1 ;;; calc-rewr.el --- rewriting functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005, 2006, 2007, 2008 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))))
194 (set-buffer trace-buffer)
195 (insert "\nrewrite to\n" fmt "\n"))))
196 (setq heads (math-rewrite-heads result heads t))))
199 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
201 (set-buffer trace-buffer)
202 (setq truncate-lines t)
203 (goto-char (point-max))
204 (insert "\n\nBegin rewriting\n" fmt "\n"))))
205 (or math-mt-many (setq math-mt-many (or (nth 1 (car crules))
206 math-rewrite-default-iters)))
207 (if (equal math-mt-many '(var inf var-inf)) (setq math-mt-many 1000000))
208 (if (equal math-mt-many '(neg (var inf var-inf))) (setq math-mt-many -1000000))
209 (math-rewrite-phase (nth 3 (car crules)))
211 (let ((fmt (math-format-stack-value (list math-rewrite-whole-expr nil nil))))
213 (set-buffer trace-buffer)
214 (insert "\nDone rewriting"
215 (if (= math-mt-many 0) " (reached iteration limit)" "")
217 math-rewrite-whole-expr))
219 (defun math-rewrite-phase (sched)
220 (while (and sched (/= math-mt-many 0))
221 (if (listp (car sched))
222 (while (let ((save-expr math-rewrite-whole-expr))
223 (math-rewrite-phase (car sched))
224 (not (equal math-rewrite-whole-expr save-expr))))
225 (if (symbolp (car sched))
227 (setq math-rewrite-whole-expr
228 (math-normalize (list (car sched) math-rewrite-whole-expr)))
230 (let ((fmt (math-format-stack-value
231 (list math-rewrite-whole-expr nil nil))))
233 (set-buffer trace-buffer)
235 (substring (symbol-name (car sched)) 9)
237 (let ((math-rewrite-phase (car sched)))
240 (set-buffer trace-buffer)
241 (insert (format "\n(Phase %d)\n" math-rewrite-phase))))
242 (while (let ((save-expr math-rewrite-whole-expr))
243 (setq math-rewrite-whole-expr (math-normalize
244 (math-map-tree-rec math-rewrite-whole-expr)))
245 (not (equal math-rewrite-whole-expr save-expr)))))))
246 (setq sched (cdr sched))))
248 (defun calcFunc-rewrite (expr rules &optional many)
249 (or (null many) (integerp many)
250 (equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf)))
251 (math-reject-arg many 'fixnump))
253 (math-rewrite expr rules (or many 1))
254 (error (math-reject-arg rules (nth 1 err)))))
256 (defun calcFunc-match (pat vec)
257 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
259 (math-match-patterns pat vec nil)
260 (error (math-reject-arg pat (nth 1 err)))))
262 (defun calcFunc-matchnot (pat vec)
263 (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
265 (math-match-patterns pat vec t)
266 (error (math-reject-arg pat (nth 1 err)))))
268 (defun math-match-patterns (pat vec &optional not-flag)
270 (crules (math-compile-patterns pat)))
271 (while (setq vec (cdr vec))
272 (if (eq (not (math-apply-rewrites (car vec) crules))
274 (setq newvec (cons (car vec) newvec))))
275 (cons 'vec (nreverse newvec))))
277 (defun calcFunc-matches (expr pat)
279 (if (math-apply-rewrites expr (math-compile-patterns pat))
282 (error (math-reject-arg pat (nth 1 err)))))
284 (defun calcFunc-vmatches (expr pat)
286 (or (math-apply-rewrites expr (math-compile-patterns pat))
288 (error (math-reject-arg pat (nth 1 err)))))
292 ;;; A compiled rule set is an a-list of entries whose cars are functors,
293 ;;; and whose cdrs are lists of rules. If there are rules with no
294 ;;; well-defined head functor, they are included on all lists and also
295 ;;; on an extra list whose car is nil.
297 ;;; The first entry in the a-list is of the form (schedule A B C ...).
299 ;;; Rule list entries take the form (regs prog head phases), where:
301 ;;; regs is a vector of match registers.
303 ;;; prog is a match program (see below).
305 ;;; head is a rare function name appearing in the rule body (but not the
306 ;;; head of the whole rule), or nil if none.
308 ;;; phases is a list of phase numbers for which the rule is enabled.
310 ;;; A match program is a list of match instructions.
312 ;;; In the following, "part" is a register number that contains the
313 ;;; subexpression to be operated on.
315 ;;; Register 0 is the whole expression being matched. The others are
316 ;;; meta-variables in the pattern, temporaries used for matching and
317 ;;; backtracking, and constant expressions.
320 ;;; The selected part must be math-equal to the contents of "reg".
322 ;;; (same-neg part reg)
323 ;;; The selected part must be math-equal to the negative of "reg".
326 ;;; The selected part is copied into "reg". (Rarely used.)
328 ;;; (copy-neg part reg)
329 ;;; The negative of the selected part is copied into "reg".
332 ;;; The selected part must be an integer.
335 ;;; The selected part must be a real.
338 ;;; The selected part must be a constant.
341 ;;; The selected part must "look" negative.
343 ;;; (rel part op reg)
344 ;;; The selected part must satisfy "part op reg", where "op"
345 ;;; is one of the 6 relational ops, and "reg" is a register.
347 ;;; (mod part modulo value)
348 ;;; The selected part must satisfy "part % modulo = value", where
349 ;;; "modulo" and "value" are constants.
351 ;;; (func part head reg1 reg2 ... regn)
352 ;;; The selected part must be an n-ary call to function "head".
353 ;;; The arguments are stored in "reg1" through "regn".
355 ;;; (func-def part head defs reg1 reg2 ... regn)
356 ;;; The selected part must be an n-ary call to function "head".
357 ;;; "Defs" is a list of value/register number pairs for default args.
358 ;;; If a match, assign default values to registers and then skip
359 ;;; immediately over any following "func-def" instructions and
360 ;;; the following "func" instruction. If wrong number of arguments,
361 ;;; proceed to the following "func-def" or "func" instruction.
363 ;;; (func-opt part head defs reg1)
364 ;;; Like func-def with "n=1", except that if the selected part is
365 ;;; not a call to "head", then the part itself successfully matches
366 ;;; "reg1" (and the defaults are assigned).
368 ;;; (try part heads mark reg1 [def])
369 ;;; The selected part must be a function of the correct type which is
370 ;;; associative and/or commutative. "Heads" is a list of acceptable
371 ;;; types. An initial assignment of arguments to "reg1" is tried.
372 ;;; If the program later fails, it backtracks to this instruction
373 ;;; and tries other assignments of arguments to "reg1".
374 ;;; If "def" exists and normal matching fails, backtrack and assign
375 ;;; "part" to "reg1", and "def" to "reg2" in the following "try2".
376 ;;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized.
377 ;;; "mark[0]" points to the argument list; "mark[1]" points to the
378 ;;; current argument; "mark[2]" is 0 if there are two arguments,
379 ;;; 1 if reg1 is matching single arguments, 2 if reg2 is matching
380 ;;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or
381 ;;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must
382 ;;; have two arguments, 1 if phase-2 can be skipped, 2 if full
383 ;;; backtracking is necessary; "mark[4]" is t if the arguments have
384 ;;; been switched from the order given in the original pattern.
387 ;;; Every "try" will be followed by a "try2" whose "try" field is
388 ;;; a pointer to the corresponding "try". The arguments which were
389 ;;; not stored in "reg1" by that "try" are now stored in "reg2".
391 ;;; (alt instr nil mark)
392 ;;; Basic backtracking. Execute the instruction sequence "instr".
393 ;;; If this fails, back up and execute following the "alt" instruction.
394 ;;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence
395 ;;; should execute "end-alt" at the end.
398 ;;; Register success of the first alternative of a previous "alt".
399 ;;; "Ptr" is a pointer to the next instruction following that "alt".
401 ;;; (apply part reg1 reg2)
402 ;;; The selected part must be a function call. The functor
403 ;;; (as a variable name) is stored in "reg1"; the arguments
404 ;;; (as a vector) are stored in "reg2".
406 ;;; (cons part reg1 reg2)
407 ;;; The selected part must be a nonempty vector. The first element
408 ;;; of the vector is stored in "reg1"; the rest of the vector
409 ;;; (as another vector) is stored in "reg2".
411 ;;; (rcons part reg1 reg2)
412 ;;; The selected part must be a nonempty vector. The last element
413 ;;; of the vector is stored in "reg2"; the rest of the vector
414 ;;; (as another vector) is stored in "reg1".
416 ;;; (select part reg)
417 ;;; If the selected part is a unary call to function "select", its
418 ;;; argument is stored in "reg"; otherwise (provided this is an `a r'
419 ;;; and not a `g r' command) the selected part is stored in "reg".
422 ;;; The "expr", with registers substituted, must simplify to
423 ;;; a non-zero value.
426 ;;; Evaluate "expr" and store the result in "reg". Always succeeds.
428 ;;; (done rhs remember)
429 ;;; Rewrite the expression to "rhs", with register substituted.
430 ;;; Normalize; if the result is different from the original
431 ;;; expression, the match has succeeded. This is the last
432 ;;; instruction of every program. If "remember" is non-nil,
433 ;;; record the result of the match as a new literal rule.
436 ;;; Pseudo-functions related to rewrites:
438 ;;; In patterns: quote, plain, condition, opt, apply, cons, select
440 ;;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp,
441 ;;; apply, cons, select
443 ;;; In conditions: let + same as for righthand sides
445 ;;; Some optimizations that would be nice to have:
447 ;;; * Merge registers with disjoint lifetimes.
448 ;;; * Merge constant registers with equivalent values.
450 ;;; * If an argument of a commutative op math-depends neither on the
451 ;;; rest of the pattern nor on any of the conditions, then no backtracking
452 ;;; should be done for that argument. (This won't apply to very many
455 ;;; * If top functor is "select", and its argument is a unique function,
456 ;;; add the rule to the lists for both "select" and that function.
457 ;;; (Currently rules like this go on the "nil" list.)
458 ;;; Same for "func-opt" functions. (Though not urgent for these.)
460 ;;; * Shouldn't evaluate a "let" condition until the end, or until it
461 ;;; would enable another condition to be evaluated.
464 ;;; Some additional features to add / things to think about:
466 ;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)".
468 ;;; * Same for interval forms.
470 ;;; * Have a name(v,pat) pattern which matches pat, and gives the
471 ;;; whole match the name v. Beware of circular structures!
474 (defun math-compile-patterns (pats)
475 (if (and (eq (car-safe pats) 'var)
476 (calc-var-value (nth 2 pats)))
477 (let ((prop (get (nth 2 pats) 'math-pattern-cache)))
479 (put (nth 2 pats) 'math-pattern-cache (setq prop (list nil))))
480 (or (eq (car prop) (symbol-value (nth 2 pats)))
482 (setcdr prop (math-compile-patterns
483 (symbol-value (nth 2 pats))))
484 (setcar prop (symbol-value (nth 2 pats)))))
486 (let ((math-rewrite-whole t))
487 (cdr (math-compile-rewrites (cons
489 (mapcar (function (lambda (x)
491 (if (eq (car-safe pats) 'vec)
495 (defvar math-rewrite-whole nil)
496 (defvar math-make-import-list nil)
498 ;; The variable math-import-list is local to part of math-compile-rewrites,
499 ;; but is also used in a different part, and so the local version could
500 ;; be affected by the non-local version when math-compile-rewrites calls itself.
501 (defvar math-import-list nil)
503 ;; The variables math-regs, math-num-regs, math-prog-last, math-bound-vars,
504 ;; math-conds, math-copy-neg, math-rhs, math-pattern, math-remembering and
505 ;; math-aliased-vars are local to math-compile-rewrites,
506 ;; but are used by many functions math-rwcomp-*, which are called by
507 ;; math-compile-rewrites.
509 (defvar math-num-regs)
510 (defvar math-prog-last)
511 (defvar math-bound-vars)
513 (defvar math-copy-neg)
515 (defvar math-pattern)
516 (defvar math-remembering)
517 (defvar math-aliased-vars)
519 (defun math-compile-rewrites (rules &optional name)
520 (if (eq (car-safe rules) 'var)
521 (let ((prop (get (nth 2 rules) 'math-rewrite-cache))
522 (math-import-list nil)
523 (math-make-import-list t)
525 (or (calc-var-value (nth 2 rules))
526 (error "Rules variable %s has no stored value" (nth 1 rules)))
528 (put (nth 2 rules) 'math-rewrite-cache
529 (setq prop (list (list (cons (nth 2 rules) nil))))))
531 (while (and p (eq (symbol-value (car (car p))) (cdr (car p))))
535 (message "Compiling rule set %s..." (nth 1 rules))
536 (setcdr prop (math-compile-rewrites
537 (symbol-value (nth 2 rules))
539 (message "Compiling rule set %s...done" (nth 1 rules))
540 (setcar prop (cons (cons (nth 2 rules)
541 (symbol-value (nth 2 rules)))
544 (if (or (not (eq (car-safe rules) 'vec))
545 (and (memq (length rules) '(3 4))
547 (while (and (setq p (cdr p))
548 (memq (car-safe (car p))
555 calcFunc-iterations))))
557 (setq rules (list rules))
558 (setq rules (cdr rules)))
559 (if (assq 'calcFunc-import rules)
560 (let ((pp (setq rules (copy-sequence rules)))
562 (while (setq p (car (cdr pp)))
563 (if (eq (car-safe p) 'calcFunc-import)
565 (setcdr pp (cdr (cdr pp)))
566 (or (and (eq (car-safe (nth 1 p)) 'var)
567 (setq part (calc-var-value (nth 2 (nth 1 p))))
568 (memq (car-safe part) '(vec
570 calcFunc-condition)))
571 (error "Argument of import() must be a rules variable"))
572 (if math-make-import-list
573 (setq math-import-list
574 (cons (cons (nth 2 (nth 1 p))
575 (symbol-value (nth 2 (nth 1 p))))
577 (while (setq p (cdr (cdr p)))
579 (error "import() must have odd number of arguments"))
580 (setq part (math-rwcomp-substitute part
582 (if (eq (car-safe part) 'vec)
583 (setq part (cdr part))
584 (setq part (list part)))
585 (setcdr pp (append part (cdr pp))))
586 (setq pp (cdr pp))))))
592 (math-iterations nil)
594 (math-all-phases nil)
595 (math-remembering nil)
596 math-pattern math-rhs math-conds)
599 ((and (eq (car-safe (car rules)) 'calcFunc-iterations)
600 (= (length (car rules)) 2))
601 (or (integerp (nth 1 (car rules)))
602 (equal (nth 1 (car rules)) '(var inf var-inf))
603 (equal (nth 1 (car rules)) '(neg (var inf var-inf)))
604 (error "Invalid argument for iterations(n)"))
606 (setq math-iterations (nth 1 (car rules)))))
607 ((eq (car-safe (car rules)) 'calcFunc-schedule)
609 (setq math-schedule (math-parse-schedule (cdr (car rules))))))
610 ((eq (car-safe (car rules)) 'calcFunc-phase)
611 (setq math-phases (cdr (car rules)))
612 (if (equal math-phases '((var all var-all)))
613 (setq math-phases nil))
614 (let ((p math-phases))
616 (or (integerp (car p))
617 (error "Phase numbers must be small integers"))
618 (or (memq (car p) math-all-phases)
619 (setq math-all-phases (cons (car p) math-all-phases)))
621 ((or (and (eq (car-safe (car rules)) 'vec)
622 (cdr (cdr (car rules)))
623 (not (nthcdr 4 (car rules)))
624 (setq math-conds (nth 3 (car rules))
625 math-rhs (nth 2 (car rules))
626 math-pattern (nth 1 (car rules))))
629 math-pattern (car rules))
630 (while (and (eq (car-safe math-pattern) 'calcFunc-condition)
631 (= (length math-pattern) 3))
632 (let ((cond (nth 2 math-pattern)))
633 (setq math-conds (if math-conds
634 (list 'calcFunc-land math-conds cond)
636 math-pattern (nth 1 math-pattern))))
637 (and (eq (car-safe math-pattern) 'calcFunc-assign)
638 (= (length math-pattern) 3)
639 (setq math-rhs (nth 2 math-pattern)
640 math-pattern (nth 1 math-pattern)))))
641 (let* ((math-prog (list nil))
642 (math-prog-last math-prog)
644 (math-regs (list (list nil 0 nil nil)))
645 (math-bound-vars nil)
646 (math-aliased-vars nil)
648 (setq math-conds (and math-conds (math-flatten-lands math-conds)))
649 (math-rwcomp-pattern math-pattern 0)
651 (let ((expr (car math-conds)))
652 (setq math-conds (cdr math-conds))
653 (math-rwcomp-cond-instr expr)))
654 (math-rwcomp-instr 'done
668 (math-rwcomp-register-expr
671 (math-rwcomp-match-vars math-rhs))
673 (setq math-prog (cdr math-prog))
674 (let* ((heads (math-rewrite-heads math-pattern))
677 (mapcar (function (lambda (x) (nth 3 x)))
682 (head (and (not (Math-primp math-pattern))
683 (not (and (eq (car (car math-prog)) 'try)
684 (nth 5 (car math-prog))))
685 (not (memq (car (car math-prog)) '(func-opt
689 (if (memq (car (car math-prog)) '(func
691 (nth 2 (car math-prog))
692 (if (eq (car math-pattern) 'calcFunc-quote)
693 (car-safe (nth 1 math-pattern))
694 (car math-pattern))))))
697 (if (setq found (assq (car heads) all-heads))
698 (setcdr found (1+ (cdr found)))
699 (setq all-heads (cons (cons (car heads) 1) all-heads)))
700 (setq heads (cdr heads))))
701 (if (eq head '-) (setq head '+))
702 (if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec))
705 (nconc (or (assq head rule-set)
706 (car (setq rule-set (cons (cons head
712 (nconc (or (assq '/ rule-set)
713 (car (setq rule-set (cons (cons
719 (setq nil-rules (nconc nil-rules (list rule)))
720 (let ((ptr rule-set))
722 (nconc (car ptr) (list rule))
723 (setq ptr (cdr ptr))))))))
725 (error "Rewrite rule set must be a vector of A := B rules")))
726 (setq rules (cdr rules)))
728 (setq rule-set (cons (cons nil nil-rules) rule-set)))
729 (setq all-heads (mapcar 'car
730 (sort all-heads (function
732 (< (cdr x) (cdr y)))))))
736 (setq rule (cdr (car set)))
738 (if (consp (setq heads (nth 2 (car rule))))
740 (setq heads (delq (car (car set)) heads)
742 (while (and ptr (not (memq (car ptr) heads)))
743 (setq ptr (cdr ptr)))
744 (setcar (nthcdr 2 (car rule)) (car ptr))))
745 (setq rule (cdr rule)))
746 (setq set (cdr set))))
747 (let ((plus (assq '+ rule-set)))
749 (setq rule-set (cons (cons '- (cdr plus)) rule-set))))
750 (cons (list 'schedule math-iterations name
752 (sort math-all-phases '<)
756 (defun math-flatten-lands (expr)
757 (if (eq (car-safe expr) 'calcFunc-land)
758 (append (math-flatten-lands (nth 1 expr))
759 (math-flatten-lands (nth 2 expr)))
762 ;; The variables math-rewrite-heads-heads (i.e.; heads for math-rewrite-heads)
763 ;; math-rewrite-heads-blanks and math-rewrite-heads-skips are local to
764 ;; math-rewrite-heads, but used by math-rewrite-heads-rec, which is called by
765 ;; math-rewrite-heads.
766 (defvar math-rewrite-heads-heads)
767 (defvar math-rewrite-heads-skips)
768 (defvar math-rewrite-heads-blanks)
770 (defun math-rewrite-heads (expr &optional more all)
771 (let ((math-rewrite-heads-heads more)
772 (math-rewrite-heads-skips (and (not all)
773 '(calcFunc-apply calcFunc-condition calcFunc-opt
774 calcFunc-por calcFunc-pnot)))
775 (math-rewrite-heads-blanks (and (not all)
776 '(calcFunc-quote calcFunc-plain calcFunc-select
777 calcFunc-cons calcFunc-rcons
779 (or (Math-primp expr)
780 (math-rewrite-heads-rec expr))
781 math-rewrite-heads-heads))
783 (defun math-rewrite-heads-rec (expr)
784 (or (memq (car expr) math-rewrite-heads-skips)
786 (or (memq (car expr) math-rewrite-heads-heads)
787 (memq (car expr) math-rewrite-heads-blanks)
788 (memq 'algebraic (get (car expr) 'math-rewrite-props))
789 (setq math-rewrite-heads-heads (cons (car expr) math-rewrite-heads-heads)))
790 (while (setq expr (cdr expr))
791 (or (Math-primp (car expr))
792 (math-rewrite-heads-rec (car expr)))))))
794 (defun math-parse-schedule (sched)
800 (math-parse-schedule (cdr s))
801 (if (eq (car-safe s) 'var)
802 (math-var-to-calcFunc s)
803 (error "Improper component in rewrite schedule"))))))
806 (defun math-rwcomp-match-vars (expr)
807 (if (Math-primp expr)
808 (if (eq (car-safe expr) 'var)
809 (let ((entry (assq (nth 2 expr) math-regs)))
811 (math-rwcomp-register-expr (nth 1 entry))
814 (if (and (eq (car expr) 'calcFunc-quote)
816 (math-rwcomp-match-vars (nth 1 expr))
817 (if (and (eq (car expr) 'calcFunc-plain)
819 (not (Math-primp (nth 1 expr))))
821 (cons (car (nth 1 expr))
822 (mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr)))))
824 (mapcar 'math-rwcomp-match-vars (cdr expr)))))))
826 (defun math-rwcomp-register-expr (num)
827 (let ((entry (nth (1- (- math-num-regs num)) math-regs)))
829 (list 'neg (list 'calcFunc-register (nth 1 entry)))
830 (list 'calcFunc-register (nth 1 entry)))))
832 ;; The variables math-rwcomp-subst-old, math-rwcomp-subst-new,
833 ;; math-rwcomp-subst-old-func and math-rwcomp-subst-new-func
834 ;; are local to math-rwcomp-substitute, but are used by
835 ;; math-rwcomp-subst-rec, which is called by math-rwcomp-substitute.
836 (defvar math-rwcomp-subst-new)
837 (defvar math-rwcomp-subst-old)
838 (defvar math-rwcomp-subst-new-func)
839 (defvar math-rwcomp-subst-old-func)
841 (defun math-rwcomp-substitute (expr math-rwcomp-subst-old math-rwcomp-subst-new)
842 (if (and (eq (car-safe math-rwcomp-subst-old) 'var)
843 (memq (car-safe math-rwcomp-subst-new) '(var calcFunc-lambda)))
844 (let ((math-rwcomp-subst-old-func (math-var-to-calcFunc math-rwcomp-subst-old))
845 (math-rwcomp-subst-new-func (math-var-to-calcFunc math-rwcomp-subst-new)))
846 (math-rwcomp-subst-rec expr))
847 (let ((math-rwcomp-subst-old-func nil))
848 (math-rwcomp-subst-rec expr))))
850 (defun math-rwcomp-subst-rec (expr)
851 (cond ((equal expr math-rwcomp-subst-old) math-rwcomp-subst-new)
852 ((Math-primp expr) expr)
853 (t (if (eq (car expr) math-rwcomp-subst-old-func)
854 (math-build-call math-rwcomp-subst-new-func
855 (mapcar 'math-rwcomp-subst-rec
858 (mapcar 'math-rwcomp-subst-rec (cdr expr)))))))
860 (defvar math-rwcomp-tracing nil)
862 (defun math-rwcomp-trace (instr)
863 (when math-rwcomp-tracing
864 (terpri) (princ instr))
867 (defun math-rwcomp-instr (&rest instr)
868 (setcdr math-prog-last
869 (setq math-prog-last (list (math-rwcomp-trace instr)))))
871 (defun math-rwcomp-multi-instr (tail &rest instr)
872 (setcdr math-prog-last
873 (setq math-prog-last (list (math-rwcomp-trace (append instr tail))))))
875 (defun math-rwcomp-bind-var (reg var)
876 (setcar (math-rwcomp-reg-entry reg) (nth 2 var))
877 (setq math-bound-vars (cons (nth 2 var) math-bound-vars))
878 (math-rwcomp-do-conditions))
880 (defun math-rwcomp-unbind-vars (mark)
881 (while (not (eq math-bound-vars mark))
882 (setcar (assq (car math-bound-vars) math-regs) nil)
883 (setq math-bound-vars (cdr math-bound-vars))))
885 (defun math-rwcomp-do-conditions ()
886 (let ((cond math-conds))
888 (if (math-rwcomp-all-regs-done (car cond))
889 (let ((expr (car cond)))
890 (setq math-conds (delq (car cond) math-conds))
892 (math-rwcomp-cond-instr expr)))
893 (setq cond (cdr cond)))))
895 (defun math-rwcomp-cond-instr (expr)
897 (cond ((and (eq (car-safe expr) 'calcFunc-matches)
899 (eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr))))
901 (math-rwcomp-pattern (nth 2 expr) (nth 1 arg)))
902 ((math-numberp (setq expr (math-rwcomp-match-vars expr)))
903 (if (Math-zerop expr)
904 (math-rwcomp-instr 'backtrack)))
905 ((and (eq (car expr) 'calcFunc-let)
907 (let ((reg (math-rwcomp-reg)))
908 (math-rwcomp-instr 'let reg (nth 2 expr))
909 (math-rwcomp-pattern (nth 1 expr) reg)))
910 ((and (eq (car expr) 'calcFunc-let)
912 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
913 (= (length (nth 1 expr)) 3))
914 (let ((reg (math-rwcomp-reg)))
915 (math-rwcomp-instr 'let reg (nth 2 (nth 1 expr)))
916 (math-rwcomp-pattern (nth 1 (nth 1 expr)) reg)))
917 ((and (setq op (cdr (assq (car-safe expr)
918 '( (calcFunc-integer . integer)
919 (calcFunc-real . real)
920 (calcFunc-constant . constant)
921 (calcFunc-negative . negative) ))))
923 (or (and (eq (car-safe (nth 1 expr)) 'neg)
924 (memq op '(integer real constant))
925 (setq arg (nth 1 (nth 1 expr))))
926 (setq arg (nth 1 expr)))
927 (eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register))
928 (math-rwcomp-instr op (nth 1 arg)))
929 ((and (assq (car-safe expr) calc-tweak-eqn-table)
931 (eq (car-safe (nth 1 expr)) 'calcFunc-register))
932 (if (math-constp (nth 2 expr))
933 (let ((reg (math-rwcomp-reg)))
934 (setcar (nthcdr 3 (car math-regs)) (nth 2 expr))
935 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
937 (if (eq (car (nth 2 expr)) 'calcFunc-register)
938 (math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
939 (car expr) (nth 1 (nth 2 expr)))
940 (math-rwcomp-instr 'cond expr))))
941 ((and (eq (car-safe expr) 'calcFunc-eq)
943 (eq (car-safe (nth 1 expr)) '%)
944 (eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register)
945 (math-constp (nth 2 (nth 1 expr)))
946 (math-constp (nth 2 expr)))
947 (math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr)))
948 (nth 2 (nth 1 expr)) (nth 2 expr)))
949 ((equal expr '(var remember var-remember))
950 (setq math-remembering 1))
951 ((and (eq (car-safe expr) 'calcFunc-remember)
953 (setq math-remembering (if math-remembering
955 math-remembering (nth 1 expr))
957 (t (math-rwcomp-instr 'cond expr)))))
959 (defun math-rwcomp-same-instr (reg1 reg2 neg)
960 (math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
961 (nth 2 (math-rwcomp-reg-entry reg2)))
967 (defun math-rwcomp-copy-instr (reg1 reg2 neg)
968 (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
969 (nth 2 (math-rwcomp-reg-entry reg2)))
971 (math-rwcomp-instr 'copy-neg reg1 reg2)
973 (math-rwcomp-instr 'copy reg1 reg2))))
975 (defun math-rwcomp-reg ()
978 (setq math-regs (cons (list nil math-num-regs nil 0) math-regs)
979 math-num-regs (1+ math-num-regs))))
981 (defun math-rwcomp-reg-entry (num)
982 (nth (1- (- math-num-regs num)) math-regs))
985 (defun math-rwcomp-pattern (expr part &optional not-direct)
986 (cond ((or (math-rwcomp-no-vars expr)
987 (and (eq (car expr) 'calcFunc-quote)
989 (setq expr (nth 1 expr))))
990 (if (eq (car-safe expr) 'calcFunc-register)
991 (math-rwcomp-same-instr part (nth 1 expr) nil)
992 (let ((reg (math-rwcomp-reg)))
993 (setcar (nthcdr 3 (car math-regs)) expr)
994 (math-rwcomp-same-instr part reg nil))))
995 ((eq (car expr) 'var)
996 (let ((entry (assq (nth 2 expr) math-regs)))
998 (math-rwcomp-same-instr part (nth 1 entry) nil)
1000 (let ((reg (math-rwcomp-reg)))
1001 (math-rwcomp-pattern expr reg)
1002 (math-rwcomp-copy-instr part reg nil))
1003 (if (setq entry (assq (nth 2 expr) math-aliased-vars))
1005 (setcar (math-rwcomp-reg-entry (nth 1 entry))
1008 (math-rwcomp-copy-instr part (nth 1 entry) nil))
1009 (math-rwcomp-bind-var part expr))))))
1010 ((and (eq (car expr) 'calcFunc-select)
1011 (= (length expr) 2))
1012 (let ((reg (math-rwcomp-reg)))
1013 (math-rwcomp-instr 'select part reg)
1014 (math-rwcomp-pattern (nth 1 expr) reg)))
1015 ((and (eq (car expr) 'calcFunc-opt)
1016 (memq (length expr) '(2 3)))
1017 (error "opt( ) occurs in context where it is not allowed"))
1018 ((eq (car expr) 'neg)
1019 (if (eq (car (nth 1 expr)) 'var)
1020 (let ((entry (assq (nth 2 (nth 1 expr)) math-regs)))
1022 (math-rwcomp-same-instr part (nth 1 entry) t)
1024 (let ((reg (math-rwcomp-best-reg (nth 1 expr))))
1025 (math-rwcomp-copy-instr part reg t)
1026 (math-rwcomp-pattern (nth 1 expr) reg))
1027 (setcar (cdr (cdr (math-rwcomp-reg-entry part))) t)
1028 (math-rwcomp-pattern (nth 1 expr) part))))
1029 (if (math-rwcomp-is-algebraic (nth 1 expr))
1030 (math-rwcomp-cond-instr (list 'calcFunc-eq
1031 (math-rwcomp-register-expr part)
1033 (let ((reg (math-rwcomp-reg)))
1034 (math-rwcomp-instr 'func part 'neg reg)
1035 (math-rwcomp-pattern (nth 1 expr) reg)))))
1036 ((and (eq (car expr) 'calcFunc-apply)
1037 (= (length expr) 3))
1038 (let ((reg1 (math-rwcomp-reg))
1039 (reg2 (math-rwcomp-reg)))
1040 (math-rwcomp-instr 'apply part reg1 reg2)
1041 (math-rwcomp-pattern (nth 1 expr) reg1)
1042 (math-rwcomp-pattern (nth 2 expr) reg2)))
1043 ((and (eq (car expr) 'calcFunc-cons)
1044 (= (length expr) 3))
1045 (let ((reg1 (math-rwcomp-reg))
1046 (reg2 (math-rwcomp-reg)))
1047 (math-rwcomp-instr 'cons part reg1 reg2)
1048 (math-rwcomp-pattern (nth 1 expr) reg1)
1049 (math-rwcomp-pattern (nth 2 expr) reg2)))
1050 ((and (eq (car expr) 'calcFunc-rcons)
1051 (= (length expr) 3))
1052 (let ((reg1 (math-rwcomp-reg))
1053 (reg2 (math-rwcomp-reg)))
1054 (math-rwcomp-instr 'rcons part reg1 reg2)
1055 (math-rwcomp-pattern (nth 1 expr) reg1)
1056 (math-rwcomp-pattern (nth 2 expr) reg2)))
1057 ((and (eq (car expr) 'calcFunc-condition)
1058 (>= (length expr) 3))
1059 (math-rwcomp-pattern (nth 1 expr) part)
1060 (setq expr (cdr expr))
1061 (while (setq expr (cdr expr))
1062 (let ((cond (math-flatten-lands (car expr))))
1064 (if (math-rwcomp-all-regs-done (car cond))
1065 (math-rwcomp-cond-instr (car cond))
1066 (setq math-conds (cons (car cond) math-conds)))
1067 (setq cond (cdr cond))))))
1068 ((and (eq (car expr) 'calcFunc-pand)
1069 (= (length expr) 3))
1070 (math-rwcomp-pattern (nth 1 expr) part)
1071 (math-rwcomp-pattern (nth 2 expr) part))
1072 ((and (eq (car expr) 'calcFunc-por)
1073 (= (length expr) 3))
1074 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1075 (let ((math-conds nil)
1076 (head math-prog-last)
1077 (mark math-bound-vars)
1079 (math-rwcomp-pattern (nth 1 expr) part t)
1080 (let ((amark math-aliased-vars)
1081 (math-aliased-vars math-aliased-vars)
1082 (tail math-prog-last)
1085 (while (not (eq p mark))
1086 (setq entry (assq (car p) math-regs)
1087 math-aliased-vars (cons (list (car p) (nth 1 entry) nil)
1090 (setcar (math-rwcomp-reg-entry (nth 1 entry)) nil))
1091 (setcar (cdr (car head)) (cdr head))
1093 (setq math-prog-last head)
1094 (math-rwcomp-pattern (nth 2 expr) part)
1095 (math-rwcomp-instr 'same 0 0)
1096 (setcdr tail math-prog-last)
1097 (setq p math-aliased-vars)
1098 (while (not (eq p amark))
1100 (setcar (math-rwcomp-reg-entry (nth 1 (car p)))
1103 (math-rwcomp-do-conditions))
1104 ((and (eq (car expr) 'calcFunc-pnot)
1105 (= (length expr) 2))
1106 (math-rwcomp-instr 'alt nil nil [nil nil 4])
1107 (let ((head math-prog-last)
1108 (mark math-bound-vars))
1109 (math-rwcomp-pattern (nth 1 expr) part)
1110 (math-rwcomp-unbind-vars mark)
1111 (math-rwcomp-instr 'end-alt head)
1112 (math-rwcomp-instr 'backtrack)
1113 (setcar (cdr (car head)) (cdr head))
1115 (setq math-prog-last head)))
1116 (t (let ((props (get (car expr) 'math-rewrite-props)))
1117 (if (and (eq (car expr) 'calcFunc-plain)
1119 (not (math-primp (nth 1 expr))))
1120 (setq expr (nth 1 expr))) ; but "props" is still nil
1121 (if (and (memq 'algebraic props)
1122 (math-rwcomp-is-algebraic expr))
1123 (math-rwcomp-cond-instr (list 'calcFunc-eq
1124 (math-rwcomp-register-expr part)
1126 (if (and (memq 'commut props)
1127 (= (length expr) 3))
1128 (let ((arg1 (nth 1 expr))
1130 try1 def code head (flip nil))
1131 (if (eq (car expr) '-)
1132 (setq arg2 (math-rwcomp-neg arg2)))
1133 (setq arg1 (cons arg1 (math-rwcomp-best-reg arg1))
1134 arg2 (cons arg2 (math-rwcomp-best-reg arg2)))
1135 (or (math-rwcomp-order arg1 arg2)
1136 (setq def arg1 arg1 arg2 arg2 def flip t))
1137 (if (math-rwcomp-optional-arg (car expr) arg1)
1138 (error "Too many opt( ) arguments in this context"))
1139 (setq def (math-rwcomp-optional-arg (car expr) arg2)
1140 head (if (memq (car expr) '(+ -))
1142 (if (eq (car expr) '*)
1145 code (if (math-rwcomp-is-constrained
1147 (if (math-rwcomp-is-constrained
1151 (math-rwcomp-multi-instr (and def (list def))
1153 (vector nil nil nil code flip)
1155 (setq try1 (car math-prog-last))
1156 (math-rwcomp-pattern (car arg1) (cdr arg1))
1157 (math-rwcomp-instr 'try2 try1 (cdr arg2))
1158 (if (and (= part 0) (not def) (not math-rewrite-whole)
1159 (not (eq math-rhs t))
1160 (setq def (get (car expr)
1161 'math-rewrite-default)))
1162 (let ((reg1 (math-rwcomp-reg))
1163 (reg2 (math-rwcomp-reg)))
1164 (if (= (aref (nth 3 try1) 3) 0)
1165 (aset (nth 3 try1) 3 1))
1166 (math-rwcomp-instr 'try (cdr arg2)
1167 (if (equal head '(* /))
1174 (setq try1 (car math-prog-last))
1175 (math-rwcomp-pattern (car arg2) reg1)
1176 (math-rwcomp-instr 'try2 try1 reg2)
1177 (setq math-rhs (list (if (eq (car expr) '-)
1180 (list 'calcFunc-register
1182 (math-rwcomp-pattern (car arg2) (cdr arg2))))
1183 (let* ((args (mapcar (function
1185 (cons x (math-rwcomp-best-reg x))))
1187 (args2 (copy-sequence args))
1188 (argp (reverse args2))
1192 (let ((def (math-rwcomp-optional-arg (car expr)
1196 (setq args2 (delq (car argp) args2)
1197 defs (cons (cons def (cdr (car argp)))
1199 (math-rwcomp-multi-instr
1201 (if (or (and (memq 'unary1 props)
1202 (= (length args2) 1)
1203 (eq (car args2) (car args)))
1204 (and (memq 'unary2 props)
1206 (eq (car args2) (nth 1 args))))
1211 (setq argp (cdr argp)))
1212 (math-rwcomp-multi-instr (mapcar 'cdr args)
1213 'func part (car expr))
1214 (setq args (sort args 'math-rwcomp-order))
1216 (math-rwcomp-pattern (car (car args)) (cdr (car args)))
1218 args (cdr args))))))))))
1220 (defun math-rwcomp-best-reg (x)
1221 (or (and (eq (car-safe x) 'var)
1222 (let ((entry (assq (nth 2 x) math-aliased-vars)))
1225 (not (nth 2 (math-rwcomp-reg-entry (nth 1 entry))))
1227 (setcar (cdr (cdr entry)) t)
1231 (defun math-rwcomp-all-regs-done (expr)
1232 (if (Math-primp expr)
1233 (or (not (eq (car-safe expr) 'var))
1234 (assq (nth 2 expr) math-regs)
1235 (eq (nth 2 expr) 'var-remember)
1236 (math-const-var expr))
1237 (if (and (eq (car expr) 'calcFunc-let)
1238 (= (length expr) 3))
1239 (math-rwcomp-all-regs-done (nth 2 expr))
1240 (if (and (eq (car expr) 'calcFunc-let)
1242 (eq (car-safe (nth 1 expr)) 'calcFunc-assign)
1243 (= (length (nth 1 expr)) 3))
1244 (math-rwcomp-all-regs-done (nth 2 (nth 1 expr)))
1245 (while (and (setq expr (cdr expr))
1246 (math-rwcomp-all-regs-done (car expr))))
1249 (defun math-rwcomp-no-vars (expr)
1250 (if (Math-primp expr)
1251 (or (not (eq (car-safe expr) 'var))
1252 (math-const-var expr))
1253 (and (not (memq (car expr) '(calcFunc-condition
1254 calcFunc-select calcFunc-quote
1255 calcFunc-plain calcFunc-opt
1256 calcFunc-por calcFunc-pand
1257 calcFunc-pnot calcFunc-apply
1258 calcFunc-cons calcFunc-rcons)))
1260 (while (and (setq expr (cdr expr))
1261 (math-rwcomp-no-vars (car expr))))
1264 (defun math-rwcomp-is-algebraic (expr)
1265 (if (Math-primp expr)
1266 (or (not (eq (car-safe expr) 'var))
1267 (math-const-var expr)
1268 (assq (nth 2 expr) math-regs))
1269 (and (memq 'algebraic (get (car expr) 'math-rewrite-props))
1271 (while (and (setq expr (cdr expr))
1272 (math-rwcomp-is-algebraic (car expr))))
1275 (defun math-rwcomp-is-constrained (expr not-these)
1276 (if (Math-primp expr)
1277 (not (eq (car-safe expr) 'var))
1278 (if (eq (car expr) 'calcFunc-plain)
1279 (math-rwcomp-is-constrained (nth 1 expr) not-these)
1280 (not (or (memq (car expr) '(neg calcFunc-select))
1281 (memq (car expr) not-these)
1282 (and (memq 'commut (get (car expr) 'math-rewrite-props))
1283 (or (eq (car-safe (nth 1 expr)) 'calcFunc-opt)
1284 (eq (car-safe (nth 2 expr)) 'calcFunc-opt))))))))
1286 (defun math-rwcomp-optional-arg (head argp)
1287 (let ((arg (car argp)))
1288 (if (eq (car-safe arg) 'calcFunc-opt)
1289 (and (memq (length arg) '(2 3))
1291 (or (eq (car-safe (nth 1 arg)) 'var)
1292 (error "First argument of opt( ) must be a variable"))
1293 (setcar argp (nth 1 arg))
1294 (if (= (length arg) 2)
1295 (or (get head 'math-rewrite-default)
1296 (error "opt( ) must include a default in this context"))
1298 (and (eq (car-safe arg) 'neg)
1299 (let* ((part (list (nth 1 arg)))
1300 (partp (math-rwcomp-optional-arg head part)))
1302 (setcar argp (math-rwcomp-neg (car part)))
1303 (math-neg partp)))))))
1305 (defun math-rwcomp-neg (expr)
1306 (if (memq (car-safe expr) '(* /))
1307 (if (eq (car-safe (nth 1 expr)) 'var)
1308 (list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr))
1309 (if (eq (car-safe (nth 2 expr)) 'var)
1310 (list (car expr) (nth 1 expr) (list 'neg (nth 2 expr)))
1314 (defun math-rwcomp-assoc-args (expr)
1315 (if (and (eq (car-safe (nth 1 expr)) (car expr))
1316 (= (length (nth 1 expr)) 3))
1317 (math-rwcomp-assoc-args (nth 1 expr)))
1318 (if (and (eq (car-safe (nth 2 expr)) (car expr))
1319 (= (length (nth 2 expr)) 3))
1320 (math-rwcomp-assoc-args (nth 2 expr))))
1322 (defun math-rwcomp-addsub-args (expr)
1323 (if (memq (car-safe (nth 1 expr)) '(+ -))
1324 (math-rwcomp-addsub-args (nth 1 expr)))
1325 (if (eq (car expr) '-)
1327 (if (eq (car-safe (nth 2 expr)) '+)
1328 (math-rwcomp-addsub-args (nth 2 expr)))))
1330 (defun math-rwcomp-order (a b)
1331 (< (math-rwcomp-priority (car a))
1332 (math-rwcomp-priority (car b))))
1334 ;;; Order of priority: 0 Constants and other exact matches (first)
1335 ;;; 10 Functions (except below)
1336 ;;; 20 Meta-variables which occur more than once
1337 ;;; 30 Algebraic functions
1338 ;;; 40 Commutative/associative functions
1339 ;;; 50 Meta-variables which occur only once
1340 ;;; +100 for every "!!!" (pnot) in the pattern
1341 ;;; 10000 Optional arguments (last)
1343 (defun math-rwcomp-priority (expr)
1344 (+ (math-rwcomp-count-pnots expr)
1345 (cond ((eq (car-safe expr) 'calcFunc-opt)
1347 ((math-rwcomp-no-vars expr)
1349 ((eq (car expr) 'calcFunc-quote)
1351 ((eq (car expr) 'var)
1352 (if (assq (nth 2 expr) math-regs)
1354 (if (= (math-rwcomp-count-refs expr) 1)
1357 (t (let ((props (get (car expr) 'math-rewrite-props)))
1358 (if (or (memq 'commut props)
1359 (memq 'assoc props))
1361 (if (memq 'algebraic props)
1365 (defun math-rwcomp-count-refs (var)
1366 (let ((count (or (math-expr-contains-count math-pattern var) 0))
1369 (if (eq (car-safe (car p)) 'calcFunc-let)
1370 (if (= (length (car p)) 3)
1371 (setq count (+ count
1372 (or (math-expr-contains-count (nth 2 (car p)) var)
1374 (if (and (= (length (car p)) 2)
1375 (eq (car-safe (nth 1 (car p))) 'calcFunc-assign)
1376 (= (length (nth 1 (car p))) 3))
1377 (setq count (+ count
1378 (or (math-expr-contains-count
1379 (nth 2 (nth 1 (car p))) var) 0))))))
1383 (defun math-rwcomp-count-pnots (expr)
1384 (if (Math-primp expr)
1386 (if (eq (car expr) 'calcFunc-pnot)
1389 (while (setq expr (cdr expr))
1390 (setq count (+ count (math-rwcomp-count-pnots (car expr)))))
1393 ;;; In the current implementation, all associative functions must
1394 ;;; also be commutative.
1396 (put '+ 'math-rewrite-props '(algebraic assoc commut))
1397 (put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below
1398 (put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below
1399 (put '/ 'math-rewrite-props '(algebraic unary1))
1400 (put '^ 'math-rewrite-props '(algebraic unary1))
1401 (put '% 'math-rewrite-props '(algebraic))
1402 (put 'neg 'math-rewrite-props '(algebraic))
1403 (put 'calcFunc-idiv 'math-rewrite-props '(algebraic))
1404 (put 'calcFunc-abs 'math-rewrite-props '(algebraic))
1405 (put 'calcFunc-sign 'math-rewrite-props '(algebraic))
1406 (put 'calcFunc-round 'math-rewrite-props '(algebraic))
1407 (put 'calcFunc-rounde 'math-rewrite-props '(algebraic))
1408 (put 'calcFunc-roundu 'math-rewrite-props '(algebraic))
1409 (put 'calcFunc-trunc 'math-rewrite-props '(algebraic))
1410 (put 'calcFunc-floor 'math-rewrite-props '(algebraic))
1411 (put 'calcFunc-ceil 'math-rewrite-props '(algebraic))
1412 (put 'calcFunc-re 'math-rewrite-props '(algebraic))
1413 (put 'calcFunc-im 'math-rewrite-props '(algebraic))
1414 (put 'calcFunc-conj 'math-rewrite-props '(algebraic))
1415 (put 'calcFunc-arg 'math-rewrite-props '(algebraic))
1416 (put 'calcFunc-and 'math-rewrite-props '(assoc commut))
1417 (put 'calcFunc-or 'math-rewrite-props '(assoc commut))
1418 (put 'calcFunc-xor 'math-rewrite-props '(assoc commut))
1419 (put 'calcFunc-eq 'math-rewrite-props '(commut))
1420 (put 'calcFunc-neq 'math-rewrite-props '(commut))
1421 (put 'calcFunc-land 'math-rewrite-props '(assoc commut))
1422 (put 'calcFunc-lor 'math-rewrite-props '(assoc commut))
1423 (put 'calcFunc-beta 'math-rewrite-props '(commut))
1424 (put 'calcFunc-gcd 'math-rewrite-props '(assoc commut))
1425 (put 'calcFunc-lcm 'math-rewrite-props '(assoc commut))
1426 (put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut))
1427 (put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut))
1428 (put 'calcFunc-vunion 'math-rewrite-props '(assoc commut))
1429 (put 'calcFunc-vint 'math-rewrite-props '(assoc commut))
1430 (put 'calcFunc-vxor 'math-rewrite-props '(assoc commut))
1432 ;;; Note: "*" is not commutative for matrix args, but we pretend it is.
1433 ;;; Also, "-" is not commutative but the code tweaks things so that it is.
1435 (put '+ 'math-rewrite-default 0)
1436 (put '- 'math-rewrite-default 0)
1437 (put '* 'math-rewrite-default 1)
1438 (put '/ 'math-rewrite-default 1)
1439 (put '^ 'math-rewrite-default 1)
1440 (put 'calcFunc-land 'math-rewrite-default 1)
1441 (put 'calcFunc-lor 'math-rewrite-default 0)
1442 (put 'calcFunc-vunion 'math-rewrite-default '(vec))
1443 (put 'calcFunc-vint 'math-rewrite-default '(vec))
1444 (put 'calcFunc-vdiff 'math-rewrite-default '(vec))
1445 (put 'calcFunc-vxor 'math-rewrite-default '(vec))
1447 (defmacro math-rwfail (&optional back)
1451 '(setq btrack (cdr btrack))
1455 ;;; This monstrosity is necessary because the use of static vectors of
1456 ;;; registers makes rewrite rules non-reentrant. Yucko!
1457 (defmacro math-rweval (form)
1458 (list 'let '((orig (car rules)))
1459 '(setcar rules (quote (nil nil nil no-phase)))
1460 (list 'unwind-protect
1462 '(setcar rules orig))))
1464 (defvar math-rewrite-phase 1)
1466 ;; The variable math-apply-rw-regs is local to math-apply-rewrites,
1467 ;; but is used by math-rwapply-replace-regs and math-rwapply-reg-looks-negp
1468 ;; which are called by math-apply-rewrites.
1469 (defvar math-apply-rw-regs)
1471 ;; The variable math-apply-rw-ruleset is local to math-apply-rewrites,
1472 ;; but is used by math-rwapply-remember.
1473 (defvar math-apply-rw-ruleset)
1475 (defun math-apply-rewrites (expr rules &optional heads math-apply-rw-ruleset)
1477 (setq rules (cdr (or (assq (car-safe expr) rules)
1480 op math-apply-rw-regs inst part pc mark btrack
1481 (tracing math-rwcomp-tracing)
1482 (phase math-rewrite-phase))
1485 (and (setq part (nth 2 (car rules)))
1487 (not (memq part heads)))
1488 (and (setq part (nth 3 (car rules)))
1489 (not (memq phase part)))
1491 (setq math-apply-rw-regs (car (car rules))
1492 pc (nth 1 (car rules))
1494 (aset math-apply-rw-regs 0 expr)
1498 (progn (terpri) (princ (car pc))
1499 (if (and (natnump (nth 1 (car pc)))
1500 (< (nth 1 (car pc)) (length math-apply-rw-regs)))
1502 (format "\n part = %s"
1503 (aref math-apply-rw-regs (nth 1 (car pc))))))))
1505 (cond ((eq (setq op (car (setq inst (car pc)))) 'func)
1507 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1509 (car (setq inst (cdr (cdr inst)))))
1511 (while (and (setq inst (cdr inst)
1514 (aset math-apply-rw-regs (car inst) (car part)))
1515 (not (or inst part))))
1520 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1521 (setq mark (aref math-apply-rw-regs (nth 2 inst))))
1522 (Math-equal part mark))
1528 (not (eq calc-matrix-mode 'scalar))
1529 (eq (car (nth 2 inst)) '*)
1530 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1532 (not (math-known-scalarp part)))
1533 (setq mark (nth 3 inst)
1537 (aset math-apply-rw-regs (nth 4 inst) (nth 2 part))
1538 (aset mark 1 (cdr (cdr part))))
1539 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1540 (aset mark 1 (cdr part)))
1541 (aset mark 0 (cdr part))
1545 (if (and (consp (setq part
1546 (aref math-apply-rw-regs (car (cdr inst)))))
1547 (memq (car part) (nth 2 inst))
1549 (or (not (eq (car part) '/))
1550 (Math-objectp (nth 2 part))))
1553 mark (car (cdr (setq inst (cdr (cdr inst))))))
1555 (memq 'assoc (get (car part) 'math-rewrite-props))
1556 (not (= (aref mark 3) 0))
1557 (while (if (and (consp (nth 1 part))
1558 (memq (car (nth 1 part)) (car inst)))
1559 (setq op (cons (if (eq (car part) '-)
1565 (if (and (consp (nth 2 part))
1566 (memq (car (nth 2 part))
1568 (not (eq (car (nth 2 part)) '-)))
1569 (setq op (cons (nth 1 part) op)
1570 part (nth 2 part))))))
1571 (setq op (cons (nth 1 part)
1572 (cons (if (eq (car part) '-)
1575 (if (eq (car part) '/)
1580 btrack (cons pc btrack)
1582 (aset math-apply-rw-regs (nth 2 inst) (car op))
1585 (aset mark 2 (if (cdr (cdr op)) 1 0)))
1587 (if (and (consp part)
1588 (eq (car part) 'neg)
1589 (eq (car (nth 2 inst)) '*)
1590 (eq (nth 5 inst) 1))
1592 (setq mark (nth 3 inst)
1594 (aset math-apply-rw-regs (nth 4 inst) (nth 1 part))
1597 (setq mark (nth 3 inst)
1599 (aset math-apply-rw-regs (nth 4 inst) part)
1604 (setq part (nth 1 inst) ; try instr
1608 (aset math-apply-rw-regs (nth 2 inst)
1611 (if (eq (aref mark 0) (aref mark 1))
1612 (nth 1 (aref mark 0))
1613 (car (aref mark 0))))
1615 (setq mark (delq (car (aref mark 1))
1616 (copy-sequence (aref mark 0)))
1617 op (car (nth 2 part)))
1620 (setq mark (nreverse mark)
1621 part (list '* (nth 1 mark) (car mark))
1623 (while (setq mark (cdr mark))
1624 (setq part (list '* (car mark) part))))
1625 (setq part (car mark)
1627 part (if (and (eq op '+)
1629 (eq (car (car mark)) 'neg))
1632 (list op part (car mark))))
1633 (while (setq mark (cdr mark))
1634 (setq part (if (and (eq op '+)
1636 (eq (car (car mark)) 'neg))
1639 (list op part (car mark))))))
1642 (car (aref mark 1)))
1643 ((eq op 3) (nth 5 part))
1644 (t (aref mark 1)))))
1648 (if (and (consp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1649 (eq (car part) 'calcFunc-select))
1650 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1651 (if math-rewrite-selections
1653 (aset math-apply-rw-regs (nth 2 inst) part))))
1656 (if (or (equal (setq part (aref math-apply-rw-regs (nth 1 inst)))
1657 (setq mark (math-neg
1658 (aref math-apply-rw-regs (nth 2 inst)))))
1659 (Math-equal part mark))
1664 (setq inst (car (car btrack)) ; "try" or "alt" instr
1665 pc (cdr (car btrack))
1666 mark (or (nth 3 inst) [nil nil 4])
1669 (if (setq op (cdr (aref mark 1)))
1670 (aset math-apply-rw-regs (nth 4 inst)
1671 (car (aset mark 1 op)))
1675 (aset math-apply-rw-regs (nth 4 inst)
1676 (aref math-apply-rw-regs (nth 1 inst))))
1679 (if (setq op (cdr (aref mark 1)))
1680 (aset math-apply-rw-regs (nth 4 inst)
1681 (car (aset mark 1 op)))
1682 (if (= (aref mark 3) 1)
1686 (aset math-apply-rw-regs (nth 4 inst)
1687 (aref math-apply-rw-regs (nth 1 inst))))
1690 (aset mark 1 (cons nil (aref mark 0)))
1693 (if (setq op (cdr (aref mark 1)))
1695 (setq mark (delq (car (aset mark 1 op))
1698 op (car (nth 2 inst)))
1701 (setq mark (nreverse mark)
1702 part (list '* (nth 1 mark)
1705 (while (setq mark (cdr mark))
1706 (setq part (list '* (car mark)
1708 (setq part (car mark)
1710 part (if (and (eq op '+)
1712 (eq (car (car mark))
1716 (list op part (car mark))))
1717 (while (setq mark (cdr mark))
1718 (setq part (if (and (eq op '+)
1720 (eq (car (car mark))
1724 (list op part (car mark))))))
1725 (aset math-apply-rw-regs (nth 4 inst) part))
1729 (aset math-apply-rw-regs (nth 4 inst)
1730 (aref math-apply-rw-regs (nth 1 inst))))
1733 (setq btrack (cdr btrack)))
1734 (t (math-rwfail t))))
1737 (if (Math-integerp (setq part
1738 (aref math-apply-rw-regs (nth 1 inst))))
1740 (if (Math-primp part)
1742 (setq part (math-rweval (math-simplify part)))
1743 (if (Math-integerp part)
1748 (if (Math-realp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1750 (if (Math-primp part)
1752 (setq part (math-rweval (math-simplify part)))
1753 (if (Math-realp part)
1758 (if (math-constp (setq part (aref math-apply-rw-regs (nth 1 inst))))
1760 (if (Math-primp part)
1762 (setq part (math-rweval (math-simplify part)))
1763 (if (math-constp part)
1768 (if (math-looks-negp (setq part
1769 (aref math-apply-rw-regs (nth 1 inst))))
1771 (if (Math-primp part)
1773 (setq part (math-rweval (math-simplify part)))
1774 (if (math-looks-negp part)
1779 (setq part (math-compare (aref math-apply-rw-regs (nth 1 inst))
1780 (aref math-apply-rw-regs (nth 3 inst)))
1783 (setq part (math-rweval
1787 (aref math-apply-rw-regs (nth 1 inst))
1788 (aref math-apply-rw-regs (nth 3 inst))))))))
1789 (if (cond ((eq op 'calcFunc-eq)
1791 ((eq op 'calcFunc-neq)
1792 (memq part '(-1 1)))
1793 ((eq op 'calcFunc-lt)
1795 ((eq op 'calcFunc-leq)
1796 (memq part '(-1 0)))
1797 ((eq op 'calcFunc-gt)
1799 ((eq op 'calcFunc-geq)
1800 (memq part '(0 1))))
1806 (consp (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1808 (car (setq inst (cdr (cdr inst))))))
1810 (setq inst (cdr inst)
1812 (while (and (setq inst (cdr inst)
1815 (aset math-apply-rw-regs (car inst) (car part)))
1818 (while (eq (car (car (setq pc (cdr pc))))
1820 (setq pc (cdr pc)) ; skip over "func"
1822 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1823 (setq mark (cdr mark)))))
1830 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1831 (eq (car part) (nth 2 inst))))
1832 (and (= (length part) 2)
1833 (setq part (nth 1 part))))
1835 (setq mark (nth 3 inst))
1836 (aset math-apply-rw-regs (nth 4 inst) part)
1837 (while (eq (car (car (setq pc (cdr pc)))) 'func-def))
1838 (setq pc (cdr pc)) ; skip over "func"
1840 (aset math-apply-rw-regs (cdr (car mark)) (car (car mark)))
1841 (setq mark (cdr mark))))
1842 (setq pc (cdr pc))))
1846 (setq part (aref math-apply-rw-regs (nth 1 inst))))
1847 (Math-zerop (nth 3 inst))
1848 (and (not (Math-zerop (nth 2 inst)))
1850 (setq part (math-mod part (nth 2 inst)))
1851 (or (Math-numberp part)
1852 (setq part (math-rweval
1853 (math-simplify part))))
1854 (Math-equal part (nth 3 inst)))))
1860 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1861 (not (Math-objvecp part))
1862 (not (eq (car part) 'var)))
1864 (aset math-apply-rw-regs (nth 2 inst)
1865 (math-calcFunc-to-var (car part)))
1866 (aset math-apply-rw-regs (nth 3 inst)
1867 (cons 'vec (cdr part)))
1873 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1874 (eq (car part) 'vec)
1877 (aset math-apply-rw-regs (nth 2 inst) (nth 1 part))
1878 (aset math-apply-rw-regs (nth 3 inst)
1879 (cons 'vec (cdr (cdr part))))
1885 (setq part (aref math-apply-rw-regs (car (cdr inst)))))
1886 (eq (car part) 'vec)
1889 (aset math-apply-rw-regs (nth 2 inst) (calcFunc-rhead part))
1890 (aset math-apply-rw-regs (nth 3 inst) (calcFunc-rtail part))
1898 (math-rwapply-replace-regs (nth 1 inst)))))
1903 (aset math-apply-rw-regs (nth 1 inst)
1906 (math-rwapply-replace-regs (nth 2 inst)))))
1910 (aset math-apply-rw-regs (nth 2 inst)
1911 (aref math-apply-rw-regs (nth 1 inst)))
1915 (aset math-apply-rw-regs (nth 2 inst)
1916 (math-rwapply-neg (aref math-apply-rw-regs (nth 1 inst))))
1920 (setq btrack (cons pc btrack)
1924 (while (and btrack (not (eq (car btrack) (nth 1 inst))))
1925 (setq btrack (cdr btrack)))
1926 (setq btrack (cdr btrack)
1930 (setq result (math-rwapply-replace-regs (nth 1 inst)))
1931 (if (or (and (eq (car-safe result) '+)
1932 (eq (nth 2 result) 0))
1933 (and (eq (car-safe result) '*)
1934 (eq (nth 2 result) 1)))
1935 (setq result (nth 1 result)))
1936 (setq part (and (nth 2 inst)
1940 (math-rwapply-replace-regs
1942 (if (or (equal result expr)
1943 (equal (setq result (math-normalize result)) expr))
1945 (if part (math-rwapply-remember expr result))
1949 (t (error "%s is not a valid rewrite opcode" op))))))
1950 (setq rules (cdr rules)))
1953 (defun math-rwapply-neg (expr)
1954 (if (and (consp expr)
1955 (memq (car expr) '(* /)))
1956 (if (Math-objectp (nth 2 expr))
1957 (list (car expr) (nth 1 expr) (math-neg (nth 2 expr)))
1959 (if (Math-objectp (nth 1 expr))
1960 (math-neg (nth 1 expr))
1961 (list '* -1 (nth 1 expr)))
1965 (defun math-rwapply-inv (expr)
1966 (if (and (Math-integerp expr)
1968 (math-make-frac 1 expr)
1971 (defun math-rwapply-replace-regs (expr)
1972 (cond ((Math-primp expr)
1974 ((eq (car expr) 'calcFunc-register)
1975 (setq expr (aref math-apply-rw-regs (nth 1 expr)))
1976 (if (eq (car-safe expr) '*)
1977 (if (eq (nth 1 expr) -1)
1978 (math-neg (nth 2 expr))
1979 (if (eq (nth 1 expr) 1)
1983 ((and (eq (car expr) 'calcFunc-eval)
1984 (= (length expr) 2))
1985 (calc-with-default-simplification
1986 (math-normalize (math-rwapply-replace-regs (nth 1 expr)))))
1987 ((and (eq (car expr) 'calcFunc-evalsimp)
1988 (= (length expr) 2))
1989 (math-simplify (math-rwapply-replace-regs (nth 1 expr))))
1990 ((and (eq (car expr) 'calcFunc-evalextsimp)
1991 (= (length expr) 2))
1992 (math-simplify-extended (math-rwapply-replace-regs (nth 1 expr))))
1993 ((and (eq (car expr) 'calcFunc-apply)
1994 (= (length expr) 3))
1995 (let ((func (math-rwapply-replace-regs (nth 1 expr)))
1996 (args (math-rwapply-replace-regs (nth 2 expr)))
1998 (if (and (math-vectorp args)
1999 (not (eq (car-safe (setq call (math-build-call
2000 (math-var-to-calcFunc func)
2004 (list 'calcFunc-apply func args))))
2005 ((and (eq (car expr) 'calcFunc-cons)
2006 (= (length expr) 3))
2007 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2008 (tail (math-rwapply-replace-regs (nth 2 expr))))
2009 (if (math-vectorp tail)
2010 (cons 'vec (cons head (cdr tail)))
2011 (list 'calcFunc-cons head tail))))
2012 ((and (eq (car expr) 'calcFunc-rcons)
2013 (= (length expr) 3))
2014 (let ((head (math-rwapply-replace-regs (nth 1 expr)))
2015 (tail (math-rwapply-replace-regs (nth 2 expr))))
2016 (if (math-vectorp head)
2017 (append head (list tail))
2018 (list 'calcFunc-rcons head tail))))
2019 ((and (eq (car expr) 'neg)
2020 (math-rwapply-reg-looks-negp (nth 1 expr)))
2021 (math-rwapply-reg-neg (nth 1 expr)))
2022 ((and (eq (car expr) 'neg)
2023 (eq (car-safe (nth 1 expr)) 'calcFunc-register)
2024 (math-scalarp (aref math-apply-rw-regs (nth 1 (nth 1 expr)))))
2025 (math-neg (math-rwapply-replace-regs (nth 1 expr))))
2026 ((and (eq (car expr) '+)
2027 (math-rwapply-reg-looks-negp (nth 1 expr)))
2028 (list '- (math-rwapply-replace-regs (nth 2 expr))
2029 (math-rwapply-reg-neg (nth 1 expr))))
2030 ((and (eq (car expr) '+)
2031 (math-rwapply-reg-looks-negp (nth 2 expr)))
2032 (list '- (math-rwapply-replace-regs (nth 1 expr))
2033 (math-rwapply-reg-neg (nth 2 expr))))
2034 ((and (eq (car expr) '-)
2035 (math-rwapply-reg-looks-negp (nth 2 expr)))
2036 (list '+ (math-rwapply-replace-regs (nth 1 expr))
2037 (math-rwapply-reg-neg (nth 2 expr))))
2039 (cond ((eq (nth 1 expr) -1)
2040 (if (math-rwapply-reg-looks-negp (nth 2 expr))
2041 (math-rwapply-reg-neg (nth 2 expr))
2042 (math-neg (math-rwapply-replace-regs (nth 2 expr)))))
2043 ((eq (nth 1 expr) 1)
2044 (math-rwapply-replace-regs (nth 2 expr)))
2045 ((eq (nth 2 expr) -1)
2046 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2047 (math-rwapply-reg-neg (nth 1 expr))
2048 (math-neg (math-rwapply-replace-regs (nth 1 expr)))))
2049 ((eq (nth 2 expr) 1)
2050 (math-rwapply-replace-regs (nth 1 expr)))
2052 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2053 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2054 (cond ((and (eq (car-safe arg1) '/)
2055 (eq (nth 1 arg1) 1))
2056 (list '/ arg2 (nth 2 arg1)))
2057 ((and (eq (car-safe arg2) '/)
2058 (eq (nth 1 arg2) 1))
2059 (list '/ arg1 (nth 2 arg2)))
2060 (t (list '* arg1 arg2)))))))
2062 (let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
2063 (arg2 (math-rwapply-replace-regs (nth 2 expr))))
2064 (if (eq (car-safe arg2) '/)
2065 (list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2))
2066 (list '/ arg1 arg2))))
2067 ((and (eq (car expr) 'calcFunc-plain)
2068 (= (length expr) 2))
2069 (if (Math-primp (nth 1 expr))
2071 (if (eq (car (nth 1 expr)) 'calcFunc-register)
2072 (aref math-apply-rw-regs (nth 1 (nth 1 expr)))
2073 (cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs
2074 (cdr (nth 1 expr)))))))
2075 (t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr))))))
2077 (defun math-rwapply-reg-looks-negp (expr)
2078 (if (eq (car-safe expr) 'calcFunc-register)
2079 (math-looks-negp (aref math-apply-rw-regs (nth 1 expr)))
2080 (if (memq (car-safe expr) '(* /))
2081 (or (math-rwapply-reg-looks-negp (nth 1 expr))
2082 (math-rwapply-reg-looks-negp (nth 2 expr))))))
2084 (defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp
2085 (if (eq (car expr) 'calcFunc-register)
2086 (math-neg (math-rwapply-replace-regs expr))
2087 (if (math-rwapply-reg-looks-negp (nth 1 expr))
2088 (math-rwapply-replace-regs (list (car expr)
2089 (math-rwapply-reg-neg (nth 1 expr))
2091 (math-rwapply-replace-regs (list (car expr)
2093 (math-rwapply-reg-neg (nth 2 expr)))))))
2095 (defun math-rwapply-remember (old new)
2096 (let ((varval (symbol-value (nth 2 (car math-apply-rw-ruleset))))
2097 (rules (assq (car-safe old) math-apply-rw-ruleset)))
2098 (if (and (eq (car-safe varval) 'vec)
2099 (not (memq (car-safe old) '(nil schedule + -)))
2102 (setcdr varval (cons (list 'calcFunc-assign
2103 (if (math-rwcomp-no-vars old)
2105 (list 'calcFunc-quote old))
2108 (setcdr rules (cons (list (vector nil old)
2109 (list (list 'same 0 1)
2110 (list 'done new nil))
2114 (provide 'calc-rewr)
2116 ;; arch-tag: ca8d7b7d-bff1-4535-90f3-e2241f5e786b
2117 ;;; calc-rewr.el ends here