))
74 (or (eq (car-safe rules) 'var)
75 (calc-record rules "rule")))
77 (setq many '(var inf var-inf))
78 (if many (setq many (prefix-numeric-value many))))
80 (setq expr (calc-replace-sub-formula (car entry)
82 (list 'calcFunc-select calc-rewr-sel)))
83 (setq expr (car entry)
85 math-rewrite-selections nil))
86 (setq expr (calc-encase-atoms
92 expr (calc-locate-select-marker expr))
93 (or (consp calc-rewr-sel) (setq calc-rewr-sel nil))
94 (if pop-rules (calc-pop-stack 1))
95 (calc-pop-push-record-list 1 (or prefix "rwrt") (list expr)
96 (- num (if pop-rules 1 0))
97 (list (and reselect calc-rewr-sel))))
100 (defun calc-locate-select-marker (expr)
101 (if (Math-primp expr)
103 (if (and (eq (car expr) 'calcFunc-select)
106 (setq calc-rewr-sel (if calc-rewr-sel t (nth 1 expr)))
109 (mapcar 'calc-locate-select-marker (cdr expr))))))
113 (defun calc-rewrite (rules-str many)
114 (interactive "sRewrite rule(s): \nP")
117 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
118 (setq expr (calc-top-n 2)
119 rules (calc-top-n 1 t)
121 (setq rules (if (stringp rules-str)
122 (math-read-exprs rules-str) rules-str))
123 (if (eq (car-safe rules) 'error)
124 (error "Bad format in expression: %s" (nth 1 rules)))
125 (if (= (length rules) 1)
126 (setq rules (car rules))
127 (setq rules (cons 'vec rules)))
128 (or (memq (car-safe rules) '(vec var calcFunc-assign
130 (let ((rhs (math-read-expr
131 (read-string (concat "Rewrite from: " rules-str
133 (if (eq (car-safe rhs) 'error)
134 (error "Bad format in expression: %s" (nth 1 rhs)))
135 (setq rules (list 'calcFunc-assign rules rhs))))
136 (or (eq (car-safe rules) 'var)
137 (calc-record rules "rule"))
138 (setq expr (calc-top-n 1)
141 (setq many '(var inf var-inf))
142 (if many (setq many (prefix-numeric-value many))))
143 (setq expr (calc-normalize (math-rewrite expr rules many)))
145 (setq expr (calc-locate-select-marker expr)))
146 (calc-pop-push-record-list n "rwrt" (list expr)))
149 (defun calc-match (pat &optional interactive)
150 (interactive "sPattern: \np")
153 (if (or (null pat) (equal pat "") (equal pat "$"))
154 (setq expr (calc-top-n 2)
157 (if interactive (setq calc-previous-alg-entry pat))
158 (setq pat (if (stringp pat) (math-read-expr pat) pat))
159 (if (eq (car-safe pat) 'error)
160 (error "Bad format in expression: %s" (nth 1 pat)))
161 (if (not (eq (car-safe pat) 'var))
162 (calc-record pat "pat"))
163 (setq expr (calc-top-n 1)
165 (or (math-vectorp expr) (error "Argument must be a vector"))
166 (if (calc-is-inverse)
167 (calc-enter-result n "mtcn" (math-match-patterns pat expr t))
168 (calc-enter-result n "mtch" (math-match-patterns pat expr nil))))))
171 (defvar math-mt-many)
173 ;; The variable math-rewrite-whole-expr is local to math-rewrite,
174 ;; but is used by math-rewrite-phase
175 (defvar math-rewrite-whole-expr)
177 (defun math-rewrite (math-rewrite-whole-expr rules &optional math-mt-many)
178 (let* ((crules (math-compile-rewrites rules))
179 (heads (math-rewrite-heads math-rewrite-whole-expr))
180 (trace-buffer (get-buffer "*Trace*"))
181 (calc-display-just 'center)
182 (calc-display-origin 39)
183 (calc-line-breaking 78)
184 (calc-line-numbering nil)
185 (calc-show-selections t)
187 (math-mt-func (function
189 (let ((result (math-apply-rewrites x (cdr crules)
194 (let ((fmt (math-format-stack-value
195 (list result nil nil))))
197 (set-buffer trace-buffer)
198 (insert "\nrewrite to\n" fmt "\n"))))
199 (setq heads (math-rewrite-heads result heads t))))
202 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
204 (set-buffer trace-buffer)
205 (setq truncate-lines t)
206 (goto-char (point-max))
207 (insert "\n\nBegin rewriting\n" fmt "\n"))))
208 (or math-mt-many (setq math-mt-many (or (nth 1 (car crules))
209 math-rewrite-default-iters)))
210 (if (equal math-mt-many '(var inf var-inf)) (setq math-mt-many 1000000))
211 (if (equal math-mt-many '(neg (var inf var-inf))) (setq math-mt-many -1000000))
212 (math-rewrite-phase (nth 3 (car crules)))
214 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
216 (set-buffer trace-buffer)
217 (insert "\nDone rewriting"
218 (if (= math-mt-many 0) " (reached iteration limit)" "")
220 math-rewrite-whole-expr))
222 (defun math-rewrite-phase (sched)
223 (while (and sched (/= math-mt-many 0))
224 (if (listp (car sched))
225 (while (let ((save-expr math-rewrite-whole-expr))
226 (math-rewrite-phase (car sched))
227 (not (equal math-rewrite-whole-expr save-expr))))
228 (if (symbolp (car sched))
230 (setq math-rewrite-whole-expr
231 (math-normalize (list (car sched) math-rewrite-whole-expr)))
233 (let ((fmt (math-format-stack-value
234 (list math-rewrite-whole-expr nil nil))))
236 (set-buffer trace-buffer)
238 (substring (symbol-name (car sched)) 9)
240 (let ((math-rewrite-phase (car sched)))
243 (set-buffer trace-buffer)
244 (insert (format "\n(Phase %d)\n" math-rewrite-phase))))
245 (while (let ((save-expr math-rewrite-whole-expr))
246 (setq math-rewrite-whole-expr (math-normalize
247 (math-map-tree-rec math-rewrite-whole-expr)))
248 (not (equal math-rewrite-whole-expr save-expr)))))))
249 (setq sched (cdr sched))))
251 (defun calcFunc-rewrite (expr rules &optional many)
252 (or (null many) (integerp many)
253 (equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf)))
254 (math-reject-arg many 'fixnump))
256 (math-rewrite expr rules (or many 1))
257 (error (math-reject-arg rules (nth 1 err)))))
259 (defun calcFunc-match (pat vec)
260 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
262 (math-match-patterns pat vec nil)
263 (error (math-reject-arg pat (nth 1 err)))))
265 (defun calcFunc-matchnot (pat vec)
266 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
268 (math-match-patterns pat vec t)
269 (error (math-reject-arg pat (nth 1 err)))))
271 (defun math-match-patterns (pat vec &optional not-flag)
273 (crules (math-compile-patterns pat)))
274 (while (setq vec (cdr vec))
275 (if (eq (not (math-apply-rewrites (car vec) crules))
277 (setq newvec (cons (car vec) newvec))))
278 (cons 'vec (nreverse newvec))))
280 (defun calcFunc-matches (expr pat)
282 (if (math-apply-rewrites expr (math-compile-patterns pat))
285 (error (math-reject-arg pat (nth 1 err)))))
287 (defun calcFunc-vmatches (expr pat)
289 (or (math-apply-rewrites expr (math-compile-patterns pat))
291 (error (math-reject-arg pat (nth 1 err)))))
295 ;;; A compiled rule set is an a-list of entries whose cars are functors,
296 ;;; and whose cdrs are lists of rules. If there are rules with no
297 ;;; well-defined head functor, they are included on all lists and also
298 ;;; on an extra list whose car is nil.
300 ;;; The first entry in the a-list is of the form (schedule A B C ...).
302 ;;; Rule list entries take the form (regs prog head phases), where:
304 ;;; regs is a vector of match registers.
306 ;;; prog is a match program (see below).
308 ;;; head is a rare function name appearing in the rule body (but not the
309 ;;; head of the whole rule), or nil if none.
311 ;;; phases is a list of phase numbers for which the rule is enabled.
313 ;;; A match program is a list of match instructions.
315 ;;; In the following, "part" is a register number that contains the
316 ;;; subexpression to be operated on.
318 ;;; Register 0 is the whole expression being matched. The others are
319 ;;; meta-variables in the pattern, temporaries used for matching and
320 ;;; backtracking, and constant expressions.
323 ;;; The selected part must be math-equal to the contents of "reg".
325 ;;; (same-neg part reg)
326 ;;; The selected part must be math-equal to the negative of "reg".
329 ;;; The selected part is copied into "reg". (Rarely used.)
331 ;;; (copy-neg part reg)
332 ;;; The negative of the selected part is copied into "reg".
335 ;;; The selected part must be an integer.
338 ;;; The selected part must be a real.
341 ;;; The selected part must be a constant.
344 ;;; The selected part must "look" negative.
346 ;;; (rel part op reg)
347 ;;; The selected part must satisfy "part op reg", where "op"
348 ;;; is one of the 6 relational ops, and "reg" is a register.
350 ;;; (mod part modulo value)
351 ;;; The selected part must satisfy "part % modulo = value", where
352 ;;; "modulo" and "value" are constants.
354 ;;; (func part head reg1 reg2 ... regn)
355 ;;; The selected part must be an n-ary call to function "head".
356 ;;; The arguments are stored in "reg1" through "regn".
358 ;;; (func-def part head defs reg1 reg2 ... regn)
359 ;;; The selected part must be an n-ary call to function "head".
360 ;;; "Defs" is a list of value/register number pairs for default args.
361 ;;; If a match, assign default values to registers and then skip
362 ;;; immediately over any following "func-def" instructions and
363 ;;; the following "func" instruction. If wrong number of arguments,
364 ;;; proceed to the following "func-def" or "func" instruction.
366 ;;; (func-opt part head defs reg1)
367 ;;; Like func-def with "n=1", except that if the selected part is
368 ;;; not a call to "head", then the part itself successfully matches
369 ;;; "reg1" (and the defaults are assigned).
371 ;;; (try part heads mark reg1 [def])
372 ;;; The selected part must be a function of the correct type which is
373 ;;; associative and/or commutative. "Heads" is a list of acceptable
374 ;;; types. An initial assignment of arguments to "reg1" is tried.
375 ;;; If the program later fails, it backtracks to this instruction
376 ;;; and tries other assignments of arguments to "reg1".
377 ;;; If "def" exists and normal matching fails, backtrack and assign
378 ;;; "part" to "reg1", and "def" to "reg2" in the following "try2".
379 ;;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized.
380 ;;; "mark[0]" points to the argument list; "mark[1]" points to the
381 ;;; current argument; "mark[2]" is 0 if there are two arguments,
382 ;;; 1 if reg1 is matching single arguments, 2 if reg2 is matching
383 ;;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or
384 ;;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must
385 ;;; have two arguments, 1 if phase-2 can be skipped, 2 if full
386 ;;; backtracking is necessary; "mark[4]" is t if the arguments have
387 ;;; been switched from the order given in the original pattern.
390 ;;; Every "try" will be followed by a "try2" whose "try" field is
391 ;;; a pointer to the corresponding "try". The arguments which were
392 ;;; not stored in "reg1" by that "try" are now stored in "reg2".
394 ;;; (alt instr nil mark)
395 ;;; Basic backtracking. Execute the instruction sequence "instr".
396 ;;; If this fails, back up and execute following the "alt" instruction.
397 ;;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence
398 ;;; should execute "end-alt" at the end.
401 ;;; Register success of the first alternative of a previous "alt".
402 ;;; "Ptr" is a pointer to the next instruction following that "alt".
404 ;;; (apply part reg1 reg2)
405 ;;; The selected part must be a function call. The functor
406 ;;; (as a variable name) is stored in "reg1"; the arguments
407 ;;; (as a vector) are stored in "reg2".
409 ;;; (cons part reg1 reg2)
410 ;;; The selected part must be a nonempty vector. The first element
411 ;;; of the vector is stored in "reg1"; the rest of the vector
412 ;;; (as another vector) is stored in "reg2".
414 ;;; (rcons part reg1 reg2)
415 ;;; The selected part must be a nonempty vector. The last element
416 ;;; of the vector is stored in "reg2"; the rest of the vector
417 ;;; (as another vector) is stored in "reg1".
419 ;;; (select part reg)
420 ;;; If the selected part is a unary call to function "select", its
421 ;;; argument is stored in "reg"; otherwise (provided this is an `a r'
422 ;;; and not a `g r' command) the selected part is stored in "reg".
425 ;;; The "expr", with registers substituted, must simplify to
426 ;;; a non-zero value.
429 ;;; Evaluate "expr" and store the result in "reg". Always succeeds.
431 ;;; (done rhs remember)
432 ;;; Rewrite the expression to "rhs", with register substituted.
433 ;;; Normalize; if the result is different from the original
434 ;;; expression, the match has succeeded. This is the last
435 ;;; instruction of every program. If "remember" is non-nil,
436 ;;; record the result of the match as a new literal rule.
439 ;;; Pseudo-functions related to rewrites:
441 ;;; In patterns: quote, plain, condition, opt, apply, cons, select
443 ;;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp,
444 ;;; apply, cons, select
446 ;;; In conditions: let + same as for righthand sides
448 ;;; Some optimizations that would be nice to have:
450 ;;; * Merge registers with disjoint lifetimes.
451 ;;; * Merge constant registers with equivalent values.
453 ;;; * If an argument of a commutative op math-depends neither on the
454 ;;; rest of the pattern nor on any of the conditions, then no backtracking
455 ;;; should be done for that argument. (This won't apply to very many
458 ;;; * If top functor is "select", and its argument is a unique function,
459 ;;; add the rule to the lists for both "select" and that function.
460 ;;; (Currently rules like this go on the "nil" list.)
461 ;;; Same for "func-opt" functions. (Though not urgent for these.)
463 ;;; * Shouldn't evaluate a "let" condition until the end, or until it
464 ;;; would enable another condition to be evaluated.
467 ;;; Some additional features to add / things to think about:
469 ;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)".
471 ;;; * Same for interval forms.
473 ;;; * Have a name(v,pat) pattern which matches pat, and gives the
474 ;;; whole match the name v. Beware of circular structures!
477 (defun math-compile-patterns (pats)
478 (if (and (eq (car-safe pats) 'var)
479 (calc-var-value (nth 2 pats)))
480 (let ((prop (get (nth 2 pats) 'math-pattern-cache)))
482 (put (nth 2 pats) 'math-pattern-cache (setq prop (list nil))))
483 (or (eq (car prop) (symbol-value (nth 2 pats)))
485 (setcdr prop (math-compile-patterns
486 (symbol-value (nth 2 pats))))
487 (setcar prop (symbol-value (nth 2 pats)))))
489 (let ((math-rewrite-whole t))
490 (cdr (math-compile-rewrites (cons
492 (mapcar (function (lambda (x)
494 (if (eq (car-safe pats) 'vec)
498 (defvar math-rewrite-whole nil)
499 (defvar math-make-import-list nil)
501 ;; The variable math-import-list is local to part of math-compile-rewrites,
502 ;; but is also used in a different part, and so the local version could
503 ;; be affected by the non-local version when math-compile-rewrites calls itself.
504 (defvar math-import-list nil)
506 ;; The variables math-regs, math-num-regs, math-prog-last, math-bound-vars,
507 ;; math-conds, math-copy-neg, math-rhs, math-pattern, math-remembering and
508 ;; math-aliased-vars are local to math-compile-rewrites,
509 ;; but are used by many functions math-rwcomp-*, which are called by
510 ;; math-compile-rewrites.
512 (defvar math-num-regs)
513 (defvar math-prog-last)
514 (defvar math-bound-vars)
516 (defvar math-copy-neg)
518 (defvar math-pattern)
519 (defvar math-remembering)
520 (defvar math-aliased-vars)
522 (defun math-compile-rewrites (rules &optional name)
523 (if (eq (car-safe rules) 'var)
524 (let ((prop (get (nth 2 rules) 'math-rewrite-cache))
525 (math-import-list nil)
526 (math-make-import-list t)
528 (or (calc-var-value (nth 2 rules))
529 (error "Rules variable %s has no stored value" (nth 1 rules)))
531 (put (nth 2 rules) 'math-rewrite-cache
532 (setq prop (list (list (cons (nth 2 rules) nil))))))
534 (while (and p (eq (symbol-value (car (car p))) (cdr (car p))))
538 (message "Compiling rule set %s..." (nth 1 rules))
539 (setcdr prop (math-compile-rewrites
540 (symbol-value (nth 2 rules))
542 (message "Compiling rule set %s...done" (nth 1 rules))
543 (setcar prop (cons (cons (nth 2 rules)
544 (symbol-value (nth 2 rules)))
547 (if (or (not (eq (car-safe rules) 'vec))
548 (and (memq (length rules) '(3 4))
550 (while (and (setq p (cdr p))
551 (memq (car-safe (car p))
558 calcFunc-iterations))))
560 (setq rules (list rules))
561 (setq rules (cdr rules)))
562 (if (assq 'calcFunc-import rules)
563 (let ((pp (setq rules (copy-sequence rules)))
565 (while (setq p (car (cdr pp)))
566 (if (eq (car-safe p) 'calcFunc-import)
568 (setcdr pp (cdr (cdr pp)))
569 (or (and (eq (car-safe (nth 1 p)) 'var)
570 (setq part (calc-var-value (nth 2 (nth 1 p))))
571 (memq (car-safe part) '(vec
573 calcFunc-condition)))
574 (error "Argument of import() must be a rules variable"))
575 (if math-make-import-list
576 (setq math-import-list
577 (cons (cons (nth 2 (nth 1 p))
578 (symbol-value (nth 2 (nth 1 p))))
580 (while (setq p (cdr (cdr p)))
582 (error "import() must have odd number of arguments"))
583 (setq part (math-rwcomp-substitute part
585 (if (eq (car-safe part) 'vec)
586 (setq part (cdr part))
587 (setq part (list part)))
588 (setcdr pp (append part (cdr pp))))
589 (setq pp (cdr pp))))))
595 (math-iterations nil)
597 (math-all-phases nil)
598 (math-remembering nil)
599 math-pattern math-rhs math-conds)
602 ((and (eq (car-safe (car rules)) 'calcFunc-iterations)
603 (= (length (car rules)) 2))
604 (or (integerp (nth 1 (car rules)))
605 (equal (nth 1 (car rules)) '(var inf var-inf))
606 (equal (nth 1 (car rules)) '(neg (var inf var-inf)))
607 (error "Invalid argument for iterations(n)"))
609 (setq math-iterations (nth 1 (car rules)))))
610 ((eq (car-safe (car rules)) 'calcFunc-schedule)
612 (setq math-schedule (math-parse-schedule (cdr (car rules))))))
613 ((eq (car-safe (car rules)) 'calcFunc-phase)
614 (setq math-phases (cdr (car rules)))
615 (if (equal math-phases '((var all var-all)))
616 (setq math-phases nil))
617 (let ((p math-phases))
619 (or (integerp (car p))
620 (error "Phase numbers must be small integers"))
621 (or (memq (car p) math-all-phases)
622 (setq math-all-phases (cons (car p) math-all-phases)))
624 ((or (and (eq (car-safe (car rules)) 'vec)
625 (cdr (cdr (car rules)))
626 (not (nthcdr 4 (car rules)))
627 (setq math-conds (nth 3 (car rules))
628 math-rhs (nth 2 (car rules))
629 math-pattern (nth 1 (car rules))))
632 math-pattern (car rules))
633 (while (and (eq (car-safe math-pattern) 'calcFunc-condition)
634 (= (length math-pattern) 3))
635 (let ((cond (nth 2 math-pattern)))
636 (setq math-conds (if math-conds
637 (list 'calcFunc-land math-conds cond)
639 math-pattern (nth 1 math-pattern))))
640 (and (eq (car-safe math-pattern) 'calcFunc-assign)
641 (= (length math-pattern) 3)
642 (setq math-rhs (nth 2 math-pattern)
643 math-pattern (nth 1 math-pattern)))))
644 (let* ((math-prog (list nil))
645 (math-prog-last math-prog)
647 (math-regs (list (list nil 0 nil nil)))
648 (math-bound-vars nil)
649 (math-aliased-vars nil)
651 (setq math-conds (and math-conds (math-flatten-lands math-conds)))
652 (math-rwcomp-pattern math-pattern 0)
654 (let ((expr (car math-conds)))
655 (setq math-conds (cdr math-conds))
656 (math-rwcomp-cond-instr expr)))
657 (math-rwcomp-instr 'done
671 (math-rwcomp-register-expr
674 (math-rwcomp-match-vars math-rhs))
676 (setq math-prog (cdr math-prog))
677 (let* ((heads (math-rewrite-heads math-pattern))
680 (mapcar (function (lambda (x) (nth 3 x)))
685 (head (and (not (Math-primp math-pattern))
686 (not (and (eq (car (car math-prog)) 'try)
687 (nth 5 (car math-prog))))
688 (not (memq (car (car math-prog)) '(func-opt
692 (if (memq (car (car math-prog)) '(func
694 (nth 2 (car math-prog))
695 (if (eq (car math-pattern) 'calcFunc-quote)
696 (car-safe (nth 1 math-pattern))
697 (car math-pattern))))))
700 (if (setq found (assq (car heads) all-heads))
701 (setcdr found (1+ (cdr found)))
702 (setq all-heads (cons (cons (car heads) 1) all-heads)))
703 (setq heads (cdr heads))))
704 (if (eq head '-) (setq head '+))
705 (if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec))
708 (nconc (or (assq head rule-set)
709 (car (setq rule-set (cons (cons head
715 (nconc (or (assq '/ rule-set)
716 (car (setq rule-set (cons (cons
722 (setq nil-rules (nconc nil-rules (list rule)))
723 (let ((ptr rule-set))
725 (nconc (car ptr) (list rule))
726 (setq ptr (cdr ptr))))))))
728 (error "Rewrite rule set must be a vector of A := B rules")))
729 (setq rules (cdr rules)))
731 (setq rule-set (cons (cons nil nil-rules) rule-set)))
732 (setq all-heads (mapcar 'car
733 (sort all-heads (function
735 (< (cdr x) (cdr y)))))))
739 (setq rule (cdr (car set)))
741 (if (consp (setq heads (nth 2 (car rule))))
743 (setq heads (delq (car (car set)) heads)
745 (while (and ptr (not (memq (car ptr) heads)))
746 (setq ptr (cdr ptr)))
747 (setcar (nthcdr 2 (car rule)) (car ptr))))
748 (setq rule (cdr rule)))
749 (setq set (cdr set))))
750 (let ((plus (assq '+ rule-set)))
752 (setq rule-set (cons (cons '- (cdr plus)) rule-set))))
753 (cons (list 'schedule math-iterations name
755 (sort math-all-phases '<)
759 (defun math-flatten-lands (expr)
760 (if (eq (car-safe expr) 'calcFunc-land)
761 (append (math-flatten-lands (nth 1 expr))
762 (math-flatten-lands (nth 2 expr)))
765 ;; The variables math-rewrite-heads-heads (i.e.; heads for math-rewrite-heads)
766 ;; math-rewrite-heads-blanks and math-rewrite-heads-skips are local to
767 ;; math-rewrite-heads, but used by math-rewrite-heads-rec, which is called by
768 ;; math-rewrite-heads.
769 (defvar math-rewrite-heads-heads)
770 (defvar math-rewrite-heads-skips)
771 (defvar math-rewrite-heads-blanks)
773 (defun math-rewrite-heads (expr &optional more all)
774 (let ((math-rewrite-heads-heads more)
775 (math-rewrite-heads-skips (and (not all)
776 '(calcFunc-apply calcFunc-condition calcFunc-opt
777 calcFunc-por calcFunc-pnot)))
778 (math-rewrite-heads-blanks (and (not all)
779 '(calcFunc-quote calcFunc-plain calcFunc-select
780 calcFunc-cons calcFunc-rcons
782 (or (Math-primp expr)
783 (math-rewrite-heads-rec expr))
784 math-rewrite-heads-heads))
786 (defun math-rewrite-heads-rec (expr)
787 (or (memq (car expr) math-rewrite-heads-skips)
789 (or (memq (car expr) math-rewrite-heads-heads)
790 (memq (car expr) math-rewrite-heads-blanks)
791 (memq 'algebraic (get (car expr) 'math-rewrite-props))
792 (setq math-rewrite-heads-heads (cons (car expr) math-rewrite-heads-heads)))
793 (while (setq expr (cdr expr))
794 (or (Math-primp (car expr))
795 (math-rewrite-heads-rec (car expr)))))))
797 (defun math-parse-schedule (sched)
803 (math-parse-schedule (cdr s))
804 (if (eq (car-safe s) 'var)
805 (math-var-to-calcFunc s)
806 (error "Improper component in rewrite schedule"))))))
809 (defun math-rwcomp-match-vars (expr)
810 (if (Math-primp expr)
811 (if (eq (car-safe expr) 'var)
812 (let ((entry (assq (nth 2 expr) math-regs)))
814 (math-rwcomp-register-expr (nth 1 entry))
817 (if (and (eq (car expr) 'calcFunc-quote)
819 (math-rwcomp-match-vars (nth 1 expr))
820 (if (and (eq (car expr) 'calcFunc-plain)
822 (not (Math-primp (nth 1 expr))))
824 (cons (car (nth 1 expr))
825 (mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr)))))
827 (mapcar 'math-rwcomp-match-vars (cdr expr)))))))
829 (defun math-rwcomp-register-expr (num)
830 (let ((entry (nth (1- (- math-num-regs num)) math-regs)))
832 (list 'neg (list 'calcFunc-register (nth 1 entry)))
833 (list 'calcFunc-register (nth 1 entry)))))
835 ;; The variables math-rwcomp-subst-old, math-rwcomp-subst-new,
836 ;; math-rwcomp-subst-old-func and math-rwcomp-subst-new-func
837 ;; are local to math-rwcomp-substitute, but are used by
838 ;; math-rwcomp-subst-rec, which is called by math-rwcomp-substitute.
839 (defvar math-rwcomp-subst-new)
840 (defvar math-rwcomp-subst-old)
841 (defvar math-rwcomp-subst-new-func)
842 (defvar math-rwcomp-subst-old-func)
844 (defun math-rwcomp-substitute (expr math-rwcomp-subst-old math-rwcomp-subst-new)
845 (if (and (eq (car-safe math-rwcomp-subst-old) 'var)
846 (memq (car-safe math-rwcomp-subst-new) '(var calcFunc-lambda)))
847 (let ((math-rwcomp-subst-old-func (math-var-to-calcFunc math-rwcomp-subst-old))
848 (math-rwcomp-subst-new-func (math-var-to-calcFunc math-rwcomp-subst-new)))
849 (math-rwcomp-subst-rec expr))
850 (let ((math-rwcomp-subst-old-func nil))
851 (math-rwcomp-subst-rec expr))))
853 (defun math-rwcomp-subst-rec (expr)
854 (cond ((equal expr math-rwcomp-subst-old) math-rwcomp-subst-new)
855 ((Math-primp expr) expr)
856 (t (if (eq (car expr) math-rwcomp-subst-old-func)
857 (math-build-call math-rwcomp-subst-new-func
858 (mapcar 'math-rwcomp-subst-rec
861 (mapcar 'math-rwcomp-subst-rec (cdr expr)))))))
863 (defvar math-rwcomp-tracing nil)
865 (defun math-rwcomp-trace (instr)
866 (when math-rwcomp-tracing
867 (terpri) (princ instr))
870 (defun math-rwcomp-instr (&rest instr)
871 (setcdr math-prog-last
872 (setq math-prog-last (list (math-rwcomp-trace instr)))))
874 (defun math-rwcomp-multi-instr (tail &rest instr)
875 (setcdr math-prog-last
876 (setq math-prog-last (list (math-rwcomp-trace (append instr tail))))))
878 (defun math-rwcomp-bind-var (reg var)
879 (setcar (math-rwcomp-reg-entry reg) (nth 2 var))
880 (setq math-bound-vars (cons (nth 2 var) math-bound-vars))
881 (math-rwcomp-do-conditions))
883 (defun math-rwcomp-unbind-vars (mark)
884 (while (not (eq math-bound-vars mark))
885 (setcar (assq (car math-bound-vars) math-regs) nil)
886 (setq math-bound-vars (cdr math-bound-vars))))
888 (defun math-rwcomp-do-conditions ()
889 (let ((cond math-conds))
891 (if (math-rwcomp-all-regs-done (car cond))
892 (let ((expr (car cond)))
893 (setq math-conds (delq (car cond) math-conds))
895 (math-rwcomp-cond-instr expr)))
896 (setq cond (cdr cond)))))
898 (defun math-rwcomp-cond-instr (expr)
900 (cond ((and (eq (car-safe expr) 'calcFunc-matches)
902 (eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr))))
904 (math-rwcomp-pattern (nth 2 expr) (nth 1 arg)))
905 ((math-numberp (setq expr (math-rwcomp-match-vars expr)))
906 (if (Math-zerop expr)
907 (math-rwcomp-instr 'backtrack)))
908 ((and (eq (car expr) 'calcFunc-let)
910 (let ((reg (math-rwcomp-reg)))
911 (math-rwcomp-instr 'let reg (nth 2 expr))
912 (math-rwcomp-pattern (nth 1 expr) reg)))
913 ((and (eq (car expr) 'calcFunc-let)
915 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
916 (= (length (nth 1 expr)) 3))
917 (let ((reg (math-rwcomp-reg)))
918 (math-rwcomp-instr 'let reg (nth 2 (nth 1 expr)))
919 (math-rwcomp-pattern (nth 1 (nth 1 expr)) reg)))
920 ((and (setq op (cdr (assq (car-safe expr)
921 '( (calcFunc-integer . integer)
922 (calcFunc-real . real)
923 (calcFunc-constant . constant)
924 (calcFunc-negative . negative) ))))
926 (or (and (eq (car-safe (nth 1 expr)) 'neg)
927 (memq op '(integer real constant))
928 (setq arg (nth 1 (nth 1 expr))))
929 (setq arg (nth 1 expr)))
930 (eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register))
931 (math-rwcomp-instr op (nth 1 arg)))
932 ((and (assq (car-safe expr) calc-tweak-eqn-table)
934 (eq (car-safe (nth 1 expr)) 'calcFunc-register))
935 (if (math-constp (nth 2 expr))
936 (let ((reg (math-rwcomp-reg)))
937 (setcar (nthcdr 3 (car math-regs)) (nth 2 expr))
938 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
940 (if (eq (car (nth 2 expr)) 'calcFunc-register)
941 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
942 (car expr) (nth 1 (nth 2 expr)))
943 (math-rwcomp-instr 'cond expr))))
944 ((and (eq (car-safe expr) 'calcFunc-eq)
946 (eq (car-safe (nth 1 expr)) '%)
947 (eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register)
948 (math-constp (nth 2 (nth 1 expr)))
949 (math-constp (nth 2 expr)))
950 (math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr)))
951 (nth 2 (nth 1 expr)) (nth 2 expr)))
952 ((equal expr '(var remember var-remember))
953 (setq math-remembering 1))
954 ((and (eq (car-safe expr) 'calcFunc-remember)
956 (setq math-remembering (if math-remembering
958 math-remembering (nth 1 expr))
960 (t (math-rwcomp-instr 'cond expr)))))
962 (defun math-rwcomp-same-instr (reg1 reg2 neg)
963 (math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
964 (nth 2 (math-rwcomp-reg-entry reg2)))
970 (defun math-rwcomp-copy-instr (reg1 reg2 neg)
971 (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
972 (nth 2 (math-rwcomp-reg-entry reg2)))
974 (math-rwcomp-instr 'copy-neg reg1 reg2)
976 (math-rwcomp-instr 'copy reg1 reg2))))
978 (defun math-rwcomp-reg ()
981 (setq math-regs (cons (list nil math-num-regs nil 0) math-regs)
982 math-num-regs (1+ math-num-regs))))
984 (defun math-rwcomp-reg-entry (num)
985 (nth (1- (- math-num-regs num)) math-regs))
988 (defun math-rwcomp-pattern (expr part &optional not-direct)
989 (cond ((or (math-rwcomp-no-vars expr)
990 (and (eq (car expr) 'calcFunc-quote)
992 (setq expr (nth 1 expr))))
993 (if (eq (car-safe expr) 'calcFunc-register)
994 (math-rwcomp-same-instr part (nth 1 expr) nil)
995 (let ((reg (math-rwcomp-reg)))
996 (setcar (nthcdr 3 (car math-regs)) expr)
997 (math-rwcomp-same-instr part reg nil))))
998 ((eq (car expr) 'var)
999 (let ((entry (assq (nth 2 expr) math-regs)))
1001 (math-rwcomp-same-instr part (nth 1 entry) nil)
1003 (let ((reg (math-rwcomp-reg)))
1004 (math-rwcomp-pattern expr reg)
1005 (math-rwcomp-copy-instr part reg nil))
1006 (if (setq entry (assq (nth 2 expr) math-aliased-vars))
1008 (setcar (math-rwcomp-reg-entry (nth 1 entry))
1011 (math-rwcomp-copy-instr part (nth 1 entry) nil))
1012 (math-rwcomp-bind-var part expr))))))
1013 ((and (eq (car expr) 'calcFunc-select)
1014 (= (length expr) 2))
1015 (let ((reg (math-rwcomp-reg)))
1016 (math-rwcomp-instr 'select part reg)
1017 (math-rwcomp-pattern (nth 1 expr) reg)))
1018 ((and (eq (car expr) 'calcFunc-opt)
1019 (memq (length expr) '(2 3)))
1020 (error "opt( ) occurs in context where it is not allowed"))
1021 ((eq (car expr) 'neg)
1022 (if (eq (car (nth 1 expr)) 'var)
1023 (let ((entry (assq (nth 2 (nth 1 expr)) math-regs)))
1025 (math-rwcomp-same-instr part (nth 1 entry) t)
1027 (let ((reg (math-rwcomp-best-reg (nth 1 expr))))
1028 (math-rwcomp-copy-instr part reg t)
1029 (math-rwcomp-pattern (nth 1 expr) reg))
1030 (setcar (cdr (cdr (math-rwcomp-reg-entry part))) t)
1031 (math-rwcomp-pattern (nth 1 expr) part))))
1032 (if (math-rwcomp-is-algebraic (nth 1 expr))
1033 (math-rwcomp-cond-instr (list 'calcFunc-eq
1034 (math-rwcomp-register-expr part)
1036 (let ((reg (math-rwcomp-reg)))
1037 (math-rwcomp-instr 'func part 'neg reg)
1038 (math-rwcomp-pattern (nth 1 expr) reg)))))
1039 ((and (eq (car expr) 'calcFunc-apply)
1040 (= (length expr) 3))
1041 (let ((reg1 (math-rwcomp-reg))
1042 (reg2 (math-rwcomp-reg)))
1043 (math-rwcomp-instr 'apply part reg1 reg2)
1044 (math-rwcomp-pattern (nth 1 expr) reg1)
1045 (math-rwcomp-pattern (nth 2 expr) reg2)))
1046 ((and (eq (car expr) 'calcFunc-cons)
1047 (= (length expr) 3))
1048 (let ((reg1 (math-rwcomp-reg))
1049 (reg2 (math-rwcomp-reg)))
1050 (math-rwcomp-instr 'cons part reg1 reg2)
1051 (math-rwcomp-pattern (nth 1 expr) reg1)
1052 (math-rwcomp-pattern (nth 2 expr) reg2)))
1053 ((and (eq (car expr) 'calcFunc-rcons)
1054 (= (length expr) 3))
1055 (let ((reg1 (math-rwcomp-reg))
1056 (reg2 (math-rwcomp-reg)))
1057 (math-rwcomp-instr 'rcons part reg1 reg2)
1058 (math-rwcomp-pattern (nth 1 expr) reg1)
1059 (math-rwcomp-pattern (nth 2 expr) reg2)))
1060 ((and (eq (car expr) 'calcFunc-condition)
1061 (>= (length expr) 3))
1062 (math-rwcomp-pattern (nth 1 expr) part)
1063 (setq expr (cdr expr))
1064 (while (setq expr (cdr expr))
1065 (let ((cond (math-flatten-lands (car expr))))
1067 (if (math-rwcomp-all-regs-done (car cond))
1068 (math-rwcomp-cond-instr (car cond))
1069 (setq math-conds (cons (car cond) math-conds)))
1070 (setq cond (cdr cond))))))
1071 ((and (eq (car expr) 'calcFunc-pand)
1072 (= (length expr) 3))
1073 (math-rwcomp-pattern (nth 1 expr) part)
1074 (math-rwcomp-pattern (nth 2 expr) part))
1075 ((and (eq (car expr) 'calcFunc-por)
1076 (= (length expr) 3))
1077 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1078 (let ((math-conds nil)
1079 (head math-prog-last)
1080 (mark math-bound-vars)
1082 (math-rwcomp-pattern (nth 1 expr) part t)
1083 (let ((amark math-aliased-vars)
1084 (math-aliased-vars math-aliased-vars)
1085 (tail math-prog-last)
1088 (while (not (eq p mark))
1089 (setq entry (assq (car p) math-regs)
1090 math-aliased-vars (cons (list (car p) (nth 1 entry) nil)
1093 (setcar (math-rwcomp-reg-entry (nth 1 entry)) nil))
1094 (setcar (cdr (car head)) (cdr head))
1096 (setq math-prog-last head)
1097 (math-rwcomp-pattern (nth 2 expr) part)
1098 (math-rwcomp-instr 'same 0 0)
1099 (setcdr tail math-prog-last)
1100 (setq p math-aliased-vars)
1101 (while (not (eq p amark))
1103 (setcar (math-rwcomp-reg-entry (nth 1 (car p)))
1106 (math-rwcomp-do-conditions))
1107 ((and (eq (car expr) 'calcFunc-pnot)
1108 (= (length expr) 2))
1109 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1110 (let ((head math-prog-last)
1111 (mark math-bound-vars))
1112 (math-rwcomp-pattern (nth 1 expr) part)
1113 (math-rwcomp-unbind-vars mark)
1114 (math-rwcomp-instr 'end-alt head)
1115 (math-rwcomp-instr 'backtrack)
1116 (setcar (cdr (car head)) (cdr head))
1118 (setq math-prog-last head)))
1119 (t (let ((props (get (car expr) 'math-rewrite-props)))
1120 (if (and (eq (car expr) 'calcFunc-plain)
1122 (not (math-primp (nth 1 expr))))
1123 (setq expr (nth 1 expr))) ; but "props" is still nil
1124 (if (and (memq 'algebraic props)
1125 (math-rwcomp-is-algebraic expr))
1126 (math-rwcomp-cond-instr (list 'calcFunc-eq
1127 (math-rwcomp-register-expr part)
1129 (if (and (memq 'commut props)
1130 (= (length expr) 3))
1131 (let ((arg1 (nth 1 expr))
1133 try1 def code head (flip nil))
1134 (if (eq (car expr) '-)
1135 (setq arg2 (math-rwcomp-neg arg2)))
1136 (setq arg1 (cons arg1 (math-rwcomp-best-reg arg1))
1137 arg2 (cons arg2 (math-rwcomp-best-reg arg2)))
1138 (or (math-rwcomp-order arg1 arg2)
1139 (setq def arg1 arg1 arg2 arg2 def flip t))
1140 (if (math-rwcomp-optional-arg (car expr) arg1)
1141 (error "Too many opt( ) arguments in this context"))
1142 (setq def (math-rwcomp-optional-arg (car expr) arg2)
1143 head (if (memq (car expr) '(+ -))
1145 (if (eq (car expr) '*)
1148 code (if (math-rwcomp-is-constrained
1150 (if (math-rwcomp-is-constrained
1154 (math-rwcomp-multi-instr (and def (list def))
1156 (vector nil nil nil code flip)
1158 (setq try1 (car math-prog-last))
1159 (math-rwcomp-pattern (car arg1) (cdr arg1))
1160 (math-rwcomp-instr 'try2 try1 (cdr arg2))
1161 (if (and (= part 0) (not def) (not math-rewrite-whole)
1162 (not (eq math-rhs t))
1163 (setq def (get (car expr)
1164 'math-rewrite-default)))
1165 (let ((reg1 (math-rwcomp-reg))
1166 (reg2 (math-rwcomp-reg)))
1167 (if (= (aref (nth 3 try1) 3) 0)
1168 (aset (nth 3 try1) 3 1))
1169 (math-rwcomp-instr 'try (cdr arg2)
1170 (if (equal head '(* /))
1177 (setq try1 (car math-prog-last))
1178 (math-rwcomp-pattern (car arg2) reg1)
1179 (math-rwcomp-instr 'try2 try1 reg2)
1180 (setq math-rhs (list (if (eq (car expr) '-)
1183 (list 'calcFunc-register
1185 (math-rwcomp-pattern (car arg2) (cdr arg2))))
1186 (let* ((args (mapcar (function
1188 (cons x (math-rwcomp-best-reg x))))
1190 (args2 (copy-sequence args))
1191 (argp (reverse args2))
1195 (let ((def (math-rwcomp-optional-arg (car expr)
1199 (setq args2 (delq (car argp) args2)
1200 defs (cons (cons def (cdr (car argp)))
1202 (math-rwcomp-multi-instr
1204 (if (or (and (memq 'unary1 props)
1205 (= (length args2) 1)
1206 (eq (car args2) (car args)))
1207 (and (memq 'unary2 props)
1209 (eq (car args2) (nth 1 args))))
1214 (setq argp (cdr argp)))
1215 (math-rwcomp-multi-instr (mapcar 'cdr args)
1216 'func part (car expr))
1217 (setq args (sort args 'math-rwcomp-order))
1219 (math-rwcomp-pattern (car (car args)) (cdr (car args)))
1221 args (cdr args))))))))))
1223 (defun math-rwcomp-best-reg (x)
1224 (or (and (eq (car-safe x) 'var)
1225 (let ((entry (assq (nth 2 x) math-aliased-vars)))
1228 (not (nth 2 (math-rwcomp-reg-entry (nth 1 entry))))
1230 (setcar (cdr (cdr entry)) t)
1234 (defun math-rwcomp-all-regs-done (expr)
1235 (if (Math-primp expr)
1236 (or (not (eq (car-safe expr) 'var))
1237 (assq (nth 2 expr) math-regs)
1238 (eq (nth 2 expr) 'var-remember)
1239 (math-const-var expr))
1240 (if (and (eq (car expr) 'calcFunc-let)
1241 (= (length expr) 3))
1242 (math-rwcomp-all-regs-done (nth 2 expr))
1243 (if (and (eq (car expr) 'calcFunc-let)
1245 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
1246 (= (length (nth 1 expr)) 3))
1247 (math-rwcomp-all-regs-done (nth 2 (nth 1 expr)))
1248 (while (and (setq expr (cdr expr))
1249 (math-rwcomp-all-regs-done (car expr))))
1252 (defun math-rwcomp-no-vars (expr)
1253 (if (Math-primp expr)
1254 (or (not (eq (car-safe expr) 'var))
1255 (math-const-var expr))
1256 (and (not (memq (car expr) '(calcFunc-condition
1257 calcFunc-select calcFunc-quote
1258 calcFunc-plain calcFunc-opt
1259 calcFunc-por calcFunc-pand
1260 calcFunc-pnot calcFunc-apply
1261 calcFunc-cons calcFunc-rcons)))
1263 (while (and (setq expr (cdr expr))
1264 (math-rwcomp-no-vars (car expr))))
1267 (defun math-rwcomp-is-algebraic (expr)
1268 (if (Math-primp expr)
1269 (or (not (eq (car-safe expr) 'var))
1270 (math-const-var expr)
1271 (assq (nth 2 expr) math-regs))
1272 (and (memq 'algebraic (get (car expr) 'math-rewrite-props))
1274 (while (and (setq expr (cdr expr))
1275 (math-rwcomp-is-algebraic (car expr))))
1278 (defun math-rwcomp-is-constrained (expr not-these)
1279 (if (Math-primp expr)
1280 (not (eq (car-safe expr) 'var))
1281 (if (eq (car expr) 'calcFunc-plain)
1282 (math-rwcomp-is-constrained (nth 1 expr) not-these)
1283 (not (or (memq (car expr) '(neg calcFunc-select))
1284 (memq (car expr) not-these)
1285 (and (memq 'commut (get (car expr) 'math-rewrite-props))
1286 (or (eq (car-safe (nth 1 expr)) 'calcFunc-opt)
1287 (eq (car-safe (nth 2 expr)) 'calcFunc-opt))))))))
1289 (defun math-rwcomp-optional-arg (head argp)
1290 (let ((arg (car argp)))
1291 (if (eq (car-safe arg) 'calcFunc-opt)
1292 (and (memq (length arg) '(2 3))
1294 (or (eq (car-safe (nth 1 arg)) 'var)
1295 (error "First argument of opt( ) must be a variable"))
1296 (setcar argp (nth 1 arg))
1297 (if (= (length arg) 2)
1298 (or (get head 'math-rewrite-default)
1299 (error "opt( ) must include a default in this context"))
1301 (and (eq (car-safe arg) 'neg)
1302 (let* ((part (list (nth 1 arg)))
1303 (partp (math-rwcomp-optional-arg head part)))
1305 (setcar argp (math-rwcomp-neg (car part)))
1306 (math-neg partp)))))))
1308 (defun math-rwcomp-neg (expr)
1309 (if (memq (car-safe expr) '(* /))
1310 (if (eq (car-safe (nth 1 expr)) 'var)
1311 (list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr))
1312 (if (eq (car-safe (nth 2 expr)) 'var)
1313 (list (car expr) (nth 1 expr) (list 'neg (nth 2 expr)))
1317 (defun math-rwcomp-assoc-args (expr)
1318 (if (and (eq (car-safe (nth 1 expr)) (car expr))
1319 (= (length (nth 1 expr)) 3))
1320 (math-rwcomp-assoc-args (nth 1 expr)))
1321 (if (and (eq (car-safe (nth 2 expr)) (car expr))
1322 (= (length (nth 2 expr)) 3))
1323 (math-rwcomp-assoc-args (nth 2 expr))))
1325 (defun math-rwcomp-addsub-args (expr)
1326 (if (memq (car-safe (nth 1 expr)) '(+ -))
1327 (math-rwcomp-addsub-args (nth 1 expr)))
1328 (if (eq (car expr) '-)
1330 (if (eq (car-safe (nth 2 expr)) '+)
1331 (math-rwcomp-addsub-args (nth 2 expr)))))
1333 (defun math-rwcomp-order (a b)
1334 (< (math-rwcomp-priority (car a))
1335 (math-rwcomp-priority (car b))))
1337 ;;; Order of priority: 0 Constants and other exact matches (first)
1338 ;;; 10 Functions (except below)
1339 ;;; 20 Meta-variables which occur more than once
1340 ;;; 30 Algebraic functions
1341 ;;; 40 Commutative/associative functions
1342 ;;; 50 Meta-variables which occur only once
1343 ;;; +100 for every "!!!" (pnot) in the pattern
1344 ;;; 10000 Optional arguments (last)
1346 (defun math-rwcomp-priority (expr)
1347 (+ (math-rwcomp-count-pnots expr)
1348 (cond ((eq (car-safe expr) 'calcFunc-opt)
1350 ((math-rwcomp-no-vars expr)
1352 ((eq (car expr) 'calcFunc-quote)
1354 ((eq (car expr) 'var)
1355 (if (assq (nth 2 expr) math-regs)
1357 (if (= (math-rwcomp-count-refs expr) 1)
1360 (t (let ((props (get (car expr) 'math-rewrite-props)))
1361 (if (or (memq 'commut props)
1362 (memq 'assoc props))
1364 (if (memq 'algebraic props)
1368 (defun math-rwcomp-count-refs (var)
1369 (let ((count (or (math-expr-contains-count math-pattern var) 0))
1372 (if (eq (car-safe (car p)) 'calcFunc-let)
1373 (if (= (length (car p)) 3)
1374 (setq count (+ count
1375 (or (math-expr-contains-count (nth 2 (car p)) var)
1377 (if (and (= (length (car p)) 2)
1378 (eq (car-safe (nth 1 (car p))) 'calcFunc-assign)
1379 (= (length (nth 1 (car p))) 3))
1380 (setq count (+ count
1381 (or (math-expr-contains-count
1382 (nth 2 (nth 1 (car p))) var) 0))))))
1386 (defun math-rwcomp-count-pnots (expr)
1387 (if (Math-primp expr)
1389 (if (eq (car expr) 'calcFunc-pnot)
1392 (while (setq expr (cdr expr))
1393 (setq count (+ count (math-rwcomp-count-pnots (car expr)))))
1396 ;;; In the current implementation, all associative functions must
1397 ;;; also be commutative.
1399 (put '+ 'math-rewrite-props '(algebraic assoc commut))
1400 (put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below
1401 (put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below
1402 (put '/ 'math-rewrite-props '(algebraic unary1))
1403 (put '^ 'math-rewrite-props '(algebraic unary1))
1404 (put '% 'math-rewrite-props '(algebraic))
1405 (put 'neg 'math-rewrite-props '(algebraic))
1406 (put 'calcFunc-idiv 'math-rewrite-props '(algebraic))
1407 (put 'calcFunc-abs 'math-rewrite-props '(algebraic))
1408 (put 'calcFunc-sign 'math-rewrite-props '(algebraic))
1409 (put 'calcFunc-round 'math-rewrite-props '(algebraic))
1410 (put 'calcFunc-rounde 'math-rewrite-props '(algebraic))
1411 (put 'calcFunc-roundu 'math-rewrite-props '(algebraic))
1412 (put 'calcFunc-trunc 'math-rewrite-props '(algebraic))
1413 (put 'calcFunc-floor 'math-rewrite-props '(algebraic))
1414 (put 'calcFunc-ceil 'math-rewrite-props '(algebraic))
1415 (put 'calcFunc-re 'math-rewrite-props '(algebraic))
1416 (put 'calcFunc-im 'math-rewrite-props '(algebraic))
1417 (put 'calcFunc-conj 'math-rewrite-props '(algebraic))
1418 (put 'calcFunc-arg 'math-rewrite-props '(algebraic))
1419 (put 'calcFunc-and 'math-rewrite-props '(assoc commut))
1420 (put 'calcFunc-or 'math-rewrite-props '(assoc commut))
1421 (put 'calcFunc-xor 'math-rewrite-props '(assoc commut))
1422 (put 'calcFunc-eq 'math-rewrite-props '(commut))
1423 (put 'calcFunc-neq 'math-rewrite-props '(commut))
1424 (put 'calcFunc-land 'math-rewrite-props '(assoc commut))
1425 (put 'calcFunc-lor 'math-rewrite-props '(assoc commut))
1426 (put 'calcFunc-beta 'math-rewrite-props '(commut))
1427 (put 'calcFunc-gcd 'math-rewrite-props '(assoc commut))
1428 (put 'calcFunc-lcm 'math-rewrite-props '(assoc commut))
1429 (put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut))
1430 (put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut))
1431 (put 'calcFunc-vunion 'math-rewrite-props '(assoc commut))
1432 (put 'calcFunc-vint 'math-rewrite-props '(assoc commut))
1433 (put 'calcFunc-vxor 'math-rewrite-props '(assoc commut))
1435 ;;; Note: "*" is not commutative for matrix args, but we pretend it is.
1436 ;;; Also, "-" is not commutative but the code tweaks things so that it is.
1438 (put '+ 'math-rewrite-default 0)
1439 (put '- 'math-rewrite-default 0)
1440 (put '* 'math-rewrite-default 1)
1441 (put '/ 'math-rewrite-default 1)
1442 (put '^ 'math-rewrite-default 1)
1443 (put 'calcFunc-land 'math-rewrite-default 1)
1444 (put 'calcFunc-lor 'math-rewrite-default 0)
1445 (put 'calcFunc-vunion 'math-rewrite-default '(vec))
1446 (put 'calcFunc-vint 'math-rewrite-default '(vec))
1447 (put 'calcFunc-vdiff 'math-rewrite-default '(vec))
1448 (put 'calcFunc-vxor 'math-rewrite-default '(vec))
1450 (defmacro math-rwfail (&optional back)
1454 '(setq btrack (cdr btrack))
1458 ;;; This monstrosity is necessary because the use of static vectors of
1459 ;;; registers makes rewrite rules non-reentrant. Yucko!
1460 (defmacro math-rweval (form)
1461 (list 'let '((orig (car rules)))
1462 '(setcar rules (quote (nil nil nil no-phase)))
1463 (list 'unwind-protect
1465 '(setcar rules orig))))
1467 (defvar math-rewrite-phase 1)
1469 ;; The variable math-apply-rw-regs is local to math-apply-rewrites,
1470 ;; but is used by math-rwapply-replace-regs and math-rwapply-reg-looks-negp
1471 ;; which are called by math-apply-rewrites.
1472 (defvar math-apply-rw-regs)
1474 ;; The variable math-apply-rw-ruleset is local to math-apply-rewrites,
1475 ;; but is used by math-rwapply-remember.
1476 (defvar math-apply-rw-ruleset)
1478 (defun math-apply-rewrites (expr rules &optional heads math-apply-rw-ruleset)
1480 (setq rules (cdr (or (assq (car-safe expr) rules)
1483 op math-apply-rw-regs inst part pc mark btrack
1484 (tracing math-rwcomp-tracing)
1485 (phase math-rewrite-phase))
1488 (and (setq part (nth 2 (car rules)))
1490 (not (memq part heads)))
1491 (and (setq part (nth 3 (car rules)))
1492 (not (memq phase part)))
1494 (setq math-apply-rw-regs (car (car rules))
1495 pc (nth 1 (car rules))
1497 (aset math-apply-rw-regs 0 expr)
1501 (progn (terpri) (princ (car pc))
1502 (if (and (natnump (nth 1 (car pc)))
1503 (< (nth 1 (car pc)) (length math-apply-rw-regs)))
1505 (format "\n part = %s"
1506 (aref math-apply-rw-regs (nth 1 (car pc))))))))
1508 (cond ((eq (setq op (car (setq inst (car pc)))) 'func)
1510 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1512 (car (setq inst (cdr (cdr inst)))))
1514 (while (and (setq inst (cdr inst)
1517 (aset math-apply-rw-regs (car inst) (car part)))
1518 (not (or inst part))))
1523 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1524 (setq mark (aref math-apply-rw-regs (nth 2 inst))))
1525 (Math-equal part mark))
1531 (not (eq calc-matrix-mode 'scalar))
1532 (eq (car (nth 2 inst)) '*)
1533 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1535 (not (math-known-scalarp part)))
1536 (setq mark (nth 3 inst)
1540 (aset math-apply-rw-regs (nth 4 inst) (nth 2 part))
1541 (aset mark 1 (cdr (cdr part))))
1542 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1543 (aset mark 1 (cdr part)))
1544 (aset mark 0 (cdr part))
1548 (if (and (consp (setq part
1549 (aref math-apply-rw-regs (car (cdr inst)))))
1550 (memq (car part) (nth 2 inst))
1552 (or (not (eq (car part) '/))
1553 (Math-objectp (nth 2 part))))
1556 mark (car (cdr (setq inst (cdr (cdr inst))))))
1558 (memq 'assoc (get (car part) 'math-rewrite-props))
1559 (not (= (aref mark 3) 0))
1560 (while (if (and (consp (nth 1 part))
1561 (memq (car (nth 1 part)) (car inst)))
1562 (setq op (cons (if (eq (car part) '-)
1568 (if (and (consp (nth 2 part))
1569 (memq (car (nth 2 part))
1571 (not (eq (car (nth 2 part)) '-)))
1572 (setq op (cons (nth 1 part) op)
1573 part (nth 2 part))))))
1574 (setq op (cons (nth 1 part)
1575 (cons (if (eq (car part) '-)
1578 (if (eq (car part) '/)
1583 btrack (cons pc btrack)
1585 (aset math-apply-rw-regs (nth 2 inst) (car op))
1588 (aset mark 2 (if (cdr (cdr op)) 1 0)))
1590 (if (and (consp part)
1591 (eq (car part) 'neg)
1592 (eq (car (nth 2 inst)) '*)
1593 (eq (nth 5 inst) 1))
1595 (setq mark (nth 3 inst)
1597 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1600 (setq mark (nth 3 inst)
1602 (aset math-apply-rw-regs (nth 4 inst) part)
1607 (setq part (nth 1 inst) ; try instr
1611 (aset math-apply-rw-regs (nth 2 inst)
1614 (if (eq (aref mark 0) (aref mark 1))
1615 (nth 1 (aref mark 0))
1616 (car (aref mark 0))))
1618 (setq mark (delq (car (aref mark 1))
1619 (copy-sequence (aref mark 0)))
1620 op (car (nth 2 part)))
1623 (setq mark (nreverse mark)
1624 part (list '* (nth 1 mark) (car mark))
1626 (while (setq mark (cdr mark))
1627 (setq part (list '* (car mark) part))))
1628 (setq part (car mark)
1630 part (if (and (eq op '+)
1632 (eq (car (car mark)) 'neg))
1635 (list op part (car mark))))
1636 (while (setq mark (cdr mark))
1637 (setq part (if (and (eq op '+)
1639 (eq (car (car mark)) 'neg))
1642 (list op part (car mark))))))
1645 (car (aref mark 1)))
1646 ((eq op 3) (nth 5 part))
1647 (t (aref mark 1)))))
1651 (if (and (consp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1652 (eq (car part) 'calcFunc-select))
1653 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1654 (if math-rewrite-selections
1656 (aset math-apply-rw-regs (nth 2 inst) part))))
1659 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1660 (setq mark (math-neg
1661 (aref math-apply-rw-regs (nth 2 inst)))))
1662 (Math-equal part mark))
1667 (setq inst (car (car btrack)) ; "try" or "alt" instr
1668 pc (cdr (car btrack))
1669 mark (or (nth 3 inst) [nil nil 4])
1672 (if (setq op (cdr (aref mark 1)))
1673 (aset math-apply-rw-regs (nth 4 inst)
1674 (car (aset mark 1 op)))
1678 (aset math-apply-rw-regs (nth 4 inst)
1679 (aref math-apply-rw-regs (nth 1 inst))))
1682 (if (setq op (cdr (aref mark 1)))
1683 (aset math-apply-rw-regs (nth 4 inst)
1684 (car (aset mark 1 op)))
1685 (if (= (aref mark 3) 1)
1689 (aset math-apply-rw-regs (nth 4 inst)
1690 (aref math-apply-rw-regs (nth 1 inst))))
1693 (aset mark 1 (cons nil (aref mark 0)))
1696 (if (setq op (cdr (aref mark 1)))
1698 (setq mark (delq (car (aset mark 1 op))
1701 op (car (nth 2 inst)))
1704 (setq mark (nreverse mark)
1705 part (list '* (nth 1 mark)
1708 (while (setq mark (cdr mark))
1709 (setq part (list '* (car mark)
1711 (setq part (car mark)
1713 part (if (and (eq op '+)
1715 (eq (car (car mark))
1719 (list op part (car mark))))
1720 (while (setq mark (cdr mark))
1721 (setq part (if (and (eq op '+)
1723 (eq (car (car mark))
1727 (list op part (car mark))))))
1728 (aset math-apply-rw-regs (nth 4 inst) part))
1732 (aset math-apply-rw-regs (nth 4 inst)
1733 (aref math-apply-rw-regs (nth 1 inst))))
1736 (setq btrack (cdr btrack)))
1737 (t (math-rwfail t))))
1740 (if (Math-integerp (setq part
1741 (aref math-apply-rw-regs (nth 1 inst))))
1743 (if (Math-primp part)
1745 (setq part (math-rweval (math-simplify part)))
1746 (if (Math-integerp part)
1751 (if (Math-realp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1753 (if (Math-primp part)
1755 (setq part (math-rweval (math-simplify part)))
1756 (if (Math-realp part)
1761 (if (math-constp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1763 (if (Math-primp part)
1765 (setq part (math-rweval (math-simplify part)))
1766 (if (math-constp part)
1771 (if (math-looks-negp (setq part
1772 (aref math-apply-rw-regs (nth 1 inst))))
1774 (if (Math-primp part)
1776 (setq part (math-rweval (math-simplify part)))
1777 (if (math-looks-negp part)
1782 (setq part (math-compare (aref math-apply-rw-regs (nth 1 inst))
1783 (aref math-apply-rw-regs (nth 3 inst)))
1786 (setq part (math-rweval
1790 (aref math-apply-rw-regs (nth 1 inst))
1791 (aref math-apply-rw-regs (nth 3 inst))))))))
1792 (if (cond ((eq op 'calcFunc-eq)
1794 ((eq op 'calcFunc-neq)
1795 (memq part '(-1 1)))
1796 ((eq op 'calcFunc-lt)
1798 ((eq op 'calcFunc-leq)
1799 (memq part '(-1 0)))
1800 ((eq op 'calcFunc-gt)
1802 ((eq op 'calcFunc-geq)
1803 (memq part '(0 1))))
1809 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1811 (car (setq inst (cdr (cdr inst))))))
1813 (setq inst (cdr inst)
1815 (while (and (setq inst (cdr inst)
1818 (aset math-apply-rw-regs (car inst) (car part)))
1821 (while (eq (car (car (setq pc (cdr pc))))
1823 (setq pc (cdr pc)) ; skip over "func"
1825 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1826 (setq mark (cdr mark)))))
1833 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1834 (eq (car part) (nth 2 inst))))
1835 (and (= (length part) 2)
1836 (setq part (nth 1 part))))
1838 (setq mark (nth 3 inst))
1839 (aset math-apply-rw-regs (nth 4 inst) part)
1840 (while (eq (car (car (setq pc (cdr pc)))) 'func-def))
1841 (setq pc (cdr pc)) ; skip over "func"
1843 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1844 (setq mark (cdr mark))))
1845 (setq pc (cdr pc))))
1849 (setq part (aref math-apply-rw-regs (nth 1 inst))))
1850 (Math-zerop (nth 3 inst))
1851 (and (not (Math-zerop (nth 2 inst)))
1853 (setq part (math-mod part (nth 2 inst)))
1854 (or (Math-numberp part)
1855 (setq part (math-rweval
1856 (math-simplify part))))
1857 (Math-equal part (nth 3 inst)))))
1863 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1864 (not (Math-objvecp part))
1865 (not (eq (car part) 'var)))
1867 (aset math-apply-rw-regs (nth 2 inst)
1868 (math-calcFunc-to-var (car part)))
1869 (aset math-apply-rw-regs (nth 3 inst)
1870 (cons 'vec (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) (nth 1 part))
1881 (aset math-apply-rw-regs (nth 3 inst)
1882 (cons 'vec (cdr (cdr part))))
1888 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1889 (eq (car part) 'vec)
1892 (aset math-apply-rw-regs (nth 2 inst) (calcFunc-rhead part))
1893 (aset math-apply-rw-regs (nth 3 inst) (calcFunc-rtail part))
1901 (math-rwapply-replace-regs (nth 1 inst)))))
1906 (aset math-apply-rw-regs (nth 1 inst)
1909 (math-rwapply-replace-regs (nth 2 inst)))))
1913 (aset math-apply-rw-regs (nth 2 inst)
1914 (aref math-apply-rw-regs (nth 1 inst)))
1918 (aset math-apply-rw-regs (nth 2 inst)
1919 (math-rwapply-neg (aref math-apply-rw-regs (nth 1 inst))))
1923 (setq btrack (cons pc btrack)
1927 (while (and btrack (not (eq (car btrack) (nth 1 inst))))
1928 (setq btrack (cdr btrack)))
1929 (setq btrack (cdr btrack)
1933 (setq result (math-rwapply-replace-regs (nth 1 inst)))
1934 (if (or (and (eq (car-safe result) '+)
1935 (eq (nth 2 result) 0))
1936 (and (eq (car-safe result) '*)
1937 (eq (nth 2 result) 1)))
1938 (setq result (nth 1 result)))
1939 (setq part (and (nth 2 inst)
1943 (math-rwapply-replace-regs
1945 (if (or (equal result expr)
1946 (equal (setq result (math-normalize result)) expr))
1948 (if part (math-rwapply-remember expr result))
1952 (t (error "%s is not a valid rewrite opcode" op))))))
1953 (setq rules (cdr rules)))
1956 (defun math-rwapply-neg (expr)
1957 (if (and (consp expr)
1958 (memq (car expr) '(* /)))
1959 (if (Math-objectp (nth 2 expr))
1960 (list (car expr) (nth 1 expr) (math-neg (nth 2 expr)))
1962 (if (Math-objectp (nth 1 expr))
1963 (math-neg (nth 1 expr))
1964 (list '* -1 (nth 1 expr)))
1968 (defun math-rwapply-inv (expr)
1969 (if (and (Math-integerp expr)
1971 (math-make-frac 1 expr)
1974 (defun math-rwapply-replace-regs (expr)
1975 (cond ((Math-primp expr)
1977 ((eq (car expr) 'calcFunc-register)
1978 (setq expr (aref math-apply-rw-regs (nth 1 expr)))
1979 (if (eq (car-safe expr) '*)
1980 (if (eq (nth 1 expr) -1)
1981 (math-neg (nth 2 expr))
1982 (if (eq (nth 1 expr) 1)
1986 ((and (eq (car expr) 'calcFunc-eval)
1987 (= (length expr) 2))
1988 (calc-with-default-simplification
1989 (math-normalize (math-rwapply-replace-regs (nth 1 expr)))))
1990 ((and (eq (car expr) 'calcFunc-evalsimp)
1991 (= (length expr) 2))
1992 (math-simplify (math-rwapply-replace-regs (nth 1 expr))))
1993 ((and (eq (car expr) 'calcFunc-evalextsimp)
1994 (= (length expr) 2))
1995 (math-simplify-extended (math-rwapply-replace-regs (nth 1 expr))))
1996 ((and (eq (car expr) 'calcFunc-apply)
1997 (= (length expr) 3))
1998 (let ((func (math-rwapply-replace-regs (nth 1 expr)))
1999 (args (math-rwapply-replace-regs (nth 2 expr)))
2001 (if (and (math-vectorp args)
2002 (not (eq (car-safe (setq call (math-build-call
2003 (math-var-to-calcFunc func)
2007 (list 'calcFunc-apply func args))))
2008 ((and (eq (car expr) 'calcFunc-cons)
2009 (= (length expr) 3))
2010 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2011 (tail (math-rwapply-replace-regs (nth 2 expr))))
2012 (if (math-vectorp tail)
2013 (cons 'vec (cons head (cdr tail)))
2014 (list 'calcFunc-cons head tail))))
2015 ((and (eq (car expr) 'calcFunc-rcons)
2016 (= (length expr) 3))
2017 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2018 (tail (math-rwapply-replace-regs (nth 2 expr))))
2019 (if (math-vectorp head)
2020 (append head (list tail))
2021 (list 'calcFunc-rcons head tail))))
2022 ((and (eq (car expr) 'neg)
2023 (math-rwapply-reg-looks-negp (nth 1 expr)))
2024 (math-rwapply-reg-neg (nth 1 expr)))
2025 ((and (eq (car expr) 'neg)
2026 (eq (car-safe (nth 1 expr)) 'calcFunc-register)
2027 (math-scalarp (aref math-apply-rw-regs (nth 1 (nth 1 expr)))))
2028 (math-neg (math-rwapply-replace-regs (nth 1 expr))))
2029 ((and (eq (car expr) '+)
2030 (math-rwapply-reg-looks-negp (nth 1 expr)))
2031 (list '- (math-rwapply-replace-regs (nth 2 expr))
2032 (math-rwapply-reg-neg (nth 1 expr))))
2033 ((and (eq (car expr) '+)
2034 (math-rwapply-reg-looks-negp (nth 2 expr)))
2035 (list '- (math-rwapply-replace-regs (nth 1 expr))
2036 (math-rwapply-reg-neg (nth 2 expr))))
2037 ((and (eq (car expr) '-)
2038 (math-rwapply-reg-looks-negp (nth 2 expr)))
2039 (list '+ (math-rwapply-replace-regs (nth 1 expr))
2040 (math-rwapply-reg-neg (nth 2 expr))))
2042 (cond ((eq (nth 1 expr) -1)
2043 (if (math-rwapply-reg-looks-negp (nth 2 expr))
2044 (math-rwapply-reg-neg (nth 2 expr))
2045 (math-neg (math-rwapply-replace-regs (nth 2 expr)))))
2046 ((eq (nth 1 expr) 1)
2047 (math-rwapply-replace-regs (nth 2 expr)))
2048 ((eq (nth 2 expr) -1)
2049 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2050 (math-rwapply-reg-neg (nth 1 expr))
2051 (math-neg (math-rwapply-replace-regs (nth 1 expr)))))
2052 ((eq (nth 2 expr) 1)
2053 (math-rwapply-replace-regs (nth 1 expr)))
2055 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2056 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2057 (cond ((and (eq (car-safe arg1) '/)
2058 (eq (nth 1 arg1) 1))
2059 (list '/ arg2 (nth 2 arg1)))
2060 ((and (eq (car-safe arg2) '/)
2061 (eq (nth 1 arg2) 1))
2062 (list '/ arg1 (nth 2 arg2)))
2063 (t (list '* arg1 arg2)))))))
2065 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2066 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2067 (if (eq (car-safe arg2) '/)
2068 (list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2))
2069 (list '/ arg1 arg2))))
2070 ((and (eq (car expr) 'calcFunc-plain)
2071 (= (length expr) 2))
2072 (if (Math-primp (nth 1 expr))
2074 (if (eq (car (nth 1 expr)) 'calcFunc-register)
2075 (aref math-apply-rw-regs (nth 1 (nth 1 expr)))
2076 (cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs
2077 (cdr (nth 1 expr)))))))
2078 (t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr))))))
2080 (defun math-rwapply-reg-looks-negp (expr)
2081 (if (eq (car-safe expr) 'calcFunc-register)
2082 (math-looks-negp (aref math-apply-rw-regs (nth 1 expr)))
2083 (if (memq (car-safe expr) '(* /))
2084 (or (math-rwapply-reg-looks-negp (nth 1 expr))
2085 (math-rwapply-reg-looks-negp (nth 2 expr))))))
2087 (defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp
2088 (if (eq (car expr) 'calcFunc-register)
2089 (math-neg (math-rwapply-replace-regs expr))
2090 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2091 (math-rwapply-replace-regs (list (car expr)
2092 (math-rwapply-reg-neg (nth 1 expr))
2094 (math-rwapply-replace-regs (list (car expr)
2096 (math-rwapply-reg-neg (nth 2 expr)))))))
2098 (defun math-rwapply-remember (old new)
2099 (let ((varval (symbol-value (nth 2 (car math-apply-rw-ruleset))))
2100 (rules (assq (car-safe old) math-apply-rw-ruleset)))
2101 (if (and (eq (car-safe varval) 'vec)
2102 (not (memq (car-safe old) '(nil schedule + -)))
2105 (setcdr varval (cons (list 'calcFunc-assign
2106 (if (math-rwcomp-no-vars old)
2108 (list 'calcFunc-quote old))
2111 (setcdr rules (cons (list (vector nil old)
2112 (list (list 'same 0 1)
2113 (list 'done new nil))
2117 (provide 'calc-rewr)
2119 ;;; arch-tag: ca8d7b7d-bff1-4535-90f3-e2241f5e786b
2120 ;;; calc-rewr.el ends here