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