1 ;;; calc-rewr.el --- rewriting functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is free software: you can redistribute it and/or modify
12 ;; it under the terms of the GNU General Public License as published by
13 ;; the Free Software Foundation, either version 3 of the License, or
14 ;; (at your option) any later version.
16 ;; GNU Emacs is distributed in the hope that it will be useful,
17 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
18 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 ;; GNU General Public License for more details.
21 ;; You should have received a copy of the GNU General Public License
22 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
28 ;; This file is autoloaded from calc-ext.el.
33 (defvar math-rewrite-default-iters 100)
35 ;; The variable calc-rewr-sel is local to calc-rewrite-selection and
36 ;; calc-rewrite, but is used by calc-locate-selection-marker.
37 (defvar calc-rewr-sel)
39 (defun calc-rewrite-selection (rules-str &optional many prefix)
40 (interactive "sRewrite rule(s): \np")
43 (let* ((num (max 1 (calc-locate-cursor-element (point))))
47 (entry (calc-top num 'entry))
49 (calc-rewr-sel (calc-auto-selection entry))
50 (math-rewrite-selections t)
51 (math-rewrite-default-iters 1))
52 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
54 (error "Can't use same stack entry for formula and rules")
55 (setq rules (calc-top-n 1 t)
57 (setq rules (if (stringp rules-str)
58 (math-read-exprs rules-str) rules-str))
59 (if (eq (car-safe rules) 'error)
60 (error "Bad format in expression: %s" (nth 1 rules)))
61 (if (= (length rules) 1)
62 (setq rules (car rules))
63 (setq rules (cons 'vec rules)))
64 (or (memq (car-safe rules) '(vec var calcFunc-assign
66 (let ((rhs (math-read-expr
67 (read-string (concat "Rewrite from: " rules-str
69 (if (eq (car-safe rhs) 'error)
70 (error "Bad format in expression: %s" (nth 1 rhs)))
71 (setq rules (list 'calcFunc-assign rules rhs))))
72 (or (eq (car-safe rules) 'var)
73 (calc-record rules "rule")))
75 (setq many '(var inf var-inf))
76 (if many (setq many (prefix-numeric-value many))))
78 (setq expr (calc-replace-sub-formula (car entry)
80 (list 'calcFunc-select calc-rewr-sel)))
81 (setq expr (car entry)
83 math-rewrite-selections nil))
84 (setq expr (calc-encase-atoms
90 expr (calc-locate-select-marker expr))
91 (or (consp calc-rewr-sel) (setq calc-rewr-sel nil))
92 (if pop-rules (calc-pop-stack 1))
93 (calc-pop-push-record-list 1 (or prefix "rwrt") (list expr)
94 (- num (if pop-rules 1 0))
95 (list (and reselect calc-rewr-sel))))
98 (defun calc-locate-select-marker (expr)
101 (if (and (eq (car expr) 'calcFunc-select)
104 (setq calc-rewr-sel (if calc-rewr-sel t (nth 1 expr)))
107 (mapcar 'calc-locate-select-marker (cdr expr))))))
111 (defun calc-rewrite (rules-str many)
112 (interactive "sRewrite rule(s): \nP")
115 (if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
116 (setq expr (calc-top-n 2)
117 rules (calc-top-n 1 t)
119 (setq rules (if (stringp rules-str)
120 (math-read-exprs rules-str) rules-str))
121 (if (eq (car-safe rules) 'error)
122 (error "Bad format in expression: %s" (nth 1 rules)))
123 (if (= (length rules) 1)
124 (setq rules (car rules))
125 (setq rules (cons 'vec rules)))
126 (or (memq (car-safe rules) '(vec var calcFunc-assign
128 (let ((rhs (math-read-expr
129 (read-string (concat "Rewrite from: " rules-str
131 (if (eq (car-safe rhs) 'error)
132 (error "Bad format in expression: %s" (nth 1 rhs)))
133 (setq rules (list 'calcFunc-assign rules rhs))))
134 (or (eq (car-safe rules) 'var)
135 (calc-record rules "rule"))
136 (setq expr (calc-top-n 1)
139 (setq many '(var inf var-inf))
140 (if many (setq many (prefix-numeric-value many))))
141 (setq expr (calc-normalize (math-rewrite expr rules many)))
143 (setq expr (calc-locate-select-marker expr)))
144 (calc-pop-push-record-list n "rwrt" (list expr)))
147 (defun calc-match (pat &optional interactive)
148 (interactive "sPattern: \np")
151 (if (or (null pat) (equal pat "") (equal pat "$"))
152 (setq expr (calc-top-n 2)
155 (setq pat (if (stringp pat) (math-read-expr pat) pat))
156 (if (eq (car-safe pat) 'error)
157 (error "Bad format in expression: %s" (nth 1 pat)))
158 (if (not (eq (car-safe pat) 'var))
159 (calc-record pat "pat"))
160 (setq expr (calc-top-n 1)
162 (or (math-vectorp expr) (error "Argument must be a vector"))
163 (if (calc-is-inverse)
164 (calc-enter-result n "mtcn" (math-match-patterns pat expr t))
165 (calc-enter-result n "mtch" (math-match-patterns pat expr nil))))))
168 (defvar math-mt-many)
170 ;; The variable math-rewrite-whole-expr is local to math-rewrite,
171 ;; but is used by math-rewrite-phase
172 (defvar math-rewrite-whole-expr)
174 (defun math-rewrite (math-rewrite-whole-expr rules &optional math-mt-many)
175 (let* ((crules (math-compile-rewrites rules))
176 (heads (math-rewrite-heads math-rewrite-whole-expr))
177 (trace-buffer (get-buffer "*Trace*"))
178 (calc-display-just 'center)
179 (calc-display-origin 39)
180 (calc-line-breaking 78)
181 (calc-line-numbering nil)
182 (calc-show-selections t)
184 (math-mt-func (function
186 (let ((result (math-apply-rewrites x (cdr crules)
191 (let ((fmt (math-format-stack-value
192 (list result nil nil))))
193 (with-current-buffer trace-buffer
194 (insert "\nrewrite to\n" fmt "\n"))))
195 (setq heads (math-rewrite-heads result heads t))))
198 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
199 (with-current-buffer trace-buffer
200 (setq truncate-lines t)
201 (goto-char (point-max))
202 (insert "\n\nBegin rewriting\n" fmt "\n"))))
203 (or math-mt-many (setq math-mt-many (or (nth 1 (car crules))
204 math-rewrite-default-iters)))
205 (if (equal math-mt-many '(var inf var-inf)) (setq math-mt-many 1000000))
206 (if (equal math-mt-many '(neg (var inf var-inf))) (setq math-mt-many -1000000))
207 (math-rewrite-phase (nth 3 (car crules)))
209 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
210 (with-current-buffer trace-buffer
211 (insert "\nDone rewriting"
212 (if (= math-mt-many 0) " (reached iteration limit)" "")
214 math-rewrite-whole-expr))
216 (defun math-rewrite-phase (sched)
217 (while (and sched (/= math-mt-many 0))
218 (if (listp (car sched))
219 (while (let ((save-expr math-rewrite-whole-expr))
220 (math-rewrite-phase (car sched))
221 (not (equal math-rewrite-whole-expr save-expr))))
222 (if (symbolp (car sched))
224 (setq math-rewrite-whole-expr
225 (math-normalize (list (car sched) math-rewrite-whole-expr)))
227 (let ((fmt (math-format-stack-value
228 (list math-rewrite-whole-expr nil nil))))
229 (with-current-buffer trace-buffer
231 (substring (symbol-name (car sched)) 9)
233 (let ((math-rewrite-phase (car sched)))
235 (with-current-buffer trace-buffer
236 (insert (format "\n(Phase %d)\n" math-rewrite-phase))))
237 (while (let ((save-expr math-rewrite-whole-expr))
238 (setq math-rewrite-whole-expr (math-normalize
239 (math-map-tree-rec math-rewrite-whole-expr)))
240 (not (equal math-rewrite-whole-expr save-expr)))))))
241 (setq sched (cdr sched))))
243 (defun calcFunc-rewrite (expr rules &optional many)
244 (or (null many) (integerp many)
245 (equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf)))
246 (math-reject-arg many 'fixnump))
248 (math-rewrite expr rules (or many 1))
249 (error (math-reject-arg rules (nth 1 err)))))
251 (defun calcFunc-match (pat vec)
252 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
254 (math-match-patterns pat vec nil)
255 (error (math-reject-arg pat (nth 1 err)))))
257 (defun calcFunc-matchnot (pat vec)
258 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
260 (math-match-patterns pat vec t)
261 (error (math-reject-arg pat (nth 1 err)))))
263 (defun math-match-patterns (pat vec &optional not-flag)
265 (crules (math-compile-patterns pat)))
266 (while (setq vec (cdr vec))
267 (if (eq (not (math-apply-rewrites (car vec) crules))
269 (setq newvec (cons (car vec) newvec))))
270 (cons 'vec (nreverse newvec))))
272 (defun calcFunc-matches (expr pat)
274 (if (math-apply-rewrites expr (math-compile-patterns pat))
277 (error (math-reject-arg pat (nth 1 err)))))
279 (defun calcFunc-vmatches (expr pat)
281 (or (math-apply-rewrites expr (math-compile-patterns pat))
283 (error (math-reject-arg pat (nth 1 err)))))
287 ;; A compiled rule set is an a-list of entries whose cars are functors,
288 ;; and whose cdrs are lists of rules. If there are rules with no
289 ;; well-defined head functor, they are included on all lists and also
290 ;; on an extra list whose car is nil.
292 ;; The first entry in the a-list is of the form (schedule A B C ...).
294 ;; Rule list entries take the form (regs prog head phases), where:
296 ;; regs is a vector of match registers.
298 ;; prog is a match program (see below).
300 ;; head is a rare function name appearing in the rule body (but not the
301 ;; head of the whole rule), or nil if none.
303 ;; phases is a list of phase numbers for which the rule is enabled.
305 ;; A match program is a list of match instructions.
307 ;; In the following, "part" is a register number that contains the
308 ;; subexpression to be operated on.
310 ;; Register 0 is the whole expression being matched. The others are
311 ;; meta-variables in the pattern, temporaries used for matching and
312 ;; backtracking, and constant expressions.
315 ;; The selected part must be math-equal to the contents of "reg".
317 ;; (same-neg part reg)
318 ;; The selected part must be math-equal to the negative of "reg".
321 ;; The selected part is copied into "reg". (Rarely used.)
323 ;; (copy-neg part reg)
324 ;; The negative of the selected part is copied into "reg".
327 ;; The selected part must be an integer.
330 ;; The selected part must be a real.
333 ;; The selected part must be a constant.
336 ;; The selected part must "look" negative.
339 ;; The selected part must satisfy "part op reg", where "op"
340 ;; is one of the 6 relational ops, and "reg" is a register.
342 ;; (mod part modulo value)
343 ;; The selected part must satisfy "part % modulo = value", where
344 ;; "modulo" and "value" are constants.
346 ;; (func part head reg1 reg2 ... regn)
347 ;; The selected part must be an n-ary call to function "head".
348 ;; The arguments are stored in "reg1" through "regn".
350 ;; (func-def part head defs reg1 reg2 ... regn)
351 ;; The selected part must be an n-ary call to function "head".
352 ;; "Defs" is a list of value/register number pairs for default args.
353 ;; If a match, assign default values to registers and then skip
354 ;; immediately over any following "func-def" instructions and
355 ;; the following "func" instruction. If wrong number of arguments,
356 ;; proceed to the following "func-def" or "func" instruction.
358 ;; (func-opt part head defs reg1)
359 ;; Like func-def with "n=1", except that if the selected part is
360 ;; not a call to "head", then the part itself successfully matches
361 ;; "reg1" (and the defaults are assigned).
363 ;; (try part heads mark reg1 [def])
364 ;; The selected part must be a function of the correct type which is
365 ;; associative and/or commutative. "Heads" is a list of acceptable
366 ;; types. An initial assignment of arguments to "reg1" is tried.
367 ;; If the program later fails, it backtracks to this instruction
368 ;; and tries other assignments of arguments to "reg1".
369 ;; If "def" exists and normal matching fails, backtrack and assign
370 ;; "part" to "reg1", and "def" to "reg2" in the following "try2".
371 ;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized.
372 ;; "mark[0]" points to the argument list; "mark[1]" points to the
373 ;; current argument; "mark[2]" is 0 if there are two arguments,
374 ;; 1 if reg1 is matching single arguments, 2 if reg2 is matching
375 ;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or
376 ;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must
377 ;; have two arguments, 1 if phase-2 can be skipped, 2 if full
378 ;; backtracking is necessary; "mark[4]" is t if the arguments have
379 ;; been switched from the order given in the original pattern.
382 ;; Every "try" will be followed by a "try2" whose "try" field is
383 ;; a pointer to the corresponding "try". The arguments which were
384 ;; not stored in "reg1" by that "try" are now stored in "reg2".
386 ;; (alt instr nil mark)
387 ;; Basic backtracking. Execute the instruction sequence "instr".
388 ;; If this fails, back up and execute following the "alt" instruction.
389 ;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence
390 ;; should execute "end-alt" at the end.
393 ;; Register success of the first alternative of a previous "alt".
394 ;; "Ptr" is a pointer to the next instruction following that "alt".
396 ;; (apply part reg1 reg2)
397 ;; The selected part must be a function call. The functor
398 ;; (as a variable name) is stored in "reg1"; the arguments
399 ;; (as a vector) are stored in "reg2".
401 ;; (cons part reg1 reg2)
402 ;; The selected part must be a nonempty vector. The first element
403 ;; of the vector is stored in "reg1"; the rest of the vector
404 ;; (as another vector) is stored in "reg2".
406 ;; (rcons part reg1 reg2)
407 ;; The selected part must be a nonempty vector. The last element
408 ;; of the vector is stored in "reg2"; the rest of the vector
409 ;; (as another vector) is stored in "reg1".
412 ;; If the selected part is a unary call to function "select", its
413 ;; argument is stored in "reg"; otherwise (provided this is an `a r'
414 ;; and not a `g r' command) the selected part is stored in "reg".
417 ;; The "expr", with registers substituted, must simplify to
421 ;; Evaluate "expr" and store the result in "reg". Always succeeds.
423 ;; (done rhs remember)
424 ;; Rewrite the expression to "rhs", with register substituted.
425 ;; Normalize; if the result is different from the original
426 ;; expression, the match has succeeded. This is the last
427 ;; instruction of every program. If "remember" is non-nil,
428 ;; record the result of the match as a new literal rule.
431 ;; Pseudo-functions related to rewrites:
433 ;; In patterns: quote, plain, condition, opt, apply, cons, select
435 ;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp,
436 ;; apply, cons, select
438 ;; In conditions: let + same as for righthand sides
440 ;; Some optimizations that would be nice to have:
442 ;; * Merge registers with disjoint lifetimes.
443 ;; * Merge constant registers with equivalent values.
445 ;; * If an argument of a commutative op math-depends neither on the
446 ;; rest of the pattern nor on any of the conditions, then no backtracking
447 ;; should be done for that argument. (This won't apply to very many
450 ;; * If top functor is "select", and its argument is a unique function,
451 ;; add the rule to the lists for both "select" and that function.
452 ;; (Currently rules like this go on the "nil" list.)
453 ;; Same for "func-opt" functions. (Though not urgent for these.)
455 ;; * Shouldn't evaluate a "let" condition until the end, or until it
456 ;; would enable another condition to be evaluated.
459 ;; Some additional features to add / things to think about:
461 ;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)".
463 ;;; * Same for interval forms.
465 ;;; * Have a name(v,pat) pattern which matches pat, and gives the
466 ;;; whole match the name v. Beware of circular structures!
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-rewrite-whole nil)
491 (defvar math-make-import-list nil)
493 ;; The variable math-import-list is local to part of math-compile-rewrites,
494 ;; but is also used in a different part, and so the local version could
495 ;; be affected by the non-local version when math-compile-rewrites calls itself.
496 (defvar math-import-list nil)
498 ;; The variables math-regs, math-num-regs, math-prog-last, math-bound-vars,
499 ;; math-conds, math-copy-neg, math-rhs, math-pattern, math-remembering and
500 ;; math-aliased-vars are local to math-compile-rewrites,
501 ;; but are used by many functions math-rwcomp-*, which are called by
502 ;; math-compile-rewrites.
504 (defvar math-num-regs)
505 (defvar math-prog-last)
506 (defvar math-bound-vars)
508 (defvar math-copy-neg)
510 (defvar math-pattern)
511 (defvar math-remembering)
512 (defvar math-aliased-vars)
514 (defun math-compile-rewrites (rules &optional name)
515 (if (eq (car-safe rules) 'var)
516 (let ((prop (get (nth 2 rules) 'math-rewrite-cache))
517 (math-import-list nil)
518 (math-make-import-list t)
520 (or (calc-var-value (nth 2 rules))
521 (error "Rules variable %s has no stored value" (nth 1 rules)))
523 (put (nth 2 rules) 'math-rewrite-cache
524 (setq prop (list (list (cons (nth 2 rules) nil))))))
526 (while (and p (eq (symbol-value (car (car p))) (cdr (car p))))
530 (message "Compiling rule set %s..." (nth 1 rules))
531 (setcdr prop (math-compile-rewrites
532 (symbol-value (nth 2 rules))
534 (message "Compiling rule set %s...done" (nth 1 rules))
535 (setcar prop (cons (cons (nth 2 rules)
536 (symbol-value (nth 2 rules)))
539 (if (or (not (eq (car-safe rules) 'vec))
540 (and (memq (length rules) '(3 4))
542 (while (and (setq p (cdr p))
543 (memq (car-safe (car p))
550 calcFunc-iterations))))
552 (setq rules (list rules))
553 (setq rules (cdr rules)))
554 (if (assq 'calcFunc-import rules)
555 (let ((pp (setq rules (copy-sequence rules)))
557 (while (setq p (car (cdr pp)))
558 (if (eq (car-safe p) 'calcFunc-import)
560 (setcdr pp (cdr (cdr pp)))
561 (or (and (eq (car-safe (nth 1 p)) 'var)
562 (setq part (calc-var-value (nth 2 (nth 1 p))))
563 (memq (car-safe part) '(vec
565 calcFunc-condition)))
566 (error "Argument of import() must be a rules variable"))
567 (if math-make-import-list
568 (setq math-import-list
569 (cons (cons (nth 2 (nth 1 p))
570 (symbol-value (nth 2 (nth 1 p))))
572 (while (setq p (cdr (cdr p)))
574 (error "import() must have odd number of arguments"))
575 (setq part (math-rwcomp-substitute part
577 (if (eq (car-safe part) 'vec)
578 (setq part (cdr part))
579 (setq part (list part)))
580 (setcdr pp (append part (cdr pp))))
581 (setq pp (cdr pp))))))
587 (math-iterations nil)
589 (math-all-phases nil)
590 (math-remembering nil)
591 math-pattern math-rhs math-conds)
594 ((and (eq (car-safe (car rules)) 'calcFunc-iterations)
595 (= (length (car rules)) 2))
596 (or (integerp (nth 1 (car rules)))
597 (equal (nth 1 (car rules)) '(var inf var-inf))
598 (equal (nth 1 (car rules)) '(neg (var inf var-inf)))
599 (error "Invalid argument for iterations(n)"))
601 (setq math-iterations (nth 1 (car rules)))))
602 ((eq (car-safe (car rules)) 'calcFunc-schedule)
604 (setq math-schedule (math-parse-schedule (cdr (car rules))))))
605 ((eq (car-safe (car rules)) 'calcFunc-phase)
606 (setq math-phases (cdr (car rules)))
607 (if (equal math-phases '((var all var-all)))
608 (setq math-phases nil))
609 (let ((p math-phases))
611 (or (integerp (car p))
612 (error "Phase numbers must be small integers"))
613 (or (memq (car p) math-all-phases)
614 (setq math-all-phases (cons (car p) math-all-phases)))
616 ((or (and (eq (car-safe (car rules)) 'vec)
617 (cdr (cdr (car rules)))
618 (not (nthcdr 4 (car rules)))
619 (setq math-conds (nth 3 (car rules))
620 math-rhs (nth 2 (car rules))
621 math-pattern (nth 1 (car rules))))
624 math-pattern (car rules))
625 (while (and (eq (car-safe math-pattern) 'calcFunc-condition)
626 (= (length math-pattern) 3))
627 (let ((cond (nth 2 math-pattern)))
628 (setq math-conds (if math-conds
629 (list 'calcFunc-land math-conds cond)
631 math-pattern (nth 1 math-pattern))))
632 (and (eq (car-safe math-pattern) 'calcFunc-assign)
633 (= (length math-pattern) 3)
634 (setq math-rhs (nth 2 math-pattern)
635 math-pattern (nth 1 math-pattern)))))
636 (let* ((math-prog (list nil))
637 (math-prog-last math-prog)
639 (math-regs (list (list nil 0 nil nil)))
640 (math-bound-vars nil)
641 (math-aliased-vars nil)
643 (setq math-conds (and math-conds (math-flatten-lands math-conds)))
644 (math-rwcomp-pattern math-pattern 0)
646 (let ((expr (car math-conds)))
647 (setq math-conds (cdr math-conds))
648 (math-rwcomp-cond-instr expr)))
649 (math-rwcomp-instr 'done
663 (math-rwcomp-register-expr
666 (math-rwcomp-match-vars math-rhs))
668 (setq math-prog (cdr math-prog))
669 (let* ((heads (math-rewrite-heads math-pattern))
672 (mapcar (function (lambda (x) (nth 3 x)))
677 (head (and (not (Math-primp math-pattern))
678 (not (and (eq (car (car math-prog)) 'try)
679 (nth 5 (car math-prog))))
680 (not (memq (car (car math-prog)) '(func-opt
684 (if (memq (car (car math-prog)) '(func
686 (nth 2 (car math-prog))
687 (if (eq (car math-pattern) 'calcFunc-quote)
688 (car-safe (nth 1 math-pattern))
689 (car math-pattern))))))
692 (if (setq found (assq (car heads) all-heads))
693 (setcdr found (1+ (cdr found)))
694 (setq all-heads (cons (cons (car heads) 1) all-heads)))
695 (setq heads (cdr heads))))
696 (if (eq head '-) (setq head '+))
697 (if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec))
700 (nconc (or (assq head rule-set)
701 (car (setq rule-set (cons (cons head
707 (nconc (or (assq '/ rule-set)
708 (car (setq rule-set (cons (cons
714 (setq nil-rules (nconc nil-rules (list rule)))
715 (let ((ptr rule-set))
717 (nconc (car ptr) (list rule))
718 (setq ptr (cdr ptr))))))))
720 (error "Rewrite rule set must be a vector of A := B rules")))
721 (setq rules (cdr rules)))
723 (setq rule-set (cons (cons nil nil-rules) rule-set)))
724 (setq all-heads (mapcar 'car
725 (sort all-heads (function
727 (< (cdr x) (cdr y)))))))
731 (setq rule (cdr (car set)))
733 (if (consp (setq heads (nth 2 (car rule))))
735 (setq heads (delq (car (car set)) heads)
737 (while (and ptr (not (memq (car ptr) heads)))
738 (setq ptr (cdr ptr)))
739 (setcar (nthcdr 2 (car rule)) (car ptr))))
740 (setq rule (cdr rule)))
741 (setq set (cdr set))))
742 (let ((plus (assq '+ rule-set)))
744 (setq rule-set (cons (cons '- (cdr plus)) rule-set))))
745 (cons (list 'schedule math-iterations name
747 (sort math-all-phases '<)
751 (defun math-flatten-lands (expr)
752 (if (eq (car-safe expr) 'calcFunc-land)
753 (append (math-flatten-lands (nth 1 expr))
754 (math-flatten-lands (nth 2 expr)))
757 ;; The variables math-rewrite-heads-heads (i.e.; heads for math-rewrite-heads)
758 ;; math-rewrite-heads-blanks and math-rewrite-heads-skips are local to
759 ;; math-rewrite-heads, but used by math-rewrite-heads-rec, which is called by
760 ;; math-rewrite-heads.
761 (defvar math-rewrite-heads-heads)
762 (defvar math-rewrite-heads-skips)
763 (defvar math-rewrite-heads-blanks)
765 (defun math-rewrite-heads (expr &optional more all)
766 (let ((math-rewrite-heads-heads more)
767 (math-rewrite-heads-skips (and (not all)
768 '(calcFunc-apply calcFunc-condition calcFunc-opt
769 calcFunc-por calcFunc-pnot)))
770 (math-rewrite-heads-blanks (and (not all)
771 '(calcFunc-quote calcFunc-plain calcFunc-select
772 calcFunc-cons calcFunc-rcons
774 (or (Math-primp expr)
775 (math-rewrite-heads-rec expr))
776 math-rewrite-heads-heads))
778 (defun math-rewrite-heads-rec (expr)
779 (or (memq (car expr) math-rewrite-heads-skips)
781 (or (memq (car expr) math-rewrite-heads-heads)
782 (memq (car expr) math-rewrite-heads-blanks)
783 (memq 'algebraic (get (car expr) 'math-rewrite-props))
784 (setq math-rewrite-heads-heads (cons (car expr) math-rewrite-heads-heads)))
785 (while (setq expr (cdr expr))
786 (or (Math-primp (car expr))
787 (math-rewrite-heads-rec (car expr)))))))
789 (defun math-parse-schedule (sched)
795 (math-parse-schedule (cdr s))
796 (if (eq (car-safe s) 'var)
797 (math-var-to-calcFunc s)
798 (error "Improper component in rewrite schedule"))))))
801 (defun math-rwcomp-match-vars (expr)
802 (if (Math-primp expr)
803 (if (eq (car-safe expr) 'var)
804 (let ((entry (assq (nth 2 expr) math-regs)))
806 (math-rwcomp-register-expr (nth 1 entry))
809 (if (and (eq (car expr) 'calcFunc-quote)
811 (math-rwcomp-match-vars (nth 1 expr))
812 (if (and (eq (car expr) 'calcFunc-plain)
814 (not (Math-primp (nth 1 expr))))
816 (cons (car (nth 1 expr))
817 (mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr)))))
819 (mapcar 'math-rwcomp-match-vars (cdr expr)))))))
821 (defun math-rwcomp-register-expr (num)
822 (let ((entry (nth (1- (- math-num-regs num)) math-regs)))
824 (list 'neg (list 'calcFunc-register (nth 1 entry)))
825 (list 'calcFunc-register (nth 1 entry)))))
827 ;; The variables math-rwcomp-subst-old, math-rwcomp-subst-new,
828 ;; math-rwcomp-subst-old-func and math-rwcomp-subst-new-func
829 ;; are local to math-rwcomp-substitute, but are used by
830 ;; math-rwcomp-subst-rec, which is called by math-rwcomp-substitute.
831 (defvar math-rwcomp-subst-new)
832 (defvar math-rwcomp-subst-old)
833 (defvar math-rwcomp-subst-new-func)
834 (defvar math-rwcomp-subst-old-func)
836 (defun math-rwcomp-substitute (expr math-rwcomp-subst-old math-rwcomp-subst-new)
837 (if (and (eq (car-safe math-rwcomp-subst-old) 'var)
838 (memq (car-safe math-rwcomp-subst-new) '(var calcFunc-lambda)))
839 (let ((math-rwcomp-subst-old-func (math-var-to-calcFunc math-rwcomp-subst-old))
840 (math-rwcomp-subst-new-func (math-var-to-calcFunc math-rwcomp-subst-new)))
841 (math-rwcomp-subst-rec expr))
842 (let ((math-rwcomp-subst-old-func nil))
843 (math-rwcomp-subst-rec expr))))
845 (defun math-rwcomp-subst-rec (expr)
846 (cond ((equal expr math-rwcomp-subst-old) math-rwcomp-subst-new)
847 ((Math-primp expr) expr)
848 (t (if (eq (car expr) math-rwcomp-subst-old-func)
849 (math-build-call math-rwcomp-subst-new-func
850 (mapcar 'math-rwcomp-subst-rec
853 (mapcar 'math-rwcomp-subst-rec (cdr expr)))))))
855 (defvar math-rwcomp-tracing nil)
857 (defun math-rwcomp-trace (instr)
858 (when math-rwcomp-tracing
859 (terpri) (princ instr))
862 (defun math-rwcomp-instr (&rest instr)
863 (setcdr math-prog-last
864 (setq math-prog-last (list (math-rwcomp-trace instr)))))
866 (defun math-rwcomp-multi-instr (tail &rest instr)
867 (setcdr math-prog-last
868 (setq math-prog-last (list (math-rwcomp-trace (append instr tail))))))
870 (defun math-rwcomp-bind-var (reg var)
871 (setcar (math-rwcomp-reg-entry reg) (nth 2 var))
872 (setq math-bound-vars (cons (nth 2 var) math-bound-vars))
873 (math-rwcomp-do-conditions))
875 (defun math-rwcomp-unbind-vars (mark)
876 (while (not (eq math-bound-vars mark))
877 (setcar (assq (car math-bound-vars) math-regs) nil)
878 (setq math-bound-vars (cdr math-bound-vars))))
880 (defun math-rwcomp-do-conditions ()
881 (let ((cond math-conds))
883 (if (math-rwcomp-all-regs-done (car cond))
884 (let ((expr (car cond)))
885 (setq math-conds (delq (car cond) math-conds))
887 (math-rwcomp-cond-instr expr)))
888 (setq cond (cdr cond)))))
890 (defun math-rwcomp-cond-instr (expr)
892 (cond ((and (eq (car-safe expr) 'calcFunc-matches)
894 (eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr))))
896 (math-rwcomp-pattern (nth 2 expr) (nth 1 arg)))
897 ((math-numberp (setq expr (math-rwcomp-match-vars expr)))
898 (if (Math-zerop expr)
899 (math-rwcomp-instr 'backtrack)))
900 ((and (eq (car expr) 'calcFunc-let)
902 (let ((reg (math-rwcomp-reg)))
903 (math-rwcomp-instr 'let reg (nth 2 expr))
904 (math-rwcomp-pattern (nth 1 expr) reg)))
905 ((and (eq (car expr) 'calcFunc-let)
907 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
908 (= (length (nth 1 expr)) 3))
909 (let ((reg (math-rwcomp-reg)))
910 (math-rwcomp-instr 'let reg (nth 2 (nth 1 expr)))
911 (math-rwcomp-pattern (nth 1 (nth 1 expr)) reg)))
912 ((and (setq op (cdr (assq (car-safe expr)
913 '( (calcFunc-integer . integer)
914 (calcFunc-real . real)
915 (calcFunc-constant . constant)
916 (calcFunc-negative . negative) ))))
918 (or (and (eq (car-safe (nth 1 expr)) 'neg)
919 (memq op '(integer real constant))
920 (setq arg (nth 1 (nth 1 expr))))
921 (setq arg (nth 1 expr)))
922 (eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register))
923 (math-rwcomp-instr op (nth 1 arg)))
924 ((and (assq (car-safe expr) calc-tweak-eqn-table)
926 (eq (car-safe (nth 1 expr)) 'calcFunc-register))
927 (if (math-constp (nth 2 expr))
928 (let ((reg (math-rwcomp-reg)))
929 (setcar (nthcdr 3 (car math-regs)) (nth 2 expr))
930 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
932 (if (eq (car (nth 2 expr)) 'calcFunc-register)
933 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
934 (car expr) (nth 1 (nth 2 expr)))
935 (math-rwcomp-instr 'cond expr))))
936 ((and (eq (car-safe expr) 'calcFunc-eq)
938 (eq (car-safe (nth 1 expr)) '%)
939 (eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register)
940 (math-constp (nth 2 (nth 1 expr)))
941 (math-constp (nth 2 expr)))
942 (math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr)))
943 (nth 2 (nth 1 expr)) (nth 2 expr)))
944 ((equal expr '(var remember var-remember))
945 (setq math-remembering 1))
946 ((and (eq (car-safe expr) 'calcFunc-remember)
948 (setq math-remembering (if math-remembering
950 math-remembering (nth 1 expr))
952 (t (math-rwcomp-instr 'cond expr)))))
954 (defun math-rwcomp-same-instr (reg1 reg2 neg)
955 (math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
956 (nth 2 (math-rwcomp-reg-entry reg2)))
962 (defun math-rwcomp-copy-instr (reg1 reg2 neg)
963 (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
964 (nth 2 (math-rwcomp-reg-entry reg2)))
966 (math-rwcomp-instr 'copy-neg reg1 reg2)
968 (math-rwcomp-instr 'copy reg1 reg2))))
970 (defun math-rwcomp-reg ()
973 (setq math-regs (cons (list nil math-num-regs nil 0) math-regs)
974 math-num-regs (1+ math-num-regs))))
976 (defun math-rwcomp-reg-entry (num)
977 (nth (1- (- math-num-regs num)) math-regs))
980 (defun math-rwcomp-pattern (expr part &optional not-direct)
981 (cond ((or (math-rwcomp-no-vars expr)
982 (and (eq (car expr) 'calcFunc-quote)
984 (setq expr (nth 1 expr))))
985 (if (eq (car-safe expr) 'calcFunc-register)
986 (math-rwcomp-same-instr part (nth 1 expr) nil)
987 (let ((reg (math-rwcomp-reg)))
988 (setcar (nthcdr 3 (car math-regs)) expr)
989 (math-rwcomp-same-instr part reg nil))))
990 ((eq (car expr) 'var)
991 (let ((entry (assq (nth 2 expr) math-regs)))
993 (math-rwcomp-same-instr part (nth 1 entry) nil)
995 (let ((reg (math-rwcomp-reg)))
996 (math-rwcomp-pattern expr reg)
997 (math-rwcomp-copy-instr part reg nil))
998 (if (setq entry (assq (nth 2 expr) math-aliased-vars))
1000 (setcar (math-rwcomp-reg-entry (nth 1 entry))
1003 (math-rwcomp-copy-instr part (nth 1 entry) nil))
1004 (math-rwcomp-bind-var part expr))))))
1005 ((and (eq (car expr) 'calcFunc-select)
1006 (= (length expr) 2))
1007 (let ((reg (math-rwcomp-reg)))
1008 (math-rwcomp-instr 'select part reg)
1009 (math-rwcomp-pattern (nth 1 expr) reg)))
1010 ((and (eq (car expr) 'calcFunc-opt)
1011 (memq (length expr) '(2 3)))
1012 (error "opt( ) occurs in context where it is not allowed"))
1013 ((eq (car expr) 'neg)
1014 (if (eq (car (nth 1 expr)) 'var)
1015 (let ((entry (assq (nth 2 (nth 1 expr)) math-regs)))
1017 (math-rwcomp-same-instr part (nth 1 entry) t)
1019 (let ((reg (math-rwcomp-best-reg (nth 1 expr))))
1020 (math-rwcomp-copy-instr part reg t)
1021 (math-rwcomp-pattern (nth 1 expr) reg))
1022 (setcar (cdr (cdr (math-rwcomp-reg-entry part))) t)
1023 (math-rwcomp-pattern (nth 1 expr) part))))
1024 (if (math-rwcomp-is-algebraic (nth 1 expr))
1025 (math-rwcomp-cond-instr (list 'calcFunc-eq
1026 (math-rwcomp-register-expr part)
1028 (let ((reg (math-rwcomp-reg)))
1029 (math-rwcomp-instr 'func part 'neg reg)
1030 (math-rwcomp-pattern (nth 1 expr) reg)))))
1031 ((and (eq (car expr) 'calcFunc-apply)
1032 (= (length expr) 3))
1033 (let ((reg1 (math-rwcomp-reg))
1034 (reg2 (math-rwcomp-reg)))
1035 (math-rwcomp-instr 'apply part reg1 reg2)
1036 (math-rwcomp-pattern (nth 1 expr) reg1)
1037 (math-rwcomp-pattern (nth 2 expr) reg2)))
1038 ((and (eq (car expr) 'calcFunc-cons)
1039 (= (length expr) 3))
1040 (let ((reg1 (math-rwcomp-reg))
1041 (reg2 (math-rwcomp-reg)))
1042 (math-rwcomp-instr 'cons part reg1 reg2)
1043 (math-rwcomp-pattern (nth 1 expr) reg1)
1044 (math-rwcomp-pattern (nth 2 expr) reg2)))
1045 ((and (eq (car expr) 'calcFunc-rcons)
1046 (= (length expr) 3))
1047 (let ((reg1 (math-rwcomp-reg))
1048 (reg2 (math-rwcomp-reg)))
1049 (math-rwcomp-instr 'rcons part reg1 reg2)
1050 (math-rwcomp-pattern (nth 1 expr) reg1)
1051 (math-rwcomp-pattern (nth 2 expr) reg2)))
1052 ((and (eq (car expr) 'calcFunc-condition)
1053 (>= (length expr) 3))
1054 (math-rwcomp-pattern (nth 1 expr) part)
1055 (setq expr (cdr expr))
1056 (while (setq expr (cdr expr))
1057 (let ((cond (math-flatten-lands (car expr))))
1059 (if (math-rwcomp-all-regs-done (car cond))
1060 (math-rwcomp-cond-instr (car cond))
1061 (setq math-conds (cons (car cond) math-conds)))
1062 (setq cond (cdr cond))))))
1063 ((and (eq (car expr) 'calcFunc-pand)
1064 (= (length expr) 3))
1065 (math-rwcomp-pattern (nth 1 expr) part)
1066 (math-rwcomp-pattern (nth 2 expr) part))
1067 ((and (eq (car expr) 'calcFunc-por)
1068 (= (length expr) 3))
1069 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1070 (let ((math-conds nil)
1071 (head math-prog-last)
1072 (mark math-bound-vars)
1074 (math-rwcomp-pattern (nth 1 expr) part t)
1075 (let ((amark math-aliased-vars)
1076 (math-aliased-vars math-aliased-vars)
1077 (tail math-prog-last)
1080 (while (not (eq p mark))
1081 (setq entry (assq (car p) math-regs)
1082 math-aliased-vars (cons (list (car p) (nth 1 entry) nil)
1085 (setcar (math-rwcomp-reg-entry (nth 1 entry)) nil))
1086 (setcar (cdr (car head)) (cdr head))
1088 (setq math-prog-last head)
1089 (math-rwcomp-pattern (nth 2 expr) part)
1090 (math-rwcomp-instr 'same 0 0)
1091 (setcdr tail math-prog-last)
1092 (setq p math-aliased-vars)
1093 (while (not (eq p amark))
1095 (setcar (math-rwcomp-reg-entry (nth 1 (car p)))
1098 (math-rwcomp-do-conditions))
1099 ((and (eq (car expr) 'calcFunc-pnot)
1100 (= (length expr) 2))
1101 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1102 (let ((head math-prog-last)
1103 (mark math-bound-vars))
1104 (math-rwcomp-pattern (nth 1 expr) part)
1105 (math-rwcomp-unbind-vars mark)
1106 (math-rwcomp-instr 'end-alt head)
1107 (math-rwcomp-instr 'backtrack)
1108 (setcar (cdr (car head)) (cdr head))
1110 (setq math-prog-last head)))
1111 (t (let ((props (get (car expr) 'math-rewrite-props)))
1112 (if (and (eq (car expr) 'calcFunc-plain)
1114 (not (math-primp (nth 1 expr))))
1115 (setq expr (nth 1 expr))) ; but "props" is still nil
1116 (if (and (memq 'algebraic props)
1117 (math-rwcomp-is-algebraic expr))
1118 (math-rwcomp-cond-instr (list 'calcFunc-eq
1119 (math-rwcomp-register-expr part)
1121 (if (and (memq 'commut props)
1122 (= (length expr) 3))
1123 (let ((arg1 (nth 1 expr))
1125 try1 def code head (flip nil))
1126 (if (eq (car expr) '-)
1127 (setq arg2 (math-rwcomp-neg arg2)))
1128 (setq arg1 (cons arg1 (math-rwcomp-best-reg arg1))
1129 arg2 (cons arg2 (math-rwcomp-best-reg arg2)))
1130 (or (math-rwcomp-order arg1 arg2)
1131 (setq def arg1 arg1 arg2 arg2 def flip t))
1132 (if (math-rwcomp-optional-arg (car expr) arg1)
1133 (error "Too many opt( ) arguments in this context"))
1134 (setq def (math-rwcomp-optional-arg (car expr) arg2)
1135 head (if (memq (car expr) '(+ -))
1137 (if (eq (car expr) '*)
1140 code (if (math-rwcomp-is-constrained
1142 (if (math-rwcomp-is-constrained
1146 (math-rwcomp-multi-instr (and def (list def))
1148 (vector nil nil nil code flip)
1150 (setq try1 (car math-prog-last))
1151 (math-rwcomp-pattern (car arg1) (cdr arg1))
1152 (math-rwcomp-instr 'try2 try1 (cdr arg2))
1153 (if (and (= part 0) (not def) (not math-rewrite-whole)
1154 (not (eq math-rhs t))
1155 (setq def (get (car expr)
1156 'math-rewrite-default)))
1157 (let ((reg1 (math-rwcomp-reg))
1158 (reg2 (math-rwcomp-reg)))
1159 (if (= (aref (nth 3 try1) 3) 0)
1160 (aset (nth 3 try1) 3 1))
1161 (math-rwcomp-instr 'try (cdr arg2)
1162 (if (equal head '(* /))
1169 (setq try1 (car math-prog-last))
1170 (math-rwcomp-pattern (car arg2) reg1)
1171 (math-rwcomp-instr 'try2 try1 reg2)
1172 (setq math-rhs (list (if (eq (car expr) '-)
1175 (list 'calcFunc-register
1177 (math-rwcomp-pattern (car arg2) (cdr arg2))))
1178 (let* ((args (mapcar (function
1180 (cons x (math-rwcomp-best-reg x))))
1182 (args2 (copy-sequence args))
1183 (argp (reverse args2))
1187 (let ((def (math-rwcomp-optional-arg (car expr)
1191 (setq args2 (delq (car argp) args2)
1192 defs (cons (cons def (cdr (car argp)))
1194 (math-rwcomp-multi-instr
1196 (if (or (and (memq 'unary1 props)
1197 (= (length args2) 1)
1198 (eq (car args2) (car args)))
1199 (and (memq 'unary2 props)
1201 (eq (car args2) (nth 1 args))))
1206 (setq argp (cdr argp)))
1207 (math-rwcomp-multi-instr (mapcar 'cdr args)
1208 'func part (car expr))
1209 (setq args (sort args 'math-rwcomp-order))
1211 (math-rwcomp-pattern (car (car args)) (cdr (car args)))
1213 args (cdr args))))))))))
1215 (defun math-rwcomp-best-reg (x)
1216 (or (and (eq (car-safe x) 'var)
1217 (let ((entry (assq (nth 2 x) math-aliased-vars)))
1220 (not (nth 2 (math-rwcomp-reg-entry (nth 1 entry))))
1222 (setcar (cdr (cdr entry)) t)
1226 (defun math-rwcomp-all-regs-done (expr)
1227 (if (Math-primp expr)
1228 (or (not (eq (car-safe expr) 'var))
1229 (assq (nth 2 expr) math-regs)
1230 (eq (nth 2 expr) 'var-remember)
1231 (math-const-var expr))
1232 (if (and (eq (car expr) 'calcFunc-let)
1233 (= (length expr) 3))
1234 (math-rwcomp-all-regs-done (nth 2 expr))
1235 (if (and (eq (car expr) 'calcFunc-let)
1237 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
1238 (= (length (nth 1 expr)) 3))
1239 (math-rwcomp-all-regs-done (nth 2 (nth 1 expr)))
1240 (while (and (setq expr (cdr expr))
1241 (math-rwcomp-all-regs-done (car expr))))
1244 (defun math-rwcomp-no-vars (expr)
1245 (if (Math-primp expr)
1246 (or (not (eq (car-safe expr) 'var))
1247 (math-const-var expr))
1248 (and (not (memq (car expr) '(calcFunc-condition
1249 calcFunc-select calcFunc-quote
1250 calcFunc-plain calcFunc-opt
1251 calcFunc-por calcFunc-pand
1252 calcFunc-pnot calcFunc-apply
1253 calcFunc-cons calcFunc-rcons)))
1255 (while (and (setq expr (cdr expr))
1256 (math-rwcomp-no-vars (car expr))))
1259 (defun math-rwcomp-is-algebraic (expr)
1260 (if (Math-primp expr)
1261 (or (not (eq (car-safe expr) 'var))
1262 (math-const-var expr)
1263 (assq (nth 2 expr) math-regs))
1264 (and (memq 'algebraic (get (car expr) 'math-rewrite-props))
1266 (while (and (setq expr (cdr expr))
1267 (math-rwcomp-is-algebraic (car expr))))
1270 (defun math-rwcomp-is-constrained (expr not-these)
1271 (if (Math-primp expr)
1272 (not (eq (car-safe expr) 'var))
1273 (if (eq (car expr) 'calcFunc-plain)
1274 (math-rwcomp-is-constrained (nth 1 expr) not-these)
1275 (not (or (memq (car expr) '(neg calcFunc-select))
1276 (memq (car expr) not-these)
1277 (and (memq 'commut (get (car expr) 'math-rewrite-props))
1278 (or (eq (car-safe (nth 1 expr)) 'calcFunc-opt)
1279 (eq (car-safe (nth 2 expr)) 'calcFunc-opt))))))))
1281 (defun math-rwcomp-optional-arg (head argp)
1282 (let ((arg (car argp)))
1283 (if (eq (car-safe arg) 'calcFunc-opt)
1284 (and (memq (length arg) '(2 3))
1286 (or (eq (car-safe (nth 1 arg)) 'var)
1287 (error "First argument of opt( ) must be a variable"))
1288 (setcar argp (nth 1 arg))
1289 (if (= (length arg) 2)
1290 (or (get head 'math-rewrite-default)
1291 (error "opt( ) must include a default in this context"))
1293 (and (eq (car-safe arg) 'neg)
1294 (let* ((part (list (nth 1 arg)))
1295 (partp (math-rwcomp-optional-arg head part)))
1297 (setcar argp (math-rwcomp-neg (car part)))
1298 (math-neg partp)))))))
1300 (defun math-rwcomp-neg (expr)
1301 (if (memq (car-safe expr) '(* /))
1302 (if (eq (car-safe (nth 1 expr)) 'var)
1303 (list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr))
1304 (if (eq (car-safe (nth 2 expr)) 'var)
1305 (list (car expr) (nth 1 expr) (list 'neg (nth 2 expr)))
1309 (defun math-rwcomp-assoc-args (expr)
1310 (if (and (eq (car-safe (nth 1 expr)) (car expr))
1311 (= (length (nth 1 expr)) 3))
1312 (math-rwcomp-assoc-args (nth 1 expr)))
1313 (if (and (eq (car-safe (nth 2 expr)) (car expr))
1314 (= (length (nth 2 expr)) 3))
1315 (math-rwcomp-assoc-args (nth 2 expr))))
1317 (defun math-rwcomp-addsub-args (expr)
1318 (if (memq (car-safe (nth 1 expr)) '(+ -))
1319 (math-rwcomp-addsub-args (nth 1 expr)))
1320 (if (eq (car expr) '-)
1322 (if (eq (car-safe (nth 2 expr)) '+)
1323 (math-rwcomp-addsub-args (nth 2 expr)))))
1325 (defun math-rwcomp-order (a b)
1326 (< (math-rwcomp-priority (car a))
1327 (math-rwcomp-priority (car b))))
1329 ;; Order of priority: 0 Constants and other exact matches (first)
1330 ;; 10 Functions (except below)
1331 ;; 20 Meta-variables which occur more than once
1332 ;; 30 Algebraic functions
1333 ;; 40 Commutative/associative functions
1334 ;; 50 Meta-variables which occur only once
1335 ;; +100 for every "!!!" (pnot) in the pattern
1336 ;; 10000 Optional arguments (last)
1338 (defun math-rwcomp-priority (expr)
1339 (+ (math-rwcomp-count-pnots expr)
1340 (cond ((eq (car-safe expr) 'calcFunc-opt)
1342 ((math-rwcomp-no-vars expr)
1344 ((eq (car expr) 'calcFunc-quote)
1346 ((eq (car expr) 'var)
1347 (if (assq (nth 2 expr) math-regs)
1349 (if (= (math-rwcomp-count-refs expr) 1)
1352 (t (let ((props (get (car expr) 'math-rewrite-props)))
1353 (if (or (memq 'commut props)
1354 (memq 'assoc props))
1356 (if (memq 'algebraic props)
1360 (defun math-rwcomp-count-refs (var)
1361 (let ((count (or (math-expr-contains-count math-pattern var) 0))
1364 (if (eq (car-safe (car p)) 'calcFunc-let)
1365 (if (= (length (car p)) 3)
1366 (setq count (+ count
1367 (or (math-expr-contains-count (nth 2 (car p)) var)
1369 (if (and (= (length (car p)) 2)
1370 (eq (car-safe (nth 1 (car p))) 'calcFunc-assign)
1371 (= (length (nth 1 (car p))) 3))
1372 (setq count (+ count
1373 (or (math-expr-contains-count
1374 (nth 2 (nth 1 (car p))) var) 0))))))
1378 (defun math-rwcomp-count-pnots (expr)
1379 (if (Math-primp expr)
1381 (if (eq (car expr) 'calcFunc-pnot)
1384 (while (setq expr (cdr expr))
1385 (setq count (+ count (math-rwcomp-count-pnots (car expr)))))
1388 ;; In the current implementation, all associative functions must
1389 ;; also be commutative.
1391 (put '+ 'math-rewrite-props '(algebraic assoc commut))
1392 (put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below
1393 (put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below
1394 (put '/ 'math-rewrite-props '(algebraic unary1))
1395 (put '^ 'math-rewrite-props '(algebraic unary1))
1396 (put '% 'math-rewrite-props '(algebraic))
1397 (put 'neg 'math-rewrite-props '(algebraic))
1398 (put 'calcFunc-idiv 'math-rewrite-props '(algebraic))
1399 (put 'calcFunc-abs 'math-rewrite-props '(algebraic))
1400 (put 'calcFunc-sign 'math-rewrite-props '(algebraic))
1401 (put 'calcFunc-round 'math-rewrite-props '(algebraic))
1402 (put 'calcFunc-rounde 'math-rewrite-props '(algebraic))
1403 (put 'calcFunc-roundu 'math-rewrite-props '(algebraic))
1404 (put 'calcFunc-trunc 'math-rewrite-props '(algebraic))
1405 (put 'calcFunc-floor 'math-rewrite-props '(algebraic))
1406 (put 'calcFunc-ceil 'math-rewrite-props '(algebraic))
1407 (put 'calcFunc-re 'math-rewrite-props '(algebraic))
1408 (put 'calcFunc-im 'math-rewrite-props '(algebraic))
1409 (put 'calcFunc-conj 'math-rewrite-props '(algebraic))
1410 (put 'calcFunc-arg 'math-rewrite-props '(algebraic))
1411 (put 'calcFunc-and 'math-rewrite-props '(assoc commut))
1412 (put 'calcFunc-or 'math-rewrite-props '(assoc commut))
1413 (put 'calcFunc-xor 'math-rewrite-props '(assoc commut))
1414 (put 'calcFunc-eq 'math-rewrite-props '(commut))
1415 (put 'calcFunc-neq 'math-rewrite-props '(commut))
1416 (put 'calcFunc-land 'math-rewrite-props '(assoc commut))
1417 (put 'calcFunc-lor 'math-rewrite-props '(assoc commut))
1418 (put 'calcFunc-beta 'math-rewrite-props '(commut))
1419 (put 'calcFunc-gcd 'math-rewrite-props '(assoc commut))
1420 (put 'calcFunc-lcm 'math-rewrite-props '(assoc commut))
1421 (put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut))
1422 (put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut))
1423 (put 'calcFunc-vunion 'math-rewrite-props '(assoc commut))
1424 (put 'calcFunc-vint 'math-rewrite-props '(assoc commut))
1425 (put 'calcFunc-vxor 'math-rewrite-props '(assoc commut))
1427 ;; Note: "*" is not commutative for matrix args, but we pretend it is.
1428 ;; Also, "-" is not commutative but the code tweaks things so that it is.
1430 (put '+ 'math-rewrite-default 0)
1431 (put '- 'math-rewrite-default 0)
1432 (put '* 'math-rewrite-default 1)
1433 (put '/ 'math-rewrite-default 1)
1434 (put '^ 'math-rewrite-default 1)
1435 (put 'calcFunc-land 'math-rewrite-default 1)
1436 (put 'calcFunc-lor 'math-rewrite-default 0)
1437 (put 'calcFunc-vunion 'math-rewrite-default '(vec))
1438 (put 'calcFunc-vint 'math-rewrite-default '(vec))
1439 (put 'calcFunc-vdiff 'math-rewrite-default '(vec))
1440 (put 'calcFunc-vxor 'math-rewrite-default '(vec))
1442 (defmacro math-rwfail (&optional back)
1446 '(setq btrack (cdr btrack))
1450 ;; This monstrosity is necessary because the use of static vectors of
1451 ;; registers makes rewrite rules non-reentrant. Yucko!
1452 (defmacro math-rweval (form)
1453 (list 'let '((orig (car rules)))
1454 '(setcar rules (quote (nil nil nil no-phase)))
1455 (list 'unwind-protect
1457 '(setcar rules orig))))
1459 (defvar math-rewrite-phase 1)
1461 ;; The variable math-apply-rw-regs is local to math-apply-rewrites,
1462 ;; but is used by math-rwapply-replace-regs and math-rwapply-reg-looks-negp
1463 ;; which are called by math-apply-rewrites.
1464 (defvar math-apply-rw-regs)
1466 ;; The variable math-apply-rw-ruleset is local to math-apply-rewrites,
1467 ;; but is used by math-rwapply-remember.
1468 (defvar math-apply-rw-ruleset)
1470 (defun math-apply-rewrites (expr rules &optional heads math-apply-rw-ruleset)
1472 (setq rules (cdr (or (assq (car-safe expr) rules)
1475 op math-apply-rw-regs inst part pc mark btrack
1476 (tracing math-rwcomp-tracing)
1477 (phase math-rewrite-phase))
1480 (and (setq part (nth 2 (car rules)))
1482 (not (memq part heads)))
1483 (and (setq part (nth 3 (car rules)))
1484 (not (memq phase part)))
1486 (setq math-apply-rw-regs (car (car rules))
1487 pc (nth 1 (car rules))
1489 (aset math-apply-rw-regs 0 expr)
1493 (progn (terpri) (princ (car pc))
1494 (if (and (natnump (nth 1 (car pc)))
1495 (< (nth 1 (car pc)) (length math-apply-rw-regs)))
1497 (format "\n part = %s"
1498 (aref math-apply-rw-regs (nth 1 (car pc))))))))
1500 (cond ((eq (setq op (car (setq inst (car pc)))) 'func)
1502 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1504 (car (setq inst (cdr (cdr inst)))))
1506 (while (and (setq inst (cdr inst)
1509 (aset math-apply-rw-regs (car inst) (car part)))
1510 (not (or inst part))))
1515 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1516 (setq mark (aref math-apply-rw-regs (nth 2 inst))))
1517 (Math-equal part mark))
1523 (not (eq calc-matrix-mode 'scalar))
1524 (eq (car (nth 2 inst)) '*)
1525 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1527 (not (math-known-scalarp part)))
1528 (setq mark (nth 3 inst)
1532 (aset math-apply-rw-regs (nth 4 inst) (nth 2 part))
1533 (aset mark 1 (cdr (cdr part))))
1534 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1535 (aset mark 1 (cdr part)))
1536 (aset mark 0 (cdr part))
1540 (if (and (consp (setq part
1541 (aref math-apply-rw-regs (car (cdr inst)))))
1542 (memq (car part) (nth 2 inst))
1544 (or (not (eq (car part) '/))
1545 (Math-objectp (nth 2 part))))
1548 mark (car (cdr (setq inst (cdr (cdr inst))))))
1550 (memq 'assoc (get (car part) 'math-rewrite-props))
1551 (not (= (aref mark 3) 0))
1552 (while (if (and (consp (nth 1 part))
1553 (memq (car (nth 1 part)) (car inst)))
1554 (setq op (cons (if (eq (car part) '-)
1560 (if (and (consp (nth 2 part))
1561 (memq (car (nth 2 part))
1563 (not (eq (car (nth 2 part)) '-)))
1564 (setq op (cons (nth 1 part) op)
1565 part (nth 2 part))))))
1566 (setq op (cons (nth 1 part)
1567 (cons (if (eq (car part) '-)
1570 (if (eq (car part) '/)
1575 btrack (cons pc btrack)
1577 (aset math-apply-rw-regs (nth 2 inst) (car op))
1580 (aset mark 2 (if (cdr (cdr op)) 1 0)))
1582 (if (and (consp part)
1583 (eq (car part) 'neg)
1584 (eq (car (nth 2 inst)) '*)
1585 (eq (nth 5 inst) 1))
1587 (setq mark (nth 3 inst)
1589 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1592 (setq mark (nth 3 inst)
1594 (aset math-apply-rw-regs (nth 4 inst) part)
1599 (setq part (nth 1 inst) ; try instr
1603 (aset math-apply-rw-regs (nth 2 inst)
1606 (if (eq (aref mark 0) (aref mark 1))
1607 (nth 1 (aref mark 0))
1608 (car (aref mark 0))))
1610 (setq mark (delq (car (aref mark 1))
1611 (copy-sequence (aref mark 0)))
1612 op (car (nth 2 part)))
1615 (setq mark (nreverse mark)
1616 part (list '* (nth 1 mark) (car mark))
1618 (while (setq mark (cdr mark))
1619 (setq part (list '* (car mark) part))))
1620 (setq part (car mark)
1622 part (if (and (eq op '+)
1624 (eq (car (car mark)) 'neg))
1627 (list op part (car mark))))
1628 (while (setq mark (cdr mark))
1629 (setq part (if (and (eq op '+)
1631 (eq (car (car mark)) 'neg))
1634 (list op part (car mark))))))
1637 (car (aref mark 1)))
1638 ((eq op 3) (nth 5 part))
1639 (t (aref mark 1)))))
1643 (if (and (consp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1644 (eq (car part) 'calcFunc-select))
1645 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1646 (if math-rewrite-selections
1648 (aset math-apply-rw-regs (nth 2 inst) part))))
1651 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1652 (setq mark (math-neg
1653 (aref math-apply-rw-regs (nth 2 inst)))))
1654 (Math-equal part mark))
1659 (setq inst (car (car btrack)) ; "try" or "alt" instr
1660 pc (cdr (car btrack))
1661 mark (or (nth 3 inst) [nil nil 4])
1664 (if (setq op (cdr (aref mark 1)))
1665 (aset math-apply-rw-regs (nth 4 inst)
1666 (car (aset mark 1 op)))
1670 (aset math-apply-rw-regs (nth 4 inst)
1671 (aref math-apply-rw-regs (nth 1 inst))))
1674 (if (setq op (cdr (aref mark 1)))
1675 (aset math-apply-rw-regs (nth 4 inst)
1676 (car (aset mark 1 op)))
1677 (if (= (aref mark 3) 1)
1681 (aset math-apply-rw-regs (nth 4 inst)
1682 (aref math-apply-rw-regs (nth 1 inst))))
1685 (aset mark 1 (cons nil (aref mark 0)))
1688 (if (setq op (cdr (aref mark 1)))
1690 (setq mark (delq (car (aset mark 1 op))
1693 op (car (nth 2 inst)))
1696 (setq mark (nreverse mark)
1697 part (list '* (nth 1 mark)
1700 (while (setq mark (cdr mark))
1701 (setq part (list '* (car mark)
1703 (setq part (car mark)
1705 part (if (and (eq op '+)
1707 (eq (car (car mark))
1711 (list op part (car mark))))
1712 (while (setq mark (cdr mark))
1713 (setq part (if (and (eq op '+)
1715 (eq (car (car mark))
1719 (list op part (car mark))))))
1720 (aset math-apply-rw-regs (nth 4 inst) part))
1724 (aset math-apply-rw-regs (nth 4 inst)
1725 (aref math-apply-rw-regs (nth 1 inst))))
1728 (setq btrack (cdr btrack)))
1729 (t (math-rwfail t))))
1732 (if (Math-integerp (setq part
1733 (aref math-apply-rw-regs (nth 1 inst))))
1735 (if (Math-primp part)
1737 (setq part (math-rweval (math-simplify part)))
1738 (if (Math-integerp part)
1743 (if (Math-realp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1745 (if (Math-primp part)
1747 (setq part (math-rweval (math-simplify part)))
1748 (if (Math-realp part)
1753 (if (math-constp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1755 (if (Math-primp part)
1757 (setq part (math-rweval (math-simplify part)))
1758 (if (math-constp part)
1763 (if (math-looks-negp (setq part
1764 (aref math-apply-rw-regs (nth 1 inst))))
1766 (if (Math-primp part)
1768 (setq part (math-rweval (math-simplify part)))
1769 (if (math-looks-negp part)
1774 (setq part (math-compare (aref math-apply-rw-regs (nth 1 inst))
1775 (aref math-apply-rw-regs (nth 3 inst)))
1778 (setq part (math-rweval
1782 (aref math-apply-rw-regs (nth 1 inst))
1783 (aref math-apply-rw-regs (nth 3 inst))))))))
1784 (if (cond ((eq op 'calcFunc-eq)
1786 ((eq op 'calcFunc-neq)
1787 (memq part '(-1 1)))
1788 ((eq op 'calcFunc-lt)
1790 ((eq op 'calcFunc-leq)
1791 (memq part '(-1 0)))
1792 ((eq op 'calcFunc-gt)
1794 ((eq op 'calcFunc-geq)
1795 (memq part '(0 1))))
1801 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1803 (car (setq inst (cdr (cdr inst))))))
1805 (setq inst (cdr inst)
1807 (while (and (setq inst (cdr inst)
1810 (aset math-apply-rw-regs (car inst) (car part)))
1813 (while (eq (car (car (setq pc (cdr pc))))
1815 (setq pc (cdr pc)) ; skip over "func"
1817 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1818 (setq mark (cdr mark)))))
1825 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1826 (eq (car part) (nth 2 inst))))
1827 (and (= (length part) 2)
1828 (setq part (nth 1 part))))
1830 (setq mark (nth 3 inst))
1831 (aset math-apply-rw-regs (nth 4 inst) part)
1832 (while (eq (car (car (setq pc (cdr pc)))) 'func-def))
1833 (setq pc (cdr pc)) ; skip over "func"
1835 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1836 (setq mark (cdr mark))))
1837 (setq pc (cdr pc))))
1841 (setq part (aref math-apply-rw-regs (nth 1 inst))))
1842 (Math-zerop (nth 3 inst))
1843 (and (not (Math-zerop (nth 2 inst)))
1845 (setq part (math-mod part (nth 2 inst)))
1846 (or (Math-numberp part)
1847 (setq part (math-rweval
1848 (math-simplify part))))
1849 (Math-equal part (nth 3 inst)))))
1855 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1856 (not (Math-objvecp part))
1857 (not (eq (car part) 'var)))
1859 (aset math-apply-rw-regs (nth 2 inst)
1860 (math-calcFunc-to-var (car part)))
1861 (aset math-apply-rw-regs (nth 3 inst)
1862 (cons 'vec (cdr part)))
1868 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1869 (eq (car part) 'vec)
1872 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1873 (aset math-apply-rw-regs (nth 3 inst)
1874 (cons 'vec (cdr (cdr part))))
1880 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1881 (eq (car part) 'vec)
1884 (aset math-apply-rw-regs (nth 2 inst) (calcFunc-rhead part))
1885 (aset math-apply-rw-regs (nth 3 inst) (calcFunc-rtail part))
1893 (math-rwapply-replace-regs (nth 1 inst)))))
1898 (aset math-apply-rw-regs (nth 1 inst)
1901 (math-rwapply-replace-regs (nth 2 inst)))))
1905 (aset math-apply-rw-regs (nth 2 inst)
1906 (aref math-apply-rw-regs (nth 1 inst)))
1910 (aset math-apply-rw-regs (nth 2 inst)
1911 (math-rwapply-neg (aref math-apply-rw-regs (nth 1 inst))))
1915 (setq btrack (cons pc btrack)
1919 (while (and btrack (not (eq (car btrack) (nth 1 inst))))
1920 (setq btrack (cdr btrack)))
1921 (setq btrack (cdr btrack)
1925 (setq result (math-rwapply-replace-regs (nth 1 inst)))
1926 (if (or (and (eq (car-safe result) '+)
1927 (eq (nth 2 result) 0))
1928 (and (eq (car-safe result) '*)
1929 (eq (nth 2 result) 1)))
1930 (setq result (nth 1 result)))
1931 (setq part (and (nth 2 inst)
1935 (math-rwapply-replace-regs
1937 (if (or (equal result expr)
1938 (equal (setq result (math-normalize result)) expr))
1940 (if part (math-rwapply-remember expr result))
1944 (t (error "%s is not a valid rewrite opcode" op))))))
1945 (setq rules (cdr rules)))
1948 (defun math-rwapply-neg (expr)
1949 (if (and (consp expr)
1950 (memq (car expr) '(* /)))
1951 (if (Math-objectp (nth 2 expr))
1952 (list (car expr) (nth 1 expr) (math-neg (nth 2 expr)))
1954 (if (Math-objectp (nth 1 expr))
1955 (math-neg (nth 1 expr))
1956 (list '* -1 (nth 1 expr)))
1960 (defun math-rwapply-inv (expr)
1961 (if (and (Math-integerp expr)
1963 (math-make-frac 1 expr)
1966 (defun math-rwapply-replace-regs (expr)
1967 (cond ((Math-primp expr)
1969 ((eq (car expr) 'calcFunc-register)
1970 (setq expr (aref math-apply-rw-regs (nth 1 expr)))
1971 (if (eq (car-safe expr) '*)
1972 (if (eq (nth 1 expr) -1)
1973 (math-neg (nth 2 expr))
1974 (if (eq (nth 1 expr) 1)
1978 ((and (eq (car expr) 'calcFunc-eval)
1979 (= (length expr) 2))
1980 (calc-with-default-simplification
1981 (math-normalize (math-rwapply-replace-regs (nth 1 expr)))))
1982 ((and (eq (car expr) 'calcFunc-evalsimp)
1983 (= (length expr) 2))
1984 (math-simplify (math-rwapply-replace-regs (nth 1 expr))))
1985 ((and (eq (car expr) 'calcFunc-evalextsimp)
1986 (= (length expr) 2))
1987 (math-simplify-extended (math-rwapply-replace-regs (nth 1 expr))))
1988 ((and (eq (car expr) 'calcFunc-apply)
1989 (= (length expr) 3))
1990 (let ((func (math-rwapply-replace-regs (nth 1 expr)))
1991 (args (math-rwapply-replace-regs (nth 2 expr)))
1993 (if (and (math-vectorp args)
1994 (not (eq (car-safe (setq call (math-build-call
1995 (math-var-to-calcFunc func)
1999 (list 'calcFunc-apply func args))))
2000 ((and (eq (car expr) 'calcFunc-cons)
2001 (= (length expr) 3))
2002 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2003 (tail (math-rwapply-replace-regs (nth 2 expr))))
2004 (if (math-vectorp tail)
2005 (cons 'vec (cons head (cdr tail)))
2006 (list 'calcFunc-cons head tail))))
2007 ((and (eq (car expr) 'calcFunc-rcons)
2008 (= (length expr) 3))
2009 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2010 (tail (math-rwapply-replace-regs (nth 2 expr))))
2011 (if (math-vectorp head)
2012 (append head (list tail))
2013 (list 'calcFunc-rcons head tail))))
2014 ((and (eq (car expr) 'neg)
2015 (math-rwapply-reg-looks-negp (nth 1 expr)))
2016 (math-rwapply-reg-neg (nth 1 expr)))
2017 ((and (eq (car expr) 'neg)
2018 (eq (car-safe (nth 1 expr)) 'calcFunc-register)
2019 (math-scalarp (aref math-apply-rw-regs (nth 1 (nth 1 expr)))))
2020 (math-neg (math-rwapply-replace-regs (nth 1 expr))))
2021 ((and (eq (car expr) '+)
2022 (math-rwapply-reg-looks-negp (nth 1 expr)))
2023 (list '- (math-rwapply-replace-regs (nth 2 expr))
2024 (math-rwapply-reg-neg (nth 1 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))))
2029 ((and (eq (car expr) '-)
2030 (math-rwapply-reg-looks-negp (nth 2 expr)))
2031 (list '+ (math-rwapply-replace-regs (nth 1 expr))
2032 (math-rwapply-reg-neg (nth 2 expr))))
2034 (cond ((eq (nth 1 expr) -1)
2035 (if (math-rwapply-reg-looks-negp (nth 2 expr))
2036 (math-rwapply-reg-neg (nth 2 expr))
2037 (math-neg (math-rwapply-replace-regs (nth 2 expr)))))
2038 ((eq (nth 1 expr) 1)
2039 (math-rwapply-replace-regs (nth 2 expr)))
2040 ((eq (nth 2 expr) -1)
2041 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2042 (math-rwapply-reg-neg (nth 1 expr))
2043 (math-neg (math-rwapply-replace-regs (nth 1 expr)))))
2044 ((eq (nth 2 expr) 1)
2045 (math-rwapply-replace-regs (nth 1 expr)))
2047 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2048 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2049 (cond ((and (eq (car-safe arg1) '/)
2050 (eq (nth 1 arg1) 1))
2051 (list '/ arg2 (nth 2 arg1)))
2052 ((and (eq (car-safe arg2) '/)
2053 (eq (nth 1 arg2) 1))
2054 (list '/ arg1 (nth 2 arg2)))
2055 (t (list '* arg1 arg2)))))))
2057 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2058 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2059 (if (eq (car-safe arg2) '/)
2060 (list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2))
2061 (list '/ arg1 arg2))))
2062 ((and (eq (car expr) 'calcFunc-plain)
2063 (= (length expr) 2))
2064 (if (Math-primp (nth 1 expr))
2066 (if (eq (car (nth 1 expr)) 'calcFunc-register)
2067 (aref math-apply-rw-regs (nth 1 (nth 1 expr)))
2068 (cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs
2069 (cdr (nth 1 expr)))))))
2070 (t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr))))))
2072 (defun math-rwapply-reg-looks-negp (expr)
2073 (if (eq (car-safe expr) 'calcFunc-register)
2074 (math-looks-negp (aref math-apply-rw-regs (nth 1 expr)))
2075 (if (memq (car-safe expr) '(* /))
2076 (or (math-rwapply-reg-looks-negp (nth 1 expr))
2077 (math-rwapply-reg-looks-negp (nth 2 expr))))))
2079 (defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp
2080 (if (eq (car expr) 'calcFunc-register)
2081 (math-neg (math-rwapply-replace-regs expr))
2082 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2083 (math-rwapply-replace-regs (list (car expr)
2084 (math-rwapply-reg-neg (nth 1 expr))
2086 (math-rwapply-replace-regs (list (car expr)
2088 (math-rwapply-reg-neg (nth 2 expr)))))))
2090 (defun math-rwapply-remember (old new)
2091 (let ((varval (symbol-value (nth 2 (car math-apply-rw-ruleset))))
2092 (rules (assq (car-safe old) math-apply-rw-ruleset)))
2093 (if (and (eq (car-safe varval) 'vec)
2094 (not (memq (car-safe old) '(nil schedule + -)))
2097 (setcdr varval (cons (list 'calcFunc-assign
2098 (if (math-rwcomp-no-vars old)
2100 (list 'calcFunc-quote old))
2103 (setcdr rules (cons (list (vector nil old)
2104 (list (list 'same 0 1)
2105 (list 'done new nil))
2109 (provide 'calc-rewr)
2111 ;;; calc-rewr.el ends here