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3132f345 CW |
1 | ;;; calc-rewr.el --- rewriting functions for Calc |
2 | ||
bf77c646 | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
6 | ;; Maintainer: Colin Walters <walters@debian.org> | |
136211a9 EZ |
7 | |
8 | ;; This file is part of GNU Emacs. | |
9 | ||
10 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
11 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
12 | ;; accepts responsibility to anyone for the consequences of using it | |
13 | ;; or for whether it serves any particular purpose or works at all, | |
14 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
15 | ;; License for full details. | |
16 | ||
17 | ;; Everyone is granted permission to copy, modify and redistribute | |
18 | ;; GNU Emacs, but only under the conditions described in the | |
19 | ;; GNU Emacs General Public License. A copy of this license is | |
20 | ;; supposed to have been given to you along with GNU Emacs so you | |
21 | ;; can know your rights and responsibilities. It should be in a | |
22 | ;; file named COPYING. Among other things, the copyright notice | |
23 | ;; and this notice must be preserved on all copies. | |
24 | ||
3132f345 | 25 | ;;; Commentary: |
136211a9 | 26 | |
3132f345 | 27 | ;;; Code: |
136211a9 EZ |
28 | |
29 | ;; This file is autoloaded from calc-ext.el. | |
30 | (require 'calc-ext) | |
31 | ||
32 | (require 'calc-macs) | |
33 | ||
34 | (defun calc-Need-calc-rewr () nil) | |
35 | ||
36 | ||
3132f345 | 37 | (defvar math-rewrite-default-iters 100) |
136211a9 EZ |
38 | (defun calc-rewrite-selection (rules-str &optional many prefix) |
39 | (interactive "sRewrite rule(s): \np") | |
40 | (calc-slow-wrapper | |
41 | (calc-preserve-point) | |
42 | (let* ((num (max 1 (calc-locate-cursor-element (point)))) | |
43 | (reselect t) | |
44 | (pop-rules nil) | |
45 | (entry (calc-top num 'entry)) | |
46 | (expr (car entry)) | |
47 | (sel (calc-auto-selection entry)) | |
48 | (math-rewrite-selections t) | |
49 | (math-rewrite-default-iters 1)) | |
50 | (if (or (null rules-str) (equal rules-str "") (equal rules-str "$")) | |
51 | (if (= num 1) | |
3132f345 | 52 | (error "Can't use same stack entry for formula and rules") |
136211a9 EZ |
53 | (setq rules (calc-top-n 1 t) |
54 | pop-rules t)) | |
55 | (setq rules (if (stringp rules-str) | |
56 | (math-read-exprs rules-str) rules-str)) | |
57 | (if (eq (car-safe rules) 'error) | |
58 | (error "Bad format in expression: %s" (nth 1 rules))) | |
59 | (if (= (length rules) 1) | |
60 | (setq rules (car rules)) | |
61 | (setq rules (cons 'vec rules))) | |
62 | (or (memq (car-safe rules) '(vec var calcFunc-assign | |
63 | calcFunc-condition)) | |
64 | (let ((rhs (math-read-expr | |
65 | (read-string (concat "Rewrite from: " rules-str | |
66 | " to: "))))) | |
67 | (if (eq (car-safe rhs) 'error) | |
68 | (error "Bad format in expression: %s" (nth 1 rhs))) | |
69 | (setq rules (list 'calcFunc-assign rules rhs)))) | |
70 | (or (eq (car-safe rules) 'var) | |
71 | (calc-record rules "rule"))) | |
72 | (if (eq many 0) | |
73 | (setq many '(var inf var-inf)) | |
74 | (if many (setq many (prefix-numeric-value many)))) | |
75 | (if sel | |
76 | (setq expr (calc-replace-sub-formula (car entry) | |
77 | sel | |
78 | (list 'calcFunc-select sel))) | |
79 | (setq expr (car entry) | |
80 | reselect nil | |
81 | math-rewrite-selections nil)) | |
82 | (setq expr (calc-encase-atoms | |
83 | (calc-normalize | |
84 | (math-rewrite | |
85 | (calc-normalize expr) | |
86 | rules many))) | |
87 | sel nil | |
88 | expr (calc-locate-select-marker expr)) | |
89 | (or (consp sel) (setq sel nil)) | |
90 | (if pop-rules (calc-pop-stack 1)) | |
91 | (calc-pop-push-record-list 1 (or prefix "rwrt") (list expr) | |
92 | (- num (if pop-rules 1 0)) | |
93 | (list (and reselect sel)))) | |
bf77c646 | 94 | (calc-handle-whys))) |
136211a9 EZ |
95 | |
96 | (defun calc-locate-select-marker (expr) ; changes "sel" | |
97 | (if (Math-primp expr) | |
98 | expr | |
99 | (if (and (eq (car expr) 'calcFunc-select) | |
100 | (= (length expr) 2)) | |
101 | (progn | |
102 | (setq sel (if sel t (nth 1 expr))) | |
103 | (nth 1 expr)) | |
104 | (cons (car expr) | |
bf77c646 | 105 | (mapcar 'calc-locate-select-marker (cdr expr)))))) |
136211a9 EZ |
106 | |
107 | ||
108 | ||
109 | (defun calc-rewrite (rules-str many) | |
110 | (interactive "sRewrite rule(s): \nP") | |
111 | (calc-slow-wrapper | |
112 | (let (n rules expr) | |
113 | (if (or (null rules-str) (equal rules-str "") (equal rules-str "$")) | |
114 | (setq expr (calc-top-n 2) | |
115 | rules (calc-top-n 1 t) | |
116 | n 2) | |
117 | (setq rules (if (stringp rules-str) | |
118 | (math-read-exprs rules-str) rules-str)) | |
119 | (if (eq (car-safe rules) 'error) | |
120 | (error "Bad format in expression: %s" (nth 1 rules))) | |
121 | (if (= (length rules) 1) | |
122 | (setq rules (car rules)) | |
123 | (setq rules (cons 'vec rules))) | |
124 | (or (memq (car-safe rules) '(vec var calcFunc-assign | |
125 | calcFunc-condition)) | |
126 | (let ((rhs (math-read-expr | |
127 | (read-string (concat "Rewrite from: " rules-str | |
128 | " to: "))))) | |
129 | (if (eq (car-safe rhs) 'error) | |
130 | (error "Bad format in expression: %s" (nth 1 rhs))) | |
131 | (setq rules (list 'calcFunc-assign rules rhs)))) | |
132 | (or (eq (car-safe rules) 'var) | |
133 | (calc-record rules "rule")) | |
134 | (setq expr (calc-top-n 1) | |
135 | n 1)) | |
136 | (if (eq many 0) | |
137 | (setq many '(var inf var-inf)) | |
138 | (if many (setq many (prefix-numeric-value many)))) | |
139 | (setq expr (calc-normalize (math-rewrite expr rules many))) | |
140 | (let (sel) | |
141 | (setq expr (calc-locate-select-marker expr))) | |
142 | (calc-pop-push-record-list n "rwrt" (list expr))) | |
bf77c646 | 143 | (calc-handle-whys))) |
136211a9 EZ |
144 | |
145 | (defun calc-match (pat) | |
146 | (interactive "sPattern: \n") | |
147 | (calc-slow-wrapper | |
148 | (let (n expr) | |
149 | (if (or (null pat) (equal pat "") (equal pat "$")) | |
150 | (setq expr (calc-top-n 2) | |
151 | pat (calc-top-n 1) | |
152 | n 2) | |
153 | (if (interactive-p) (setq calc-previous-alg-entry pat)) | |
154 | (setq pat (if (stringp pat) (math-read-expr pat) pat)) | |
155 | (if (eq (car-safe pat) 'error) | |
156 | (error "Bad format in expression: %s" (nth 1 pat))) | |
157 | (if (not (eq (car-safe pat) 'var)) | |
158 | (calc-record pat "pat")) | |
159 | (setq expr (calc-top-n 1) | |
160 | n 1)) | |
161 | (or (math-vectorp expr) (error "Argument must be a vector")) | |
162 | (if (calc-is-inverse) | |
163 | (calc-enter-result n "mtcn" (math-match-patterns pat expr t)) | |
bf77c646 | 164 | (calc-enter-result n "mtch" (math-match-patterns pat expr nil)))))) |
136211a9 EZ |
165 | |
166 | ||
167 | ||
168 | (defun math-rewrite (whole-expr rules &optional mmt-many) | |
169 | (let ((crules (math-compile-rewrites rules)) | |
170 | (heads (math-rewrite-heads whole-expr)) | |
171 | (trace-buffer (get-buffer "*Trace*")) | |
172 | (calc-display-just 'center) | |
173 | (calc-display-origin 39) | |
174 | (calc-line-breaking 78) | |
175 | (calc-line-numbering nil) | |
176 | (calc-show-selections t) | |
177 | (calc-why nil) | |
178 | (mmt-func (function | |
179 | (lambda (x) | |
180 | (let ((result (math-apply-rewrites x (cdr crules) | |
181 | heads crules))) | |
182 | (if result | |
183 | (progn | |
184 | (if trace-buffer | |
185 | (let ((fmt (math-format-stack-value | |
186 | (list result nil nil)))) | |
187 | (save-excursion | |
188 | (set-buffer trace-buffer) | |
189 | (insert "\nrewrite to\n" fmt "\n")))) | |
190 | (setq heads (math-rewrite-heads result heads t)))) | |
191 | result))))) | |
192 | (if trace-buffer | |
193 | (let ((fmt (math-format-stack-value (list whole-expr nil nil)))) | |
194 | (save-excursion | |
195 | (set-buffer trace-buffer) | |
196 | (setq truncate-lines t) | |
197 | (goto-char (point-max)) | |
198 | (insert "\n\nBegin rewriting\n" fmt "\n")))) | |
199 | (or mmt-many (setq mmt-many (or (nth 1 (car crules)) | |
200 | math-rewrite-default-iters))) | |
201 | (if (equal mmt-many '(var inf var-inf)) (setq mmt-many 1000000)) | |
202 | (if (equal mmt-many '(neg (var inf var-inf))) (setq mmt-many -1000000)) | |
203 | (math-rewrite-phase (nth 3 (car crules))) | |
204 | (if trace-buffer | |
205 | (let ((fmt (math-format-stack-value (list whole-expr nil nil)))) | |
206 | (save-excursion | |
207 | (set-buffer trace-buffer) | |
208 | (insert "\nDone rewriting" | |
209 | (if (= mmt-many 0) " (reached iteration limit)" "") | |
210 | ":\n" fmt "\n")))) | |
bf77c646 | 211 | whole-expr)) |
136211a9 EZ |
212 | |
213 | (defun math-rewrite-phase (sched) | |
214 | (while (and sched (/= mmt-many 0)) | |
215 | (if (listp (car sched)) | |
216 | (while (let ((save-expr whole-expr)) | |
217 | (math-rewrite-phase (car sched)) | |
218 | (not (equal whole-expr save-expr)))) | |
219 | (if (symbolp (car sched)) | |
220 | (progn | |
221 | (setq whole-expr (math-normalize (list (car sched) whole-expr))) | |
222 | (if trace-buffer | |
223 | (let ((fmt (math-format-stack-value | |
224 | (list whole-expr nil nil)))) | |
225 | (save-excursion | |
226 | (set-buffer trace-buffer) | |
227 | (insert "\ncall " | |
228 | (substring (symbol-name (car sched)) 9) | |
229 | ":\n" fmt "\n"))))) | |
230 | (let ((math-rewrite-phase (car sched))) | |
231 | (if trace-buffer | |
232 | (save-excursion | |
233 | (set-buffer trace-buffer) | |
234 | (insert (format "\n(Phase %d)\n" math-rewrite-phase)))) | |
235 | (while (let ((save-expr whole-expr)) | |
236 | (setq whole-expr (math-normalize | |
237 | (math-map-tree-rec whole-expr))) | |
238 | (not (equal whole-expr save-expr))))))) | |
bf77c646 | 239 | (setq sched (cdr sched)))) |
136211a9 EZ |
240 | |
241 | (defun calcFunc-rewrite (expr rules &optional many) | |
242 | (or (null many) (integerp many) | |
243 | (equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf))) | |
244 | (math-reject-arg many 'fixnump)) | |
245 | (condition-case err | |
246 | (math-rewrite expr rules (or many 1)) | |
bf77c646 | 247 | (error (math-reject-arg rules (nth 1 err))))) |
136211a9 EZ |
248 | |
249 | (defun calcFunc-match (pat vec) | |
250 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
251 | (condition-case err | |
252 | (math-match-patterns pat vec nil) | |
bf77c646 | 253 | (error (math-reject-arg pat (nth 1 err))))) |
136211a9 EZ |
254 | |
255 | (defun calcFunc-matchnot (pat vec) | |
256 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
257 | (condition-case err | |
258 | (math-match-patterns pat vec t) | |
bf77c646 | 259 | (error (math-reject-arg pat (nth 1 err))))) |
136211a9 EZ |
260 | |
261 | (defun math-match-patterns (pat vec &optional not-flag) | |
262 | (let ((newvec nil) | |
263 | (crules (math-compile-patterns pat))) | |
264 | (while (setq vec (cdr vec)) | |
265 | (if (eq (not (math-apply-rewrites (car vec) crules)) | |
266 | not-flag) | |
267 | (setq newvec (cons (car vec) newvec)))) | |
bf77c646 | 268 | (cons 'vec (nreverse newvec)))) |
136211a9 EZ |
269 | |
270 | (defun calcFunc-matches (expr pat) | |
271 | (condition-case err | |
272 | (if (math-apply-rewrites expr (math-compile-patterns pat)) | |
273 | 1 | |
274 | 0) | |
bf77c646 | 275 | (error (math-reject-arg pat (nth 1 err))))) |
136211a9 EZ |
276 | |
277 | (defun calcFunc-vmatches (expr pat) | |
278 | (condition-case err | |
279 | (or (math-apply-rewrites expr (math-compile-patterns pat)) | |
280 | 0) | |
bf77c646 | 281 | (error (math-reject-arg pat (nth 1 err))))) |
136211a9 EZ |
282 | |
283 | ||
284 | ||
285 | ;;; A compiled rule set is an a-list of entries whose cars are functors, | |
286 | ;;; and whose cdrs are lists of rules. If there are rules with no | |
287 | ;;; well-defined head functor, they are included on all lists and also | |
288 | ;;; on an extra list whose car is nil. | |
289 | ;;; | |
290 | ;;; The first entry in the a-list is of the form (schedule A B C ...). | |
291 | ;;; | |
292 | ;;; Rule list entries take the form (regs prog head phases), where: | |
293 | ;;; | |
294 | ;;; regs is a vector of match registers. | |
295 | ;;; | |
296 | ;;; prog is a match program (see below). | |
297 | ;;; | |
298 | ;;; head is a rare function name appearing in the rule body (but not the | |
299 | ;;; head of the whole rule), or nil if none. | |
300 | ;;; | |
301 | ;;; phases is a list of phase numbers for which the rule is enabled. | |
302 | ;;; | |
303 | ;;; A match program is a list of match instructions. | |
304 | ;;; | |
305 | ;;; In the following, "part" is a register number that contains the | |
306 | ;;; subexpression to be operated on. | |
307 | ;;; | |
308 | ;;; Register 0 is the whole expression being matched. The others are | |
309 | ;;; meta-variables in the pattern, temporaries used for matching and | |
310 | ;;; backtracking, and constant expressions. | |
311 | ;;; | |
312 | ;;; (same part reg) | |
313 | ;;; The selected part must be math-equal to the contents of "reg". | |
314 | ;;; | |
315 | ;;; (same-neg part reg) | |
316 | ;;; The selected part must be math-equal to the negative of "reg". | |
317 | ;;; | |
318 | ;;; (copy part reg) | |
319 | ;;; The selected part is copied into "reg". (Rarely used.) | |
320 | ;;; | |
321 | ;;; (copy-neg part reg) | |
322 | ;;; The negative of the selected part is copied into "reg". | |
323 | ;;; | |
324 | ;;; (integer part) | |
325 | ;;; The selected part must be an integer. | |
326 | ;;; | |
327 | ;;; (real part) | |
328 | ;;; The selected part must be a real. | |
329 | ;;; | |
330 | ;;; (constant part) | |
331 | ;;; The selected part must be a constant. | |
332 | ;;; | |
333 | ;;; (negative part) | |
334 | ;;; The selected part must "look" negative. | |
335 | ;;; | |
336 | ;;; (rel part op reg) | |
337 | ;;; The selected part must satisfy "part op reg", where "op" | |
338 | ;;; is one of the 6 relational ops, and "reg" is a register. | |
339 | ;;; | |
340 | ;;; (mod part modulo value) | |
341 | ;;; The selected part must satisfy "part % modulo = value", where | |
342 | ;;; "modulo" and "value" are constants. | |
343 | ;;; | |
344 | ;;; (func part head reg1 reg2 ... regn) | |
345 | ;;; The selected part must be an n-ary call to function "head". | |
346 | ;;; The arguments are stored in "reg1" through "regn". | |
347 | ;;; | |
348 | ;;; (func-def part head defs reg1 reg2 ... regn) | |
349 | ;;; The selected part must be an n-ary call to function "head". | |
350 | ;;; "Defs" is a list of value/register number pairs for default args. | |
351 | ;;; If a match, assign default values to registers and then skip | |
352 | ;;; immediately over any following "func-def" instructions and | |
353 | ;;; the following "func" instruction. If wrong number of arguments, | |
354 | ;;; proceed to the following "func-def" or "func" instruction. | |
355 | ;;; | |
356 | ;;; (func-opt part head defs reg1) | |
357 | ;;; Like func-def with "n=1", except that if the selected part is | |
358 | ;;; not a call to "head", then the part itself successfully matches | |
359 | ;;; "reg1" (and the defaults are assigned). | |
360 | ;;; | |
361 | ;;; (try part heads mark reg1 [def]) | |
362 | ;;; The selected part must be a function of the correct type which is | |
363 | ;;; associative and/or commutative. "Heads" is a list of acceptable | |
364 | ;;; types. An initial assignment of arguments to "reg1" is tried. | |
365 | ;;; If the program later fails, it backtracks to this instruction | |
366 | ;;; and tries other assignments of arguments to "reg1". | |
367 | ;;; If "def" exists and normal matching fails, backtrack and assign | |
368 | ;;; "part" to "reg1", and "def" to "reg2" in the following "try2". | |
369 | ;;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized. | |
370 | ;;; "mark[0]" points to the argument list; "mark[1]" points to the | |
371 | ;;; current argument; "mark[2]" is 0 if there are two arguments, | |
372 | ;;; 1 if reg1 is matching single arguments, 2 if reg2 is matching | |
373 | ;;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or | |
374 | ;;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must | |
375 | ;;; have two arguments, 1 if phase-2 can be skipped, 2 if full | |
376 | ;;; backtracking is necessary; "mark[4]" is t if the arguments have | |
377 | ;;; been switched from the order given in the original pattern. | |
378 | ;;; | |
379 | ;;; (try2 try reg2) | |
380 | ;;; Every "try" will be followed by a "try2" whose "try" field is | |
381 | ;;; a pointer to the corresponding "try". The arguments which were | |
382 | ;;; not stored in "reg1" by that "try" are now stored in "reg2". | |
383 | ;;; | |
384 | ;;; (alt instr nil mark) | |
385 | ;;; Basic backtracking. Execute the instruction sequence "instr". | |
386 | ;;; If this fails, back up and execute following the "alt" instruction. | |
387 | ;;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence | |
388 | ;;; should execute "end-alt" at the end. | |
389 | ;;; | |
390 | ;;; (end-alt ptr) | |
391 | ;;; Register success of the first alternative of a previous "alt". | |
392 | ;;; "Ptr" is a pointer to the next instruction following that "alt". | |
393 | ;;; | |
394 | ;;; (apply part reg1 reg2) | |
395 | ;;; The selected part must be a function call. The functor | |
396 | ;;; (as a variable name) is stored in "reg1"; the arguments | |
397 | ;;; (as a vector) are stored in "reg2". | |
398 | ;;; | |
399 | ;;; (cons part reg1 reg2) | |
400 | ;;; The selected part must be a nonempty vector. The first element | |
401 | ;;; of the vector is stored in "reg1"; the rest of the vector | |
402 | ;;; (as another vector) is stored in "reg2". | |
403 | ;;; | |
404 | ;;; (rcons part reg1 reg2) | |
405 | ;;; The selected part must be a nonempty vector. The last element | |
406 | ;;; of the vector is stored in "reg2"; the rest of the vector | |
407 | ;;; (as another vector) is stored in "reg1". | |
408 | ;;; | |
409 | ;;; (select part reg) | |
410 | ;;; If the selected part is a unary call to function "select", its | |
411 | ;;; argument is stored in "reg"; otherwise (provided this is an `a r' | |
412 | ;;; and not a `g r' command) the selected part is stored in "reg". | |
413 | ;;; | |
414 | ;;; (cond expr) | |
415 | ;;; The "expr", with registers substituted, must simplify to | |
416 | ;;; a non-zero value. | |
417 | ;;; | |
418 | ;;; (let reg expr) | |
419 | ;;; Evaluate "expr" and store the result in "reg". Always succeeds. | |
420 | ;;; | |
421 | ;;; (done rhs remember) | |
422 | ;;; Rewrite the expression to "rhs", with register substituted. | |
423 | ;;; Normalize; if the result is different from the original | |
424 | ;;; expression, the match has succeeded. This is the last | |
425 | ;;; instruction of every program. If "remember" is non-nil, | |
426 | ;;; record the result of the match as a new literal rule. | |
427 | ||
428 | ||
429 | ;;; Pseudo-functions related to rewrites: | |
430 | ;;; | |
431 | ;;; In patterns: quote, plain, condition, opt, apply, cons, select | |
432 | ;;; | |
433 | ;;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp, | |
434 | ;;; apply, cons, select | |
435 | ;;; | |
436 | ;;; In conditions: let + same as for righthand sides | |
437 | ||
438 | ;;; Some optimizations that would be nice to have: | |
439 | ;;; | |
440 | ;;; * Merge registers with disjoint lifetimes. | |
441 | ;;; * Merge constant registers with equivalent values. | |
442 | ;;; | |
443 | ;;; * If an argument of a commutative op math-depends neither on the | |
444 | ;;; rest of the pattern nor on any of the conditions, then no backtracking | |
445 | ;;; should be done for that argument. (This won't apply to very many | |
446 | ;;; cases.) | |
447 | ;;; | |
448 | ;;; * If top functor is "select", and its argument is a unique function, | |
449 | ;;; add the rule to the lists for both "select" and that function. | |
450 | ;;; (Currently rules like this go on the "nil" list.) | |
451 | ;;; Same for "func-opt" functions. (Though not urgent for these.) | |
452 | ;;; | |
453 | ;;; * Shouldn't evaluate a "let" condition until the end, or until it | |
454 | ;;; would enable another condition to be evaluated. | |
455 | ;;; | |
456 | ||
457 | ;;; Some additional features to add / things to think about: | |
458 | ;;; | |
459 | ;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)". | |
460 | ;;; | |
461 | ;;; * Same for interval forms. | |
462 | ;;; | |
463 | ;;; * Have a name(v,pat) pattern which matches pat, and gives the | |
464 | ;;; whole match the name v. Beware of circular structures! | |
465 | ;;; | |
466 | ||
467 | (defun math-compile-patterns (pats) | |
468 | (if (and (eq (car-safe pats) 'var) | |
469 | (calc-var-value (nth 2 pats))) | |
470 | (let ((prop (get (nth 2 pats) 'math-pattern-cache))) | |
471 | (or prop | |
472 | (put (nth 2 pats) 'math-pattern-cache (setq prop (list nil)))) | |
473 | (or (eq (car prop) (symbol-value (nth 2 pats))) | |
474 | (progn | |
475 | (setcdr prop (math-compile-patterns | |
476 | (symbol-value (nth 2 pats)))) | |
477 | (setcar prop (symbol-value (nth 2 pats))))) | |
478 | (cdr prop)) | |
479 | (let ((math-rewrite-whole t)) | |
480 | (cdr (math-compile-rewrites (cons | |
481 | 'vec | |
482 | (mapcar (function (lambda (x) | |
483 | (list 'vec x t))) | |
484 | (if (eq (car-safe pats) 'vec) | |
485 | (cdr pats) | |
bf77c646 | 486 | (list pats))))))))) |
136211a9 | 487 | |
3132f345 CW |
488 | (defvar math-rewrite-whole nil) |
489 | (defvar math-make-import-list nil) | |
136211a9 EZ |
490 | (defun math-compile-rewrites (rules &optional name) |
491 | (if (eq (car-safe rules) 'var) | |
492 | (let ((prop (get (nth 2 rules) 'math-rewrite-cache)) | |
493 | (math-import-list nil) | |
494 | (math-make-import-list t) | |
495 | p) | |
496 | (or (calc-var-value (nth 2 rules)) | |
497 | (error "Rules variable %s has no stored value" (nth 1 rules))) | |
498 | (or prop | |
499 | (put (nth 2 rules) 'math-rewrite-cache | |
500 | (setq prop (list (list (cons (nth 2 rules) nil)))))) | |
501 | (setq p (car prop)) | |
502 | (while (and p (eq (symbol-value (car (car p))) (cdr (car p)))) | |
503 | (setq p (cdr p))) | |
504 | (or (null p) | |
505 | (progn | |
506 | (message "Compiling rule set %s..." (nth 1 rules)) | |
507 | (setcdr prop (math-compile-rewrites | |
508 | (symbol-value (nth 2 rules)) | |
509 | (nth 2 rules))) | |
510 | (message "Compiling rule set %s...done" (nth 1 rules)) | |
511 | (setcar prop (cons (cons (nth 2 rules) | |
512 | (symbol-value (nth 2 rules))) | |
513 | math-import-list)))) | |
514 | (cdr prop)) | |
515 | (if (or (not (eq (car-safe rules) 'vec)) | |
516 | (and (memq (length rules) '(3 4)) | |
517 | (let ((p rules)) | |
518 | (while (and (setq p (cdr p)) | |
519 | (memq (car-safe (car p)) | |
520 | '(vec | |
521 | calcFunc-assign | |
522 | calcFunc-condition | |
523 | calcFunc-import | |
524 | calcFunc-phase | |
525 | calcFunc-schedule | |
526 | calcFunc-iterations)))) | |
527 | p))) | |
528 | (setq rules (list rules)) | |
529 | (setq rules (cdr rules))) | |
530 | (if (assq 'calcFunc-import rules) | |
531 | (let ((pp (setq rules (copy-sequence rules))) | |
532 | p part) | |
533 | (while (setq p (car (cdr pp))) | |
534 | (if (eq (car-safe p) 'calcFunc-import) | |
535 | (progn | |
536 | (setcdr pp (cdr (cdr pp))) | |
537 | (or (and (eq (car-safe (nth 1 p)) 'var) | |
538 | (setq part (calc-var-value (nth 2 (nth 1 p)))) | |
539 | (memq (car-safe part) '(vec | |
540 | calcFunc-assign | |
541 | calcFunc-condition))) | |
542 | (error "Argument of import() must be a rules variable")) | |
543 | (if math-make-import-list | |
544 | (setq math-import-list | |
545 | (cons (cons (nth 2 (nth 1 p)) | |
546 | (symbol-value (nth 2 (nth 1 p)))) | |
547 | math-import-list))) | |
548 | (while (setq p (cdr (cdr p))) | |
549 | (or (cdr p) | |
550 | (error "import() must have odd number of arguments")) | |
551 | (setq part (math-rwcomp-substitute part | |
552 | (car p) (nth 1 p)))) | |
553 | (if (eq (car-safe part) 'vec) | |
554 | (setq part (cdr part)) | |
555 | (setq part (list part))) | |
556 | (setcdr pp (append part (cdr pp)))) | |
557 | (setq pp (cdr pp)))))) | |
558 | (let ((rule-set nil) | |
559 | (all-heads nil) | |
560 | (nil-rules nil) | |
561 | (rule-count 0) | |
562 | (math-schedule nil) | |
563 | (math-iterations nil) | |
564 | (math-phases nil) | |
565 | (math-all-phases nil) | |
566 | (math-remembering nil) | |
567 | math-pattern math-rhs math-conds) | |
568 | (while rules | |
569 | (cond | |
570 | ((and (eq (car-safe (car rules)) 'calcFunc-iterations) | |
571 | (= (length (car rules)) 2)) | |
572 | (or (integerp (nth 1 (car rules))) | |
573 | (equal (nth 1 (car rules)) '(var inf var-inf)) | |
574 | (equal (nth 1 (car rules)) '(neg (var inf var-inf))) | |
575 | (error "Invalid argument for iterations(n)")) | |
576 | (or math-iterations | |
577 | (setq math-iterations (nth 1 (car rules))))) | |
578 | ((eq (car-safe (car rules)) 'calcFunc-schedule) | |
579 | (or math-schedule | |
580 | (setq math-schedule (math-parse-schedule (cdr (car rules)))))) | |
581 | ((eq (car-safe (car rules)) 'calcFunc-phase) | |
582 | (setq math-phases (cdr (car rules))) | |
583 | (if (equal math-phases '((var all var-all))) | |
584 | (setq math-phases nil)) | |
585 | (let ((p math-phases)) | |
586 | (while p | |
587 | (or (integerp (car p)) | |
588 | (error "Phase numbers must be small integers")) | |
589 | (or (memq (car p) math-all-phases) | |
590 | (setq math-all-phases (cons (car p) math-all-phases))) | |
591 | (setq p (cdr p))))) | |
592 | ((or (and (eq (car-safe (car rules)) 'vec) | |
593 | (cdr (cdr (car rules))) | |
594 | (not (nthcdr 4 (car rules))) | |
595 | (setq math-conds (nth 3 (car rules)) | |
596 | math-rhs (nth 2 (car rules)) | |
597 | math-pattern (nth 1 (car rules)))) | |
598 | (progn | |
599 | (setq math-conds nil | |
600 | math-pattern (car rules)) | |
601 | (while (and (eq (car-safe math-pattern) 'calcFunc-condition) | |
602 | (= (length math-pattern) 3)) | |
603 | (let ((cond (nth 2 math-pattern))) | |
604 | (setq math-conds (if math-conds | |
605 | (list 'calcFunc-land math-conds cond) | |
606 | cond) | |
607 | math-pattern (nth 1 math-pattern)))) | |
608 | (and (eq (car-safe math-pattern) 'calcFunc-assign) | |
609 | (= (length math-pattern) 3) | |
610 | (setq math-rhs (nth 2 math-pattern) | |
611 | math-pattern (nth 1 math-pattern))))) | |
612 | (let* ((math-prog (list nil)) | |
613 | (math-prog-last math-prog) | |
614 | (math-num-regs 1) | |
615 | (math-regs (list (list nil 0 nil nil))) | |
616 | (math-bound-vars nil) | |
617 | (math-aliased-vars nil) | |
618 | (math-copy-neg nil)) | |
619 | (setq math-conds (and math-conds (math-flatten-lands math-conds))) | |
620 | (math-rwcomp-pattern math-pattern 0) | |
621 | (while math-conds | |
622 | (let ((expr (car math-conds))) | |
623 | (setq math-conds (cdr math-conds)) | |
624 | (math-rwcomp-cond-instr expr))) | |
625 | (math-rwcomp-instr 'done | |
626 | (if (eq math-rhs t) | |
627 | (cons 'vec | |
628 | (delq | |
629 | nil | |
630 | (nreverse | |
631 | (mapcar | |
632 | (function | |
633 | (lambda (v) | |
634 | (and (car v) | |
635 | (list | |
636 | 'calcFunc-assign | |
637 | (math-build-var-name | |
638 | (car v)) | |
639 | (math-rwcomp-register-expr | |
640 | (nth 1 v)))))) | |
641 | math-regs)))) | |
642 | (math-rwcomp-match-vars math-rhs)) | |
643 | math-remembering) | |
644 | (setq math-prog (cdr math-prog)) | |
645 | (let* ((heads (math-rewrite-heads math-pattern)) | |
646 | (rule (list (vconcat | |
647 | (nreverse | |
648 | (mapcar (function (lambda (x) (nth 3 x))) | |
649 | math-regs))) | |
650 | math-prog | |
651 | heads | |
652 | math-phases)) | |
653 | (head (and (not (Math-primp math-pattern)) | |
654 | (not (and (eq (car (car math-prog)) 'try) | |
655 | (nth 5 (car math-prog)))) | |
656 | (not (memq (car (car math-prog)) '(func-opt | |
657 | apply | |
658 | select | |
659 | alt))) | |
660 | (if (memq (car (car math-prog)) '(func | |
661 | func-def)) | |
662 | (nth 2 (car math-prog)) | |
663 | (if (eq (car math-pattern) 'calcFunc-quote) | |
664 | (car-safe (nth 1 math-pattern)) | |
665 | (car math-pattern)))))) | |
666 | (let (found) | |
667 | (while heads | |
668 | (if (setq found (assq (car heads) all-heads)) | |
669 | (setcdr found (1+ (cdr found))) | |
670 | (setq all-heads (cons (cons (car heads) 1) all-heads))) | |
671 | (setq heads (cdr heads)))) | |
672 | (if (eq head '-) (setq head '+)) | |
673 | (if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec)) | |
674 | (if head | |
675 | (progn | |
676 | (nconc (or (assq head rule-set) | |
677 | (car (setq rule-set (cons (cons head | |
678 | (copy-sequence | |
679 | nil-rules)) | |
680 | rule-set)))) | |
681 | (list rule)) | |
682 | (if (eq head '*) | |
683 | (nconc (or (assq '/ rule-set) | |
684 | (car (setq rule-set (cons (cons | |
685 | '/ | |
686 | (copy-sequence | |
687 | nil-rules)) | |
688 | rule-set)))) | |
689 | (list rule)))) | |
690 | (setq nil-rules (nconc nil-rules (list rule))) | |
691 | (let ((ptr rule-set)) | |
692 | (while ptr | |
693 | (nconc (car ptr) (list rule)) | |
694 | (setq ptr (cdr ptr)))))))) | |
695 | (t | |
696 | (error "Rewrite rule set must be a vector of A := B rules"))) | |
697 | (setq rules (cdr rules))) | |
698 | (if nil-rules | |
699 | (setq rule-set (cons (cons nil nil-rules) rule-set))) | |
700 | (setq all-heads (mapcar 'car | |
701 | (sort all-heads (function | |
702 | (lambda (x y) | |
703 | (< (cdr x) (cdr y))))))) | |
704 | (let ((set rule-set) | |
705 | rule heads ptr) | |
706 | (while set | |
707 | (setq rule (cdr (car set))) | |
708 | (while rule | |
709 | (if (consp (setq heads (nth 2 (car rule)))) | |
710 | (progn | |
711 | (setq heads (delq (car (car set)) heads) | |
712 | ptr all-heads) | |
713 | (while (and ptr (not (memq (car ptr) heads))) | |
714 | (setq ptr (cdr ptr))) | |
715 | (setcar (nthcdr 2 (car rule)) (car ptr)))) | |
716 | (setq rule (cdr rule))) | |
717 | (setq set (cdr set)))) | |
718 | (let ((plus (assq '+ rule-set))) | |
719 | (if plus | |
720 | (setq rule-set (cons (cons '- (cdr plus)) rule-set)))) | |
721 | (cons (list 'schedule math-iterations name | |
722 | (or math-schedule | |
723 | (sort math-all-phases '<) | |
724 | (list 1))) | |
bf77c646 | 725 | rule-set)))) |
136211a9 EZ |
726 | |
727 | (defun math-flatten-lands (expr) | |
728 | (if (eq (car-safe expr) 'calcFunc-land) | |
729 | (append (math-flatten-lands (nth 1 expr)) | |
730 | (math-flatten-lands (nth 2 expr))) | |
bf77c646 | 731 | (list expr))) |
136211a9 EZ |
732 | |
733 | (defun math-rewrite-heads (expr &optional more all) | |
734 | (let ((heads more) | |
735 | (skips (and (not all) | |
736 | '(calcFunc-apply calcFunc-condition calcFunc-opt | |
737 | calcFunc-por calcFunc-pnot))) | |
738 | (blanks (and (not all) | |
739 | '(calcFunc-quote calcFunc-plain calcFunc-select | |
740 | calcFunc-cons calcFunc-rcons | |
741 | calcFunc-pand)))) | |
742 | (or (Math-primp expr) | |
743 | (math-rewrite-heads-rec expr)) | |
bf77c646 | 744 | heads)) |
136211a9 EZ |
745 | |
746 | (defun math-rewrite-heads-rec (expr) | |
747 | (or (memq (car expr) skips) | |
748 | (progn | |
749 | (or (memq (car expr) heads) | |
750 | (memq (car expr) blanks) | |
751 | (memq 'algebraic (get (car expr) 'math-rewrite-props)) | |
752 | (setq heads (cons (car expr) heads))) | |
753 | (while (setq expr (cdr expr)) | |
754 | (or (Math-primp (car expr)) | |
bf77c646 | 755 | (math-rewrite-heads-rec (car expr))))))) |
136211a9 EZ |
756 | |
757 | (defun math-parse-schedule (sched) | |
758 | (mapcar (function | |
759 | (lambda (s) | |
760 | (if (integerp s) | |
761 | s | |
762 | (if (math-vectorp s) | |
763 | (math-parse-schedule (cdr s)) | |
764 | (if (eq (car-safe s) 'var) | |
765 | (math-var-to-calcFunc s) | |
766 | (error "Improper component in rewrite schedule")))))) | |
bf77c646 | 767 | sched)) |
136211a9 EZ |
768 | |
769 | (defun math-rwcomp-match-vars (expr) | |
770 | (if (Math-primp expr) | |
771 | (if (eq (car-safe expr) 'var) | |
772 | (let ((entry (assq (nth 2 expr) math-regs))) | |
773 | (if entry | |
774 | (math-rwcomp-register-expr (nth 1 entry)) | |
775 | expr)) | |
776 | expr) | |
777 | (if (and (eq (car expr) 'calcFunc-quote) | |
778 | (= (length expr) 2)) | |
779 | (math-rwcomp-match-vars (nth 1 expr)) | |
780 | (if (and (eq (car expr) 'calcFunc-plain) | |
781 | (= (length expr) 2) | |
782 | (not (Math-primp (nth 1 expr)))) | |
783 | (list (car expr) | |
784 | (cons (car (nth 1 expr)) | |
785 | (mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr))))) | |
786 | (cons (car expr) | |
bf77c646 | 787 | (mapcar 'math-rwcomp-match-vars (cdr expr))))))) |
136211a9 EZ |
788 | |
789 | (defun math-rwcomp-register-expr (num) | |
790 | (let ((entry (nth (1- (- math-num-regs num)) math-regs))) | |
791 | (if (nth 2 entry) | |
792 | (list 'neg (list 'calcFunc-register (nth 1 entry))) | |
bf77c646 | 793 | (list 'calcFunc-register (nth 1 entry))))) |
136211a9 EZ |
794 | |
795 | (defun math-rwcomp-substitute (expr old new) | |
796 | (if (and (eq (car-safe old) 'var) | |
797 | (memq (car-safe new) '(var calcFunc-lambda))) | |
798 | (let ((old-func (math-var-to-calcFunc old)) | |
799 | (new-func (math-var-to-calcFunc new))) | |
800 | (math-rwcomp-subst-rec expr)) | |
801 | (let ((old-func nil)) | |
bf77c646 | 802 | (math-rwcomp-subst-rec expr)))) |
136211a9 EZ |
803 | |
804 | (defun math-rwcomp-subst-rec (expr) | |
805 | (cond ((equal expr old) new) | |
806 | ((Math-primp expr) expr) | |
807 | (t (if (eq (car expr) old-func) | |
808 | (math-build-call new-func (mapcar 'math-rwcomp-subst-rec | |
809 | (cdr expr))) | |
810 | (cons (car expr) | |
bf77c646 | 811 | (mapcar 'math-rwcomp-subst-rec (cdr expr))))))) |
136211a9 | 812 | |
3132f345 | 813 | (defvar math-rwcomp-tracing nil) |
136211a9 EZ |
814 | |
815 | (defun math-rwcomp-trace (instr) | |
3132f345 CW |
816 | (when math-rwcomp-tracing |
817 | (terpri) (princ instr)) | |
bf77c646 | 818 | instr) |
136211a9 EZ |
819 | |
820 | (defun math-rwcomp-instr (&rest instr) | |
821 | (setcdr math-prog-last | |
bf77c646 | 822 | (setq math-prog-last (list (math-rwcomp-trace instr))))) |
136211a9 EZ |
823 | |
824 | (defun math-rwcomp-multi-instr (tail &rest instr) | |
825 | (setcdr math-prog-last | |
bf77c646 | 826 | (setq math-prog-last (list (math-rwcomp-trace (append instr tail)))))) |
136211a9 EZ |
827 | |
828 | (defun math-rwcomp-bind-var (reg var) | |
829 | (setcar (math-rwcomp-reg-entry reg) (nth 2 var)) | |
830 | (setq math-bound-vars (cons (nth 2 var) math-bound-vars)) | |
bf77c646 | 831 | (math-rwcomp-do-conditions)) |
136211a9 EZ |
832 | |
833 | (defun math-rwcomp-unbind-vars (mark) | |
834 | (while (not (eq math-bound-vars mark)) | |
835 | (setcar (assq (car math-bound-vars) math-regs) nil) | |
bf77c646 | 836 | (setq math-bound-vars (cdr math-bound-vars)))) |
136211a9 EZ |
837 | |
838 | (defun math-rwcomp-do-conditions () | |
839 | (let ((cond math-conds)) | |
840 | (while cond | |
841 | (if (math-rwcomp-all-regs-done (car cond)) | |
842 | (let ((expr (car cond))) | |
843 | (setq math-conds (delq (car cond) math-conds)) | |
844 | (setcar cond 1) | |
845 | (math-rwcomp-cond-instr expr))) | |
bf77c646 | 846 | (setq cond (cdr cond))))) |
136211a9 EZ |
847 | |
848 | (defun math-rwcomp-cond-instr (expr) | |
849 | (let (op arg) | |
850 | (cond ((and (eq (car-safe expr) 'calcFunc-matches) | |
851 | (= (length expr) 3) | |
852 | (eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr)))) | |
853 | 'calcFunc-register)) | |
854 | (math-rwcomp-pattern (nth 2 expr) (nth 1 arg))) | |
855 | ((math-numberp (setq expr (math-rwcomp-match-vars expr))) | |
856 | (if (Math-zerop expr) | |
857 | (math-rwcomp-instr 'backtrack))) | |
858 | ((and (eq (car expr) 'calcFunc-let) | |
859 | (= (length expr) 3)) | |
860 | (let ((reg (math-rwcomp-reg))) | |
861 | (math-rwcomp-instr 'let reg (nth 2 expr)) | |
862 | (math-rwcomp-pattern (nth 1 expr) reg))) | |
863 | ((and (eq (car expr) 'calcFunc-let) | |
864 | (= (length expr) 2) | |
865 | (eq (car-safe (nth 1 expr)) 'calcFunc-assign) | |
866 | (= (length (nth 1 expr)) 3)) | |
867 | (let ((reg (math-rwcomp-reg))) | |
868 | (math-rwcomp-instr 'let reg (nth 2 (nth 1 expr))) | |
869 | (math-rwcomp-pattern (nth 1 (nth 1 expr)) reg))) | |
870 | ((and (setq op (cdr (assq (car-safe expr) | |
871 | '( (calcFunc-integer . integer) | |
872 | (calcFunc-real . real) | |
873 | (calcFunc-constant . constant) | |
874 | (calcFunc-negative . negative) )))) | |
875 | (= (length expr) 2) | |
876 | (or (and (eq (car-safe (nth 1 expr)) 'neg) | |
877 | (memq op '(integer real constant)) | |
878 | (setq arg (nth 1 (nth 1 expr)))) | |
879 | (setq arg (nth 1 expr))) | |
880 | (eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register)) | |
881 | (math-rwcomp-instr op (nth 1 arg))) | |
882 | ((and (assq (car-safe expr) calc-tweak-eqn-table) | |
883 | (= (length expr) 3) | |
884 | (eq (car-safe (nth 1 expr)) 'calcFunc-register)) | |
885 | (if (math-constp (nth 2 expr)) | |
886 | (let ((reg (math-rwcomp-reg))) | |
887 | (setcar (nthcdr 3 (car math-regs)) (nth 2 expr)) | |
888 | (math-rwcomp-instr 'rel (nth 1 (nth 1 expr)) | |
889 | (car expr) reg)) | |
890 | (if (eq (car (nth 2 expr)) 'calcFunc-register) | |
891 | (math-rwcomp-instr 'rel (nth 1 (nth 1 expr)) | |
892 | (car expr) (nth 1 (nth 2 expr))) | |
893 | (math-rwcomp-instr 'cond expr)))) | |
894 | ((and (eq (car-safe expr) 'calcFunc-eq) | |
895 | (= (length expr) 3) | |
896 | (eq (car-safe (nth 1 expr)) '%) | |
897 | (eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register) | |
898 | (math-constp (nth 2 (nth 1 expr))) | |
899 | (math-constp (nth 2 expr))) | |
900 | (math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr))) | |
901 | (nth 2 (nth 1 expr)) (nth 2 expr))) | |
902 | ((equal expr '(var remember var-remember)) | |
903 | (setq math-remembering 1)) | |
904 | ((and (eq (car-safe expr) 'calcFunc-remember) | |
905 | (= (length expr) 2)) | |
906 | (setq math-remembering (if math-remembering | |
907 | (list 'calcFunc-lor | |
908 | math-remembering (nth 1 expr)) | |
909 | (nth 1 expr)))) | |
bf77c646 | 910 | (t (math-rwcomp-instr 'cond expr))))) |
136211a9 EZ |
911 | |
912 | (defun math-rwcomp-same-instr (reg1 reg2 neg) | |
913 | (math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1)) | |
914 | (nth 2 (math-rwcomp-reg-entry reg2))) | |
915 | neg) | |
916 | 'same-neg | |
917 | 'same) | |
bf77c646 | 918 | reg1 reg2)) |
136211a9 EZ |
919 | |
920 | (defun math-rwcomp-copy-instr (reg1 reg2 neg) | |
921 | (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1)) | |
922 | (nth 2 (math-rwcomp-reg-entry reg2))) | |
923 | neg) | |
924 | (math-rwcomp-instr 'copy-neg reg1 reg2) | |
925 | (or (eq reg1 reg2) | |
bf77c646 | 926 | (math-rwcomp-instr 'copy reg1 reg2)))) |
136211a9 EZ |
927 | |
928 | (defun math-rwcomp-reg () | |
929 | (prog1 | |
930 | math-num-regs | |
931 | (setq math-regs (cons (list nil math-num-regs nil 0) math-regs) | |
bf77c646 | 932 | math-num-regs (1+ math-num-regs)))) |
136211a9 EZ |
933 | |
934 | (defun math-rwcomp-reg-entry (num) | |
bf77c646 | 935 | (nth (1- (- math-num-regs num)) math-regs)) |
136211a9 EZ |
936 | |
937 | ||
938 | (defun math-rwcomp-pattern (expr part &optional not-direct) | |
939 | (cond ((or (math-rwcomp-no-vars expr) | |
940 | (and (eq (car expr) 'calcFunc-quote) | |
941 | (= (length expr) 2) | |
942 | (setq expr (nth 1 expr)))) | |
943 | (if (eq (car-safe expr) 'calcFunc-register) | |
944 | (math-rwcomp-same-instr part (nth 1 expr) nil) | |
945 | (let ((reg (math-rwcomp-reg))) | |
946 | (setcar (nthcdr 3 (car math-regs)) expr) | |
947 | (math-rwcomp-same-instr part reg nil)))) | |
948 | ((eq (car expr) 'var) | |
949 | (let ((entry (assq (nth 2 expr) math-regs))) | |
950 | (if entry | |
951 | (math-rwcomp-same-instr part (nth 1 entry) nil) | |
952 | (if not-direct | |
953 | (let ((reg (math-rwcomp-reg))) | |
954 | (math-rwcomp-pattern expr reg) | |
955 | (math-rwcomp-copy-instr part reg nil)) | |
956 | (if (setq entry (assq (nth 2 expr) math-aliased-vars)) | |
957 | (progn | |
958 | (setcar (math-rwcomp-reg-entry (nth 1 entry)) | |
959 | (nth 2 expr)) | |
960 | (setcar entry nil) | |
961 | (math-rwcomp-copy-instr part (nth 1 entry) nil)) | |
962 | (math-rwcomp-bind-var part expr)))))) | |
963 | ((and (eq (car expr) 'calcFunc-select) | |
964 | (= (length expr) 2)) | |
965 | (let ((reg (math-rwcomp-reg))) | |
966 | (math-rwcomp-instr 'select part reg) | |
967 | (math-rwcomp-pattern (nth 1 expr) reg))) | |
968 | ((and (eq (car expr) 'calcFunc-opt) | |
969 | (memq (length expr) '(2 3))) | |
970 | (error "opt( ) occurs in context where it is not allowed")) | |
971 | ((eq (car expr) 'neg) | |
972 | (if (eq (car (nth 1 expr)) 'var) | |
973 | (let ((entry (assq (nth 2 (nth 1 expr)) math-regs))) | |
974 | (if entry | |
975 | (math-rwcomp-same-instr part (nth 1 entry) t) | |
976 | (if math-copy-neg | |
977 | (let ((reg (math-rwcomp-best-reg (nth 1 expr)))) | |
978 | (math-rwcomp-copy-instr part reg t) | |
979 | (math-rwcomp-pattern (nth 1 expr) reg)) | |
980 | (setcar (cdr (cdr (math-rwcomp-reg-entry part))) t) | |
981 | (math-rwcomp-pattern (nth 1 expr) part)))) | |
982 | (if (math-rwcomp-is-algebraic (nth 1 expr)) | |
983 | (math-rwcomp-cond-instr (list 'calcFunc-eq | |
984 | (math-rwcomp-register-expr part) | |
985 | expr)) | |
986 | (let ((reg (math-rwcomp-reg))) | |
987 | (math-rwcomp-instr 'func part 'neg reg) | |
988 | (math-rwcomp-pattern (nth 1 expr) reg))))) | |
989 | ((and (eq (car expr) 'calcFunc-apply) | |
990 | (= (length expr) 3)) | |
991 | (let ((reg1 (math-rwcomp-reg)) | |
992 | (reg2 (math-rwcomp-reg))) | |
993 | (math-rwcomp-instr 'apply part reg1 reg2) | |
994 | (math-rwcomp-pattern (nth 1 expr) reg1) | |
995 | (math-rwcomp-pattern (nth 2 expr) reg2))) | |
996 | ((and (eq (car expr) 'calcFunc-cons) | |
997 | (= (length expr) 3)) | |
998 | (let ((reg1 (math-rwcomp-reg)) | |
999 | (reg2 (math-rwcomp-reg))) | |
1000 | (math-rwcomp-instr 'cons part reg1 reg2) | |
1001 | (math-rwcomp-pattern (nth 1 expr) reg1) | |
1002 | (math-rwcomp-pattern (nth 2 expr) reg2))) | |
1003 | ((and (eq (car expr) 'calcFunc-rcons) | |
1004 | (= (length expr) 3)) | |
1005 | (let ((reg1 (math-rwcomp-reg)) | |
1006 | (reg2 (math-rwcomp-reg))) | |
1007 | (math-rwcomp-instr 'rcons part reg1 reg2) | |
1008 | (math-rwcomp-pattern (nth 1 expr) reg1) | |
1009 | (math-rwcomp-pattern (nth 2 expr) reg2))) | |
1010 | ((and (eq (car expr) 'calcFunc-condition) | |
1011 | (>= (length expr) 3)) | |
1012 | (math-rwcomp-pattern (nth 1 expr) part) | |
1013 | (setq expr (cdr expr)) | |
1014 | (while (setq expr (cdr expr)) | |
1015 | (let ((cond (math-flatten-lands (car expr)))) | |
1016 | (while cond | |
1017 | (if (math-rwcomp-all-regs-done (car cond)) | |
1018 | (math-rwcomp-cond-instr (car cond)) | |
1019 | (setq math-conds (cons (car cond) math-conds))) | |
1020 | (setq cond (cdr cond)))))) | |
1021 | ((and (eq (car expr) 'calcFunc-pand) | |
1022 | (= (length expr) 3)) | |
1023 | (math-rwcomp-pattern (nth 1 expr) part) | |
1024 | (math-rwcomp-pattern (nth 2 expr) part)) | |
1025 | ((and (eq (car expr) 'calcFunc-por) | |
1026 | (= (length expr) 3)) | |
1027 | (math-rwcomp-instr 'alt nil nil [nil nil 4]) | |
1028 | (let ((math-conds nil) | |
1029 | (head math-prog-last) | |
1030 | (mark math-bound-vars) | |
1031 | (math-copy-neg t)) | |
1032 | (math-rwcomp-pattern (nth 1 expr) part t) | |
1033 | (let ((amark math-aliased-vars) | |
1034 | (math-aliased-vars math-aliased-vars) | |
1035 | (tail math-prog-last) | |
1036 | (p math-bound-vars) | |
1037 | entry) | |
1038 | (while (not (eq p mark)) | |
1039 | (setq entry (assq (car p) math-regs) | |
1040 | math-aliased-vars (cons (list (car p) (nth 1 entry) nil) | |
1041 | math-aliased-vars) | |
1042 | p (cdr p)) | |
1043 | (setcar (math-rwcomp-reg-entry (nth 1 entry)) nil)) | |
1044 | (setcar (cdr (car head)) (cdr head)) | |
1045 | (setcdr head nil) | |
1046 | (setq math-prog-last head) | |
1047 | (math-rwcomp-pattern (nth 2 expr) part) | |
1048 | (math-rwcomp-instr 'same 0 0) | |
1049 | (setcdr tail math-prog-last) | |
1050 | (setq p math-aliased-vars) | |
1051 | (while (not (eq p amark)) | |
1052 | (if (car (car p)) | |
1053 | (setcar (math-rwcomp-reg-entry (nth 1 (car p))) | |
1054 | (car (car p)))) | |
1055 | (setq p (cdr p))))) | |
1056 | (math-rwcomp-do-conditions)) | |
1057 | ((and (eq (car expr) 'calcFunc-pnot) | |
1058 | (= (length expr) 2)) | |
1059 | (math-rwcomp-instr 'alt nil nil [nil nil 4]) | |
1060 | (let ((head math-prog-last) | |
1061 | (mark math-bound-vars)) | |
1062 | (math-rwcomp-pattern (nth 1 expr) part) | |
1063 | (math-rwcomp-unbind-vars mark) | |
1064 | (math-rwcomp-instr 'end-alt head) | |
1065 | (math-rwcomp-instr 'backtrack) | |
1066 | (setcar (cdr (car head)) (cdr head)) | |
1067 | (setcdr head nil) | |
1068 | (setq math-prog-last head))) | |
1069 | (t (let ((props (get (car expr) 'math-rewrite-props))) | |
1070 | (if (and (eq (car expr) 'calcFunc-plain) | |
1071 | (= (length expr) 2) | |
1072 | (not (math-primp (nth 1 expr)))) | |
1073 | (setq expr (nth 1 expr))) ; but "props" is still nil | |
1074 | (if (and (memq 'algebraic props) | |
1075 | (math-rwcomp-is-algebraic expr)) | |
1076 | (math-rwcomp-cond-instr (list 'calcFunc-eq | |
1077 | (math-rwcomp-register-expr part) | |
1078 | expr)) | |
1079 | (if (and (memq 'commut props) | |
1080 | (= (length expr) 3)) | |
1081 | (let ((arg1 (nth 1 expr)) | |
1082 | (arg2 (nth 2 expr)) | |
1083 | try1 def code head (flip nil)) | |
1084 | (if (eq (car expr) '-) | |
1085 | (setq arg2 (math-rwcomp-neg arg2))) | |
1086 | (setq arg1 (cons arg1 (math-rwcomp-best-reg arg1)) | |
1087 | arg2 (cons arg2 (math-rwcomp-best-reg arg2))) | |
1088 | (or (math-rwcomp-order arg1 arg2) | |
1089 | (setq def arg1 arg1 arg2 arg2 def flip t)) | |
1090 | (if (math-rwcomp-optional-arg (car expr) arg1) | |
1091 | (error "Too many opt( ) arguments in this context")) | |
1092 | (setq def (math-rwcomp-optional-arg (car expr) arg2) | |
1093 | head (if (memq (car expr) '(+ -)) | |
1094 | '(+ -) | |
1095 | (if (eq (car expr) '*) | |
1096 | '(* /) | |
1097 | (list (car expr)))) | |
1098 | code (if (math-rwcomp-is-constrained | |
1099 | (car arg1) head) | |
1100 | (if (math-rwcomp-is-constrained | |
1101 | (car arg2) head) | |
1102 | 0 1) | |
1103 | 2)) | |
1104 | (math-rwcomp-multi-instr (and def (list def)) | |
1105 | 'try part head | |
1106 | (vector nil nil nil code flip) | |
1107 | (cdr arg1)) | |
1108 | (setq try1 (car math-prog-last)) | |
1109 | (math-rwcomp-pattern (car arg1) (cdr arg1)) | |
1110 | (math-rwcomp-instr 'try2 try1 (cdr arg2)) | |
1111 | (if (and (= part 0) (not def) (not math-rewrite-whole) | |
1112 | (not (eq math-rhs t)) | |
1113 | (setq def (get (car expr) | |
1114 | 'math-rewrite-default))) | |
1115 | (let ((reg1 (math-rwcomp-reg)) | |
1116 | (reg2 (math-rwcomp-reg))) | |
1117 | (if (= (aref (nth 3 try1) 3) 0) | |
1118 | (aset (nth 3 try1) 3 1)) | |
1119 | (math-rwcomp-instr 'try (cdr arg2) | |
1120 | (if (equal head '(* /)) | |
1121 | '(*) head) | |
1122 | (vector nil nil nil | |
1123 | (if (= code 0) | |
1124 | 1 2) | |
1125 | nil) | |
1126 | reg1 def) | |
1127 | (setq try1 (car math-prog-last)) | |
1128 | (math-rwcomp-pattern (car arg2) reg1) | |
1129 | (math-rwcomp-instr 'try2 try1 reg2) | |
1130 | (setq math-rhs (list (if (eq (car expr) '-) | |
1131 | '+ (car expr)) | |
1132 | math-rhs | |
1133 | (list 'calcFunc-register | |
1134 | reg2)))) | |
1135 | (math-rwcomp-pattern (car arg2) (cdr arg2)))) | |
1136 | (let* ((args (mapcar (function | |
1137 | (lambda (x) | |
1138 | (cons x (math-rwcomp-best-reg x)))) | |
1139 | (cdr expr))) | |
1140 | (args2 (copy-sequence args)) | |
1141 | (argp (reverse args2)) | |
1142 | (defs nil) | |
1143 | (num 1)) | |
1144 | (while argp | |
1145 | (let ((def (math-rwcomp-optional-arg (car expr) | |
1146 | (car argp)))) | |
1147 | (if def | |
1148 | (progn | |
1149 | (setq args2 (delq (car argp) args2) | |
1150 | defs (cons (cons def (cdr (car argp))) | |
1151 | defs)) | |
1152 | (math-rwcomp-multi-instr | |
1153 | (mapcar 'cdr args2) | |
1154 | (if (or (and (memq 'unary1 props) | |
1155 | (= (length args2) 1) | |
1156 | (eq (car args2) (car args))) | |
1157 | (and (memq 'unary2 props) | |
1158 | (= (length args) 2) | |
1159 | (eq (car args2) (nth 1 args)))) | |
1160 | 'func-opt | |
1161 | 'func-def) | |
1162 | part (car expr) | |
1163 | defs)))) | |
1164 | (setq argp (cdr argp))) | |
1165 | (math-rwcomp-multi-instr (mapcar 'cdr args) | |
1166 | 'func part (car expr)) | |
1167 | (setq args (sort args 'math-rwcomp-order)) | |
1168 | (while args | |
1169 | (math-rwcomp-pattern (car (car args)) (cdr (car args))) | |
1170 | (setq num (1+ num) | |
bf77c646 | 1171 | args (cdr args)))))))))) |
136211a9 EZ |
1172 | |
1173 | (defun math-rwcomp-best-reg (x) | |
1174 | (or (and (eq (car-safe x) 'var) | |
1175 | (let ((entry (assq (nth 2 x) math-aliased-vars))) | |
1176 | (and entry | |
1177 | (not (nth 2 entry)) | |
1178 | (not (nth 2 (math-rwcomp-reg-entry (nth 1 entry)))) | |
1179 | (progn | |
1180 | (setcar (cdr (cdr entry)) t) | |
1181 | (nth 1 entry))))) | |
bf77c646 | 1182 | (math-rwcomp-reg))) |
136211a9 EZ |
1183 | |
1184 | (defun math-rwcomp-all-regs-done (expr) | |
1185 | (if (Math-primp expr) | |
1186 | (or (not (eq (car-safe expr) 'var)) | |
1187 | (assq (nth 2 expr) math-regs) | |
1188 | (eq (nth 2 expr) 'var-remember) | |
1189 | (math-const-var expr)) | |
1190 | (if (and (eq (car expr) 'calcFunc-let) | |
1191 | (= (length expr) 3)) | |
1192 | (math-rwcomp-all-regs-done (nth 2 expr)) | |
1193 | (if (and (eq (car expr) 'calcFunc-let) | |
1194 | (= (length expr) 2) | |
1195 | (eq (car-safe (nth 1 expr)) 'calcFunc-assign) | |
1196 | (= (length (nth 1 expr)) 3)) | |
1197 | (math-rwcomp-all-regs-done (nth 2 (nth 1 expr))) | |
1198 | (while (and (setq expr (cdr expr)) | |
1199 | (math-rwcomp-all-regs-done (car expr)))) | |
bf77c646 | 1200 | (null expr))))) |
136211a9 EZ |
1201 | |
1202 | (defun math-rwcomp-no-vars (expr) | |
1203 | (if (Math-primp expr) | |
1204 | (or (not (eq (car-safe expr) 'var)) | |
1205 | (math-const-var expr)) | |
1206 | (and (not (memq (car expr) '(calcFunc-condition | |
1207 | calcFunc-select calcFunc-quote | |
1208 | calcFunc-plain calcFunc-opt | |
1209 | calcFunc-por calcFunc-pand | |
1210 | calcFunc-pnot calcFunc-apply | |
1211 | calcFunc-cons calcFunc-rcons))) | |
1212 | (progn | |
1213 | (while (and (setq expr (cdr expr)) | |
1214 | (math-rwcomp-no-vars (car expr)))) | |
bf77c646 | 1215 | (null expr))))) |
136211a9 EZ |
1216 | |
1217 | (defun math-rwcomp-is-algebraic (expr) | |
1218 | (if (Math-primp expr) | |
1219 | (or (not (eq (car-safe expr) 'var)) | |
1220 | (math-const-var expr) | |
1221 | (assq (nth 2 expr) math-regs)) | |
1222 | (and (memq 'algebraic (get (car expr) 'math-rewrite-props)) | |
1223 | (progn | |
1224 | (while (and (setq expr (cdr expr)) | |
1225 | (math-rwcomp-is-algebraic (car expr)))) | |
bf77c646 | 1226 | (null expr))))) |
136211a9 EZ |
1227 | |
1228 | (defun math-rwcomp-is-constrained (expr not-these) | |
1229 | (if (Math-primp expr) | |
1230 | (not (eq (car-safe expr) 'var)) | |
1231 | (if (eq (car expr) 'calcFunc-plain) | |
1232 | (math-rwcomp-is-constrained (nth 1 expr) not-these) | |
1233 | (not (or (memq (car expr) '(neg calcFunc-select)) | |
1234 | (memq (car expr) not-these) | |
1235 | (and (memq 'commut (get (car expr) 'math-rewrite-props)) | |
1236 | (or (eq (car-safe (nth 1 expr)) 'calcFunc-opt) | |
bf77c646 | 1237 | (eq (car-safe (nth 2 expr)) 'calcFunc-opt)))))))) |
136211a9 EZ |
1238 | |
1239 | (defun math-rwcomp-optional-arg (head argp) | |
1240 | (let ((arg (car argp))) | |
1241 | (if (eq (car-safe arg) 'calcFunc-opt) | |
1242 | (and (memq (length arg) '(2 3)) | |
1243 | (progn | |
1244 | (or (eq (car-safe (nth 1 arg)) 'var) | |
1245 | (error "First argument of opt( ) must be a variable")) | |
1246 | (setcar argp (nth 1 arg)) | |
1247 | (if (= (length arg) 2) | |
1248 | (or (get head 'math-rewrite-default) | |
1249 | (error "opt( ) must include a default in this context")) | |
1250 | (nth 2 arg)))) | |
1251 | (and (eq (car-safe arg) 'neg) | |
1252 | (let* ((part (list (nth 1 arg))) | |
1253 | (partp (math-rwcomp-optional-arg head part))) | |
1254 | (and partp | |
1255 | (setcar argp (math-rwcomp-neg (car part))) | |
bf77c646 | 1256 | (math-neg partp))))))) |
136211a9 EZ |
1257 | |
1258 | (defun math-rwcomp-neg (expr) | |
1259 | (if (memq (car-safe expr) '(* /)) | |
1260 | (if (eq (car-safe (nth 1 expr)) 'var) | |
1261 | (list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr)) | |
1262 | (if (eq (car-safe (nth 2 expr)) 'var) | |
1263 | (list (car expr) (nth 1 expr) (list 'neg (nth 2 expr))) | |
1264 | (math-neg expr))) | |
bf77c646 | 1265 | (math-neg expr))) |
136211a9 EZ |
1266 | |
1267 | (defun math-rwcomp-assoc-args (expr) | |
1268 | (if (and (eq (car-safe (nth 1 expr)) (car expr)) | |
1269 | (= (length (nth 1 expr)) 3)) | |
1270 | (math-rwcomp-assoc-args (nth 1 expr)) | |
1271 | (setq math-args (cons (nth 1 expr) math-args))) | |
1272 | (if (and (eq (car-safe (nth 2 expr)) (car expr)) | |
1273 | (= (length (nth 2 expr)) 3)) | |
1274 | (math-rwcomp-assoc-args (nth 2 expr)) | |
bf77c646 | 1275 | (setq math-args (cons (nth 2 expr) math-args)))) |
136211a9 EZ |
1276 | |
1277 | (defun math-rwcomp-addsub-args (expr) | |
1278 | (if (memq (car-safe (nth 1 expr)) '(+ -)) | |
1279 | (math-rwcomp-addsub-args (nth 1 expr)) | |
1280 | (setq math-args (cons (nth 1 expr) math-args))) | |
1281 | (if (eq (car expr) '-) | |
1282 | (setq math-args (cons (math-rwcomp-neg (nth 2 expr)) math-args)) | |
1283 | (if (eq (car-safe (nth 2 expr)) '+) | |
1284 | (math-rwcomp-addsub-args (nth 2 expr)) | |
bf77c646 | 1285 | (setq math-args (cons (nth 2 expr) math-args))))) |
136211a9 EZ |
1286 | |
1287 | (defun math-rwcomp-order (a b) | |
1288 | (< (math-rwcomp-priority (car a)) | |
bf77c646 | 1289 | (math-rwcomp-priority (car b)))) |
136211a9 EZ |
1290 | |
1291 | ;;; Order of priority: 0 Constants and other exact matches (first) | |
1292 | ;;; 10 Functions (except below) | |
1293 | ;;; 20 Meta-variables which occur more than once | |
1294 | ;;; 30 Algebraic functions | |
1295 | ;;; 40 Commutative/associative functions | |
1296 | ;;; 50 Meta-variables which occur only once | |
1297 | ;;; +100 for every "!!!" (pnot) in the pattern | |
1298 | ;;; 10000 Optional arguments (last) | |
1299 | ||
1300 | (defun math-rwcomp-priority (expr) | |
1301 | (+ (math-rwcomp-count-pnots expr) | |
1302 | (cond ((eq (car-safe expr) 'calcFunc-opt) | |
1303 | 10000) | |
1304 | ((math-rwcomp-no-vars expr) | |
1305 | 0) | |
1306 | ((eq (car expr) 'calcFunc-quote) | |
1307 | 0) | |
1308 | ((eq (car expr) 'var) | |
1309 | (if (assq (nth 2 expr) math-regs) | |
1310 | 0 | |
1311 | (if (= (math-rwcomp-count-refs expr) 1) | |
1312 | 50 | |
1313 | 20))) | |
1314 | (t (let ((props (get (car expr) 'math-rewrite-props))) | |
1315 | (if (or (memq 'commut props) | |
1316 | (memq 'assoc props)) | |
1317 | 40 | |
1318 | (if (memq 'algebraic props) | |
1319 | 30 | |
bf77c646 | 1320 | 10))))))) |
136211a9 EZ |
1321 | |
1322 | (defun math-rwcomp-count-refs (var) | |
1323 | (let ((count (or (math-expr-contains-count math-pattern var) 0)) | |
1324 | (p math-conds)) | |
1325 | (while p | |
1326 | (if (eq (car-safe (car p)) 'calcFunc-let) | |
1327 | (if (= (length (car p)) 3) | |
1328 | (setq count (+ count | |
1329 | (or (math-expr-contains-count (nth 2 (car p)) var) | |
1330 | 0))) | |
1331 | (if (and (= (length (car p)) 2) | |
1332 | (eq (car-safe (nth 1 (car p))) 'calcFunc-assign) | |
1333 | (= (length (nth 1 (car p))) 3)) | |
1334 | (setq count (+ count | |
1335 | (or (math-expr-contains-count | |
1336 | (nth 2 (nth 1 (car p))) var) 0)))))) | |
1337 | (setq p (cdr p))) | |
bf77c646 | 1338 | count)) |
136211a9 EZ |
1339 | |
1340 | (defun math-rwcomp-count-pnots (expr) | |
1341 | (if (Math-primp expr) | |
1342 | 0 | |
1343 | (if (eq (car expr) 'calcFunc-pnot) | |
1344 | 100 | |
1345 | (let ((count 0)) | |
1346 | (while (setq expr (cdr expr)) | |
1347 | (setq count (+ count (math-rwcomp-count-pnots (car expr))))) | |
bf77c646 | 1348 | count)))) |
136211a9 EZ |
1349 | |
1350 | ;;; In the current implementation, all associative functions must | |
1351 | ;;; also be commutative. | |
1352 | ||
1353 | (put '+ 'math-rewrite-props '(algebraic assoc commut)) | |
1354 | (put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below | |
1355 | (put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below | |
1356 | (put '/ 'math-rewrite-props '(algebraic unary1)) | |
1357 | (put '^ 'math-rewrite-props '(algebraic unary1)) | |
1358 | (put '% 'math-rewrite-props '(algebraic)) | |
1359 | (put 'neg 'math-rewrite-props '(algebraic)) | |
1360 | (put 'calcFunc-idiv 'math-rewrite-props '(algebraic)) | |
1361 | (put 'calcFunc-abs 'math-rewrite-props '(algebraic)) | |
1362 | (put 'calcFunc-sign 'math-rewrite-props '(algebraic)) | |
1363 | (put 'calcFunc-round 'math-rewrite-props '(algebraic)) | |
1364 | (put 'calcFunc-rounde 'math-rewrite-props '(algebraic)) | |
1365 | (put 'calcFunc-roundu 'math-rewrite-props '(algebraic)) | |
1366 | (put 'calcFunc-trunc 'math-rewrite-props '(algebraic)) | |
1367 | (put 'calcFunc-floor 'math-rewrite-props '(algebraic)) | |
1368 | (put 'calcFunc-ceil 'math-rewrite-props '(algebraic)) | |
1369 | (put 'calcFunc-re 'math-rewrite-props '(algebraic)) | |
1370 | (put 'calcFunc-im 'math-rewrite-props '(algebraic)) | |
1371 | (put 'calcFunc-conj 'math-rewrite-props '(algebraic)) | |
1372 | (put 'calcFunc-arg 'math-rewrite-props '(algebraic)) | |
1373 | (put 'calcFunc-and 'math-rewrite-props '(assoc commut)) | |
1374 | (put 'calcFunc-or 'math-rewrite-props '(assoc commut)) | |
1375 | (put 'calcFunc-xor 'math-rewrite-props '(assoc commut)) | |
1376 | (put 'calcFunc-eq 'math-rewrite-props '(commut)) | |
1377 | (put 'calcFunc-neq 'math-rewrite-props '(commut)) | |
1378 | (put 'calcFunc-land 'math-rewrite-props '(assoc commut)) | |
1379 | (put 'calcFunc-lor 'math-rewrite-props '(assoc commut)) | |
1380 | (put 'calcFunc-beta 'math-rewrite-props '(commut)) | |
1381 | (put 'calcFunc-gcd 'math-rewrite-props '(assoc commut)) | |
1382 | (put 'calcFunc-lcm 'math-rewrite-props '(assoc commut)) | |
1383 | (put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut)) | |
1384 | (put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut)) | |
1385 | (put 'calcFunc-vunion 'math-rewrite-props '(assoc commut)) | |
1386 | (put 'calcFunc-vint 'math-rewrite-props '(assoc commut)) | |
1387 | (put 'calcFunc-vxor 'math-rewrite-props '(assoc commut)) | |
1388 | ||
1389 | ;;; Note: "*" is not commutative for matrix args, but we pretend it is. | |
1390 | ;;; Also, "-" is not commutative but the code tweaks things so that it is. | |
1391 | ||
1392 | (put '+ 'math-rewrite-default 0) | |
1393 | (put '- 'math-rewrite-default 0) | |
1394 | (put '* 'math-rewrite-default 1) | |
1395 | (put '/ 'math-rewrite-default 1) | |
1396 | (put '^ 'math-rewrite-default 1) | |
1397 | (put 'calcFunc-land 'math-rewrite-default 1) | |
1398 | (put 'calcFunc-lor 'math-rewrite-default 0) | |
1399 | (put 'calcFunc-vunion 'math-rewrite-default '(vec)) | |
1400 | (put 'calcFunc-vint 'math-rewrite-default '(vec)) | |
1401 | (put 'calcFunc-vdiff 'math-rewrite-default '(vec)) | |
1402 | (put 'calcFunc-vxor 'math-rewrite-default '(vec)) | |
1403 | ||
1404 | (defmacro math-rwfail (&optional back) | |
1405 | (list 'setq 'pc | |
1406 | (list 'and | |
1407 | (if back | |
1408 | '(setq btrack (cdr btrack)) | |
1409 | 'btrack) | |
bf77c646 | 1410 | ''((backtrack))))) |
136211a9 EZ |
1411 | |
1412 | ;;; This monstrosity is necessary because the use of static vectors of | |
1413 | ;;; registers makes rewrite rules non-reentrant. Yucko! | |
1414 | (defmacro math-rweval (form) | |
1415 | (list 'let '((orig (car rules))) | |
1416 | '(setcar rules (quote (nil nil nil no-phase))) | |
1417 | (list 'unwind-protect | |
1418 | form | |
bf77c646 | 1419 | '(setcar rules orig)))) |
136211a9 EZ |
1420 | |
1421 | (setq math-rewrite-phase 1) | |
1422 | ||
1423 | (defun math-apply-rewrites (expr rules &optional heads ruleset) | |
1424 | (and | |
1425 | (setq rules (cdr (or (assq (car-safe expr) rules) | |
1426 | (assq nil rules)))) | |
1427 | (let ((result nil) | |
1428 | op regs inst part pc mark btrack | |
1429 | (tracing math-rwcomp-tracing) | |
1430 | (phase math-rewrite-phase)) | |
1431 | (while rules | |
1432 | (or | |
1433 | (and (setq part (nth 2 (car rules))) | |
1434 | heads | |
1435 | (not (memq part heads))) | |
1436 | (and (setq part (nth 3 (car rules))) | |
1437 | (not (memq phase part))) | |
1438 | (progn | |
1439 | (setq regs (car (car rules)) | |
1440 | pc (nth 1 (car rules)) | |
1441 | btrack nil) | |
1442 | (aset regs 0 expr) | |
1443 | (while pc | |
1444 | ||
1445 | (and tracing | |
1446 | (progn (terpri) (princ (car pc)) | |
1447 | (if (and (natnump (nth 1 (car pc))) | |
1448 | (< (nth 1 (car pc)) (length regs))) | |
1449 | (princ (format "\n part = %s" | |
1450 | (aref regs (nth 1 (car pc)))))))) | |
1451 | ||
1452 | (cond ((eq (setq op (car (setq inst (car pc)))) 'func) | |
1453 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1454 | (eq (car part) | |
1455 | (car (setq inst (cdr (cdr inst))))) | |
1456 | (progn | |
1457 | (while (and (setq inst (cdr inst) | |
1458 | part (cdr part)) | |
1459 | inst) | |
1460 | (aset regs (car inst) (car part))) | |
1461 | (not (or inst part)))) | |
1462 | (setq pc (cdr pc)) | |
1463 | (math-rwfail))) | |
1464 | ||
1465 | ((eq op 'same) | |
1466 | (if (or (equal (setq part (aref regs (nth 1 inst))) | |
1467 | (setq mark (aref regs (nth 2 inst)))) | |
1468 | (Math-equal part mark)) | |
1469 | (setq pc (cdr pc)) | |
1470 | (math-rwfail))) | |
1471 | ||
1472 | ((and (eq op 'try) | |
1473 | calc-matrix-mode | |
1474 | (not (eq calc-matrix-mode 'scalar)) | |
1475 | (eq (car (nth 2 inst)) '*) | |
1476 | (consp (setq part (aref regs (car (cdr inst))))) | |
1477 | (eq (car part) '*) | |
1478 | (not (math-known-scalarp part))) | |
1479 | (setq mark (nth 3 inst) | |
1480 | pc (cdr pc)) | |
1481 | (if (aref mark 4) | |
1482 | (progn | |
1483 | (aset regs (nth 4 inst) (nth 2 part)) | |
1484 | (aset mark 1 (cdr (cdr part)))) | |
1485 | (aset regs (nth 4 inst) (nth 1 part)) | |
1486 | (aset mark 1 (cdr part))) | |
1487 | (aset mark 0 (cdr part)) | |
1488 | (aset mark 2 0)) | |
1489 | ||
1490 | ((eq op 'try) | |
1491 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1492 | (memq (car part) (nth 2 inst)) | |
1493 | (= (length part) 3) | |
1494 | (or (not (eq (car part) '/)) | |
1495 | (Math-objectp (nth 2 part)))) | |
1496 | (progn | |
1497 | (setq op nil | |
1498 | mark (car (cdr (setq inst (cdr (cdr inst)))))) | |
1499 | (and | |
1500 | (memq 'assoc (get (car part) 'math-rewrite-props)) | |
1501 | (not (= (aref mark 3) 0)) | |
1502 | (while (if (and (consp (nth 1 part)) | |
1503 | (memq (car (nth 1 part)) (car inst))) | |
1504 | (setq op (cons (if (eq (car part) '-) | |
1505 | (math-rwapply-neg | |
1506 | (nth 2 part)) | |
1507 | (nth 2 part)) | |
1508 | op) | |
1509 | part (nth 1 part)) | |
1510 | (if (and (consp (nth 2 part)) | |
1511 | (memq (car (nth 2 part)) | |
1512 | (car inst)) | |
1513 | (not (eq (car (nth 2 part)) '-))) | |
1514 | (setq op (cons (nth 1 part) op) | |
1515 | part (nth 2 part)))))) | |
1516 | (setq op (cons (nth 1 part) | |
1517 | (cons (if (eq (car part) '-) | |
1518 | (math-rwapply-neg | |
1519 | (nth 2 part)) | |
1520 | (if (eq (car part) '/) | |
1521 | (math-rwapply-inv | |
1522 | (nth 2 part)) | |
1523 | (nth 2 part))) | |
1524 | op)) | |
1525 | btrack (cons pc btrack) | |
1526 | pc (cdr pc)) | |
1527 | (aset regs (nth 2 inst) (car op)) | |
1528 | (aset mark 0 op) | |
1529 | (aset mark 1 op) | |
1530 | (aset mark 2 (if (cdr (cdr op)) 1 0))) | |
1531 | (if (nth 5 inst) | |
1532 | (if (and (consp part) | |
1533 | (eq (car part) 'neg) | |
1534 | (eq (car (nth 2 inst)) '*) | |
1535 | (eq (nth 5 inst) 1)) | |
1536 | (progn | |
1537 | (setq mark (nth 3 inst) | |
1538 | pc (cdr pc)) | |
1539 | (aset regs (nth 4 inst) (nth 1 part)) | |
1540 | (aset mark 1 -1) | |
1541 | (aset mark 2 4)) | |
1542 | (setq mark (nth 3 inst) | |
1543 | pc (cdr pc)) | |
1544 | (aset regs (nth 4 inst) part) | |
1545 | (aset mark 2 3)) | |
1546 | (math-rwfail)))) | |
1547 | ||
1548 | ((eq op 'try2) | |
1549 | (setq part (nth 1 inst) ; try instr | |
1550 | mark (nth 3 part) | |
1551 | op (aref mark 2) | |
1552 | pc (cdr pc)) | |
1553 | (aset regs (nth 2 inst) | |
1554 | (cond | |
1555 | ((eq op 0) | |
1556 | (if (eq (aref mark 0) (aref mark 1)) | |
1557 | (nth 1 (aref mark 0)) | |
1558 | (car (aref mark 0)))) | |
1559 | ((eq op 1) | |
1560 | (setq mark (delq (car (aref mark 1)) | |
1561 | (copy-sequence (aref mark 0))) | |
1562 | op (car (nth 2 part))) | |
1563 | (if (eq op '*) | |
1564 | (progn | |
1565 | (setq mark (nreverse mark) | |
1566 | part (list '* (nth 1 mark) (car mark)) | |
1567 | mark (cdr mark)) | |
1568 | (while (setq mark (cdr mark)) | |
1569 | (setq part (list '* (car mark) part)))) | |
1570 | (setq part (car mark) | |
1571 | mark (cdr mark) | |
1572 | part (if (and (eq op '+) | |
1573 | (consp (car mark)) | |
1574 | (eq (car (car mark)) 'neg)) | |
1575 | (list '- part | |
1576 | (nth 1 (car mark))) | |
1577 | (list op part (car mark)))) | |
1578 | (while (setq mark (cdr mark)) | |
1579 | (setq part (if (and (eq op '+) | |
1580 | (consp (car mark)) | |
1581 | (eq (car (car mark)) 'neg)) | |
1582 | (list '- part | |
1583 | (nth 1 (car mark))) | |
1584 | (list op part (car mark)))))) | |
1585 | part) | |
1586 | ((eq op 2) | |
1587 | (car (aref mark 1))) | |
1588 | ((eq op 3) (nth 5 part)) | |
1589 | (t (aref mark 1))))) | |
1590 | ||
1591 | ((eq op 'select) | |
1592 | (setq pc (cdr pc)) | |
1593 | (if (and (consp (setq part (aref regs (nth 1 inst)))) | |
1594 | (eq (car part) 'calcFunc-select)) | |
1595 | (aset regs (nth 2 inst) (nth 1 part)) | |
1596 | (if math-rewrite-selections | |
1597 | (math-rwfail) | |
1598 | (aset regs (nth 2 inst) part)))) | |
1599 | ||
1600 | ((eq op 'same-neg) | |
1601 | (if (or (equal (setq part (aref regs (nth 1 inst))) | |
1602 | (setq mark (math-neg | |
1603 | (aref regs (nth 2 inst))))) | |
1604 | (Math-equal part mark)) | |
1605 | (setq pc (cdr pc)) | |
1606 | (math-rwfail))) | |
1607 | ||
1608 | ((eq op 'backtrack) | |
1609 | (setq inst (car (car btrack)) ; "try" or "alt" instr | |
1610 | pc (cdr (car btrack)) | |
1611 | mark (or (nth 3 inst) [nil nil 4]) | |
1612 | op (aref mark 2)) | |
1613 | (cond ((eq op 0) | |
1614 | (if (setq op (cdr (aref mark 1))) | |
1615 | (aset regs (nth 4 inst) (car (aset mark 1 op))) | |
1616 | (if (nth 5 inst) | |
1617 | (progn | |
1618 | (aset mark 2 3) | |
1619 | (aset regs (nth 4 inst) | |
1620 | (aref regs (nth 1 inst)))) | |
1621 | (math-rwfail t)))) | |
1622 | ((eq op 1) | |
1623 | (if (setq op (cdr (aref mark 1))) | |
1624 | (aset regs (nth 4 inst) (car (aset mark 1 op))) | |
1625 | (if (= (aref mark 3) 1) | |
1626 | (if (nth 5 inst) | |
1627 | (progn | |
1628 | (aset mark 2 3) | |
1629 | (aset regs (nth 4 inst) | |
1630 | (aref regs (nth 1 inst)))) | |
1631 | (math-rwfail t)) | |
1632 | (aset mark 2 2) | |
1633 | (aset mark 1 (cons nil (aref mark 0))) | |
1634 | (math-rwfail)))) | |
1635 | ((eq op 2) | |
1636 | (if (setq op (cdr (aref mark 1))) | |
1637 | (progn | |
1638 | (setq mark (delq (car (aset mark 1 op)) | |
1639 | (copy-sequence | |
1640 | (aref mark 0))) | |
1641 | op (car (nth 2 inst))) | |
1642 | (if (eq op '*) | |
1643 | (progn | |
1644 | (setq mark (nreverse mark) | |
1645 | part (list '* (nth 1 mark) | |
1646 | (car mark)) | |
1647 | mark (cdr mark)) | |
1648 | (while (setq mark (cdr mark)) | |
1649 | (setq part (list '* (car mark) | |
1650 | part)))) | |
1651 | (setq part (car mark) | |
1652 | mark (cdr mark) | |
1653 | part (if (and (eq op '+) | |
1654 | (consp (car mark)) | |
1655 | (eq (car (car mark)) | |
1656 | 'neg)) | |
1657 | (list '- part | |
1658 | (nth 1 (car mark))) | |
1659 | (list op part (car mark)))) | |
1660 | (while (setq mark (cdr mark)) | |
1661 | (setq part (if (and (eq op '+) | |
1662 | (consp (car mark)) | |
1663 | (eq (car (car mark)) | |
1664 | 'neg)) | |
1665 | (list '- part | |
1666 | (nth 1 (car mark))) | |
1667 | (list op part (car mark)))))) | |
1668 | (aset regs (nth 4 inst) part)) | |
1669 | (if (nth 5 inst) | |
1670 | (progn | |
1671 | (aset mark 2 3) | |
1672 | (aset regs (nth 4 inst) | |
1673 | (aref regs (nth 1 inst)))) | |
1674 | (math-rwfail t)))) | |
1675 | ((eq op 4) | |
1676 | (setq btrack (cdr btrack))) | |
1677 | (t (math-rwfail t)))) | |
1678 | ||
1679 | ((eq op 'integer) | |
1680 | (if (Math-integerp (setq part (aref regs (nth 1 inst)))) | |
1681 | (setq pc (cdr pc)) | |
1682 | (if (Math-primp part) | |
1683 | (math-rwfail) | |
1684 | (setq part (math-rweval (math-simplify part))) | |
1685 | (if (Math-integerp part) | |
1686 | (setq pc (cdr pc)) | |
1687 | (math-rwfail))))) | |
1688 | ||
1689 | ((eq op 'real) | |
1690 | (if (Math-realp (setq part (aref regs (nth 1 inst)))) | |
1691 | (setq pc (cdr pc)) | |
1692 | (if (Math-primp part) | |
1693 | (math-rwfail) | |
1694 | (setq part (math-rweval (math-simplify part))) | |
1695 | (if (Math-realp part) | |
1696 | (setq pc (cdr pc)) | |
1697 | (math-rwfail))))) | |
1698 | ||
1699 | ((eq op 'constant) | |
1700 | (if (math-constp (setq part (aref regs (nth 1 inst)))) | |
1701 | (setq pc (cdr pc)) | |
1702 | (if (Math-primp part) | |
1703 | (math-rwfail) | |
1704 | (setq part (math-rweval (math-simplify part))) | |
1705 | (if (math-constp part) | |
1706 | (setq pc (cdr pc)) | |
1707 | (math-rwfail))))) | |
1708 | ||
1709 | ((eq op 'negative) | |
1710 | (if (math-looks-negp (setq part (aref regs (nth 1 inst)))) | |
1711 | (setq pc (cdr pc)) | |
1712 | (if (Math-primp part) | |
1713 | (math-rwfail) | |
1714 | (setq part (math-rweval (math-simplify part))) | |
1715 | (if (math-looks-negp part) | |
1716 | (setq pc (cdr pc)) | |
1717 | (math-rwfail))))) | |
1718 | ||
1719 | ((eq op 'rel) | |
1720 | (setq part (math-compare (aref regs (nth 1 inst)) | |
1721 | (aref regs (nth 3 inst))) | |
1722 | op (nth 2 inst)) | |
1723 | (if (= part 2) | |
1724 | (setq part (math-rweval | |
1725 | (math-simplify | |
1726 | (calcFunc-sign | |
1727 | (math-sub (aref regs (nth 1 inst)) | |
1728 | (aref regs (nth 3 inst)))))))) | |
1729 | (if (cond ((eq op 'calcFunc-eq) | |
1730 | (eq part 0)) | |
1731 | ((eq op 'calcFunc-neq) | |
1732 | (memq part '(-1 1))) | |
1733 | ((eq op 'calcFunc-lt) | |
1734 | (eq part -1)) | |
1735 | ((eq op 'calcFunc-leq) | |
1736 | (memq part '(-1 0))) | |
1737 | ((eq op 'calcFunc-gt) | |
1738 | (eq part 1)) | |
1739 | ((eq op 'calcFunc-geq) | |
1740 | (memq part '(0 1)))) | |
1741 | (setq pc (cdr pc)) | |
1742 | (math-rwfail))) | |
1743 | ||
1744 | ((eq op 'func-def) | |
1745 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1746 | (eq (car part) | |
1747 | (car (setq inst (cdr (cdr inst)))))) | |
1748 | (progn | |
1749 | (setq inst (cdr inst) | |
1750 | mark (car inst)) | |
1751 | (while (and (setq inst (cdr inst) | |
1752 | part (cdr part)) | |
1753 | inst) | |
1754 | (aset regs (car inst) (car part))) | |
1755 | (if (or inst part) | |
1756 | (setq pc (cdr pc)) | |
1757 | (while (eq (car (car (setq pc (cdr pc)))) | |
1758 | 'func-def)) | |
1759 | (setq pc (cdr pc)) ; skip over "func" | |
1760 | (while mark | |
1761 | (aset regs (cdr (car mark)) (car (car mark))) | |
1762 | (setq mark (cdr mark))))) | |
1763 | (math-rwfail))) | |
1764 | ||
1765 | ((eq op 'func-opt) | |
1766 | (if (or (not (and (consp | |
1767 | (setq part (aref regs (car (cdr inst))))) | |
1768 | (eq (car part) (nth 2 inst)))) | |
1769 | (and (= (length part) 2) | |
1770 | (setq part (nth 1 part)))) | |
1771 | (progn | |
1772 | (setq mark (nth 3 inst)) | |
1773 | (aset regs (nth 4 inst) part) | |
1774 | (while (eq (car (car (setq pc (cdr pc)))) 'func-def)) | |
1775 | (setq pc (cdr pc)) ; skip over "func" | |
1776 | (while mark | |
1777 | (aset regs (cdr (car mark)) (car (car mark))) | |
1778 | (setq mark (cdr mark)))) | |
1779 | (setq pc (cdr pc)))) | |
1780 | ||
1781 | ((eq op 'mod) | |
1782 | (if (if (Math-zerop (setq part (aref regs (nth 1 inst)))) | |
1783 | (Math-zerop (nth 3 inst)) | |
1784 | (and (not (Math-zerop (nth 2 inst))) | |
1785 | (progn | |
1786 | (setq part (math-mod part (nth 2 inst))) | |
1787 | (or (Math-numberp part) | |
1788 | (setq part (math-rweval | |
1789 | (math-simplify part)))) | |
1790 | (Math-equal part (nth 3 inst))))) | |
1791 | (setq pc (cdr pc)) | |
1792 | (math-rwfail))) | |
1793 | ||
1794 | ((eq op 'apply) | |
1795 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1796 | (not (Math-objvecp part)) | |
1797 | (not (eq (car part) 'var))) | |
1798 | (progn | |
1799 | (aset regs (nth 2 inst) | |
1800 | (math-calcFunc-to-var (car part))) | |
1801 | (aset regs (nth 3 inst) | |
1802 | (cons 'vec (cdr part))) | |
1803 | (setq pc (cdr pc))) | |
1804 | (math-rwfail))) | |
1805 | ||
1806 | ((eq op 'cons) | |
1807 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1808 | (eq (car part) 'vec) | |
1809 | (cdr part)) | |
1810 | (progn | |
1811 | (aset regs (nth 2 inst) (nth 1 part)) | |
1812 | (aset regs (nth 3 inst) (cons 'vec (cdr (cdr part)))) | |
1813 | (setq pc (cdr pc))) | |
1814 | (math-rwfail))) | |
1815 | ||
1816 | ((eq op 'rcons) | |
1817 | (if (and (consp (setq part (aref regs (car (cdr inst))))) | |
1818 | (eq (car part) 'vec) | |
1819 | (cdr part)) | |
1820 | (progn | |
1821 | (aset regs (nth 2 inst) (calcFunc-rhead part)) | |
1822 | (aset regs (nth 3 inst) (calcFunc-rtail part)) | |
1823 | (setq pc (cdr pc))) | |
1824 | (math-rwfail))) | |
1825 | ||
1826 | ((eq op 'cond) | |
1827 | (if (math-is-true | |
1828 | (math-rweval | |
1829 | (math-simplify | |
1830 | (math-rwapply-replace-regs (nth 1 inst))))) | |
1831 | (setq pc (cdr pc)) | |
1832 | (math-rwfail))) | |
1833 | ||
1834 | ((eq op 'let) | |
1835 | (aset regs (nth 1 inst) | |
1836 | (math-rweval | |
1837 | (math-normalize | |
1838 | (math-rwapply-replace-regs (nth 2 inst))))) | |
1839 | (setq pc (cdr pc))) | |
1840 | ||
1841 | ((eq op 'copy) | |
1842 | (aset regs (nth 2 inst) (aref regs (nth 1 inst))) | |
1843 | (setq pc (cdr pc))) | |
1844 | ||
1845 | ((eq op 'copy-neg) | |
1846 | (aset regs (nth 2 inst) | |
1847 | (math-rwapply-neg (aref regs (nth 1 inst)))) | |
1848 | (setq pc (cdr pc))) | |
1849 | ||
1850 | ((eq op 'alt) | |
1851 | (setq btrack (cons pc btrack) | |
1852 | pc (nth 1 inst))) | |
1853 | ||
1854 | ((eq op 'end-alt) | |
1855 | (while (and btrack (not (eq (car btrack) (nth 1 inst)))) | |
1856 | (setq btrack (cdr btrack))) | |
1857 | (setq btrack (cdr btrack) | |
1858 | pc (cdr pc))) | |
1859 | ||
1860 | ((eq op 'done) | |
1861 | (setq result (math-rwapply-replace-regs (nth 1 inst))) | |
1862 | (if (or (and (eq (car-safe result) '+) | |
1863 | (eq (nth 2 result) 0)) | |
1864 | (and (eq (car-safe result) '*) | |
1865 | (eq (nth 2 result) 1))) | |
1866 | (setq result (nth 1 result))) | |
1867 | (setq part (and (nth 2 inst) | |
1868 | (math-is-true | |
1869 | (math-rweval | |
1870 | (math-simplify | |
1871 | (math-rwapply-replace-regs | |
1872 | (nth 2 inst))))))) | |
1873 | (if (or (equal result expr) | |
1874 | (equal (setq result (math-normalize result)) expr)) | |
1875 | (setq result nil) | |
1876 | (if part (math-rwapply-remember expr result)) | |
1877 | (setq rules nil)) | |
1878 | (setq pc nil)) | |
1879 | ||
1880 | (t (error "%s is not a valid rewrite opcode" op)))))) | |
1881 | (setq rules (cdr rules))) | |
bf77c646 | 1882 | result))) |
136211a9 EZ |
1883 | |
1884 | (defun math-rwapply-neg (expr) | |
1885 | (if (and (consp expr) | |
1886 | (memq (car expr) '(* /))) | |
1887 | (if (Math-objectp (nth 2 expr)) | |
1888 | (list (car expr) (nth 1 expr) (math-neg (nth 2 expr))) | |
1889 | (list (car expr) | |
1890 | (if (Math-objectp (nth 1 expr)) | |
1891 | (math-neg (nth 1 expr)) | |
1892 | (list '* -1 (nth 1 expr))) | |
1893 | (nth 2 expr))) | |
bf77c646 | 1894 | (math-neg expr))) |
136211a9 EZ |
1895 | |
1896 | (defun math-rwapply-inv (expr) | |
1897 | (if (and (Math-integerp expr) | |
1898 | calc-prefer-frac) | |
1899 | (math-make-frac 1 expr) | |
bf77c646 | 1900 | (list '/ 1 expr))) |
136211a9 EZ |
1901 | |
1902 | (defun math-rwapply-replace-regs (expr) | |
1903 | (cond ((Math-primp expr) | |
1904 | expr) | |
1905 | ((eq (car expr) 'calcFunc-register) | |
1906 | (setq expr (aref regs (nth 1 expr))) | |
1907 | (if (eq (car-safe expr) '*) | |
1908 | (if (eq (nth 1 expr) -1) | |
1909 | (math-neg (nth 2 expr)) | |
1910 | (if (eq (nth 1 expr) 1) | |
1911 | (nth 2 expr) | |
1912 | expr)) | |
1913 | expr)) | |
1914 | ((and (eq (car expr) 'calcFunc-eval) | |
1915 | (= (length expr) 2)) | |
1916 | (calc-with-default-simplification | |
1917 | (math-normalize (math-rwapply-replace-regs (nth 1 expr))))) | |
1918 | ((and (eq (car expr) 'calcFunc-evalsimp) | |
1919 | (= (length expr) 2)) | |
1920 | (math-simplify (math-rwapply-replace-regs (nth 1 expr)))) | |
1921 | ((and (eq (car expr) 'calcFunc-evalextsimp) | |
1922 | (= (length expr) 2)) | |
1923 | (math-simplify-extended (math-rwapply-replace-regs (nth 1 expr)))) | |
1924 | ((and (eq (car expr) 'calcFunc-apply) | |
1925 | (= (length expr) 3)) | |
1926 | (let ((func (math-rwapply-replace-regs (nth 1 expr))) | |
1927 | (args (math-rwapply-replace-regs (nth 2 expr))) | |
1928 | call) | |
1929 | (if (and (math-vectorp args) | |
1930 | (not (eq (car-safe (setq call (math-build-call | |
1931 | (math-var-to-calcFunc func) | |
1932 | (cdr args)))) | |
1933 | 'calcFunc-call))) | |
1934 | call | |
1935 | (list 'calcFunc-apply func args)))) | |
1936 | ((and (eq (car expr) 'calcFunc-cons) | |
1937 | (= (length expr) 3)) | |
1938 | (let ((head (math-rwapply-replace-regs (nth 1 expr))) | |
1939 | (tail (math-rwapply-replace-regs (nth 2 expr)))) | |
1940 | (if (math-vectorp tail) | |
1941 | (cons 'vec (cons head (cdr tail))) | |
1942 | (list 'calcFunc-cons head tail)))) | |
1943 | ((and (eq (car expr) 'calcFunc-rcons) | |
1944 | (= (length expr) 3)) | |
1945 | (let ((head (math-rwapply-replace-regs (nth 1 expr))) | |
1946 | (tail (math-rwapply-replace-regs (nth 2 expr)))) | |
1947 | (if (math-vectorp head) | |
1948 | (append head (list tail)) | |
1949 | (list 'calcFunc-rcons head tail)))) | |
1950 | ((and (eq (car expr) 'neg) | |
1951 | (math-rwapply-reg-looks-negp (nth 1 expr))) | |
1952 | (math-rwapply-reg-neg (nth 1 expr))) | |
1953 | ((and (eq (car expr) 'neg) | |
1954 | (eq (car-safe (nth 1 expr)) 'calcFunc-register) | |
1955 | (math-scalarp (aref regs (nth 1 (nth 1 expr))))) | |
1956 | (math-neg (math-rwapply-replace-regs (nth 1 expr)))) | |
1957 | ((and (eq (car expr) '+) | |
1958 | (math-rwapply-reg-looks-negp (nth 1 expr))) | |
1959 | (list '- (math-rwapply-replace-regs (nth 2 expr)) | |
1960 | (math-rwapply-reg-neg (nth 1 expr)))) | |
1961 | ((and (eq (car expr) '+) | |
1962 | (math-rwapply-reg-looks-negp (nth 2 expr))) | |
1963 | (list '- (math-rwapply-replace-regs (nth 1 expr)) | |
1964 | (math-rwapply-reg-neg (nth 2 expr)))) | |
1965 | ((and (eq (car expr) '-) | |
1966 | (math-rwapply-reg-looks-negp (nth 2 expr))) | |
1967 | (list '+ (math-rwapply-replace-regs (nth 1 expr)) | |
1968 | (math-rwapply-reg-neg (nth 2 expr)))) | |
1969 | ((eq (car expr) '*) | |
1970 | (cond ((eq (nth 1 expr) -1) | |
1971 | (if (math-rwapply-reg-looks-negp (nth 2 expr)) | |
1972 | (math-rwapply-reg-neg (nth 2 expr)) | |
1973 | (math-neg (math-rwapply-replace-regs (nth 2 expr))))) | |
1974 | ((eq (nth 1 expr) 1) | |
1975 | (math-rwapply-replace-regs (nth 2 expr))) | |
1976 | ((eq (nth 2 expr) -1) | |
1977 | (if (math-rwapply-reg-looks-negp (nth 1 expr)) | |
1978 | (math-rwapply-reg-neg (nth 1 expr)) | |
1979 | (math-neg (math-rwapply-replace-regs (nth 1 expr))))) | |
1980 | ((eq (nth 2 expr) 1) | |
1981 | (math-rwapply-replace-regs (nth 1 expr))) | |
1982 | (t | |
1983 | (let ((arg1 (math-rwapply-replace-regs (nth 1 expr))) | |
1984 | (arg2 (math-rwapply-replace-regs (nth 2 expr)))) | |
1985 | (cond ((and (eq (car-safe arg1) '/) | |
1986 | (eq (nth 1 arg1) 1)) | |
1987 | (list '/ arg2 (nth 2 arg1))) | |
1988 | ((and (eq (car-safe arg2) '/) | |
1989 | (eq (nth 1 arg2) 1)) | |
1990 | (list '/ arg1 (nth 2 arg2))) | |
1991 | (t (list '* arg1 arg2))))))) | |
1992 | ((eq (car expr) '/) | |
1993 | (let ((arg1 (math-rwapply-replace-regs (nth 1 expr))) | |
1994 | (arg2 (math-rwapply-replace-regs (nth 2 expr)))) | |
1995 | (if (eq (car-safe arg2) '/) | |
1996 | (list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2)) | |
1997 | (list '/ arg1 arg2)))) | |
1998 | ((and (eq (car expr) 'calcFunc-plain) | |
1999 | (= (length expr) 2)) | |
2000 | (if (Math-primp (nth 1 expr)) | |
2001 | (nth 1 expr) | |
2002 | (if (eq (car (nth 1 expr)) 'calcFunc-register) | |
2003 | (aref regs (nth 1 (nth 1 expr))) | |
2004 | (cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs | |
2005 | (cdr (nth 1 expr))))))) | |
bf77c646 | 2006 | (t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr)))))) |
136211a9 EZ |
2007 | |
2008 | (defun math-rwapply-reg-looks-negp (expr) | |
2009 | (if (eq (car-safe expr) 'calcFunc-register) | |
2010 | (math-looks-negp (aref regs (nth 1 expr))) | |
2011 | (if (memq (car-safe expr) '(* /)) | |
2012 | (or (math-rwapply-reg-looks-negp (nth 1 expr)) | |
bf77c646 | 2013 | (math-rwapply-reg-looks-negp (nth 2 expr)))))) |
136211a9 EZ |
2014 | |
2015 | (defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp | |
2016 | (if (eq (car expr) 'calcFunc-register) | |
2017 | (math-neg (math-rwapply-replace-regs expr)) | |
2018 | (if (math-rwapply-reg-looks-negp (nth 1 expr)) | |
2019 | (math-rwapply-replace-regs (list (car expr) | |
2020 | (math-rwapply-reg-neg (nth 1 expr)) | |
2021 | (nth 2 expr))) | |
2022 | (math-rwapply-replace-regs (list (car expr) | |
2023 | (nth 1 expr) | |
bf77c646 | 2024 | (math-rwapply-reg-neg (nth 2 expr))))))) |
136211a9 EZ |
2025 | |
2026 | (defun math-rwapply-remember (old new) | |
2027 | (let ((varval (symbol-value (nth 2 (car ruleset)))) | |
2028 | (rules (assq (car-safe old) ruleset))) | |
2029 | (if (and (eq (car-safe varval) 'vec) | |
2030 | (not (memq (car-safe old) '(nil schedule + -))) | |
2031 | rules) | |
2032 | (progn | |
2033 | (setcdr varval (cons (list 'calcFunc-assign | |
2034 | (if (math-rwcomp-no-vars old) | |
2035 | old | |
2036 | (list 'calcFunc-quote old)) | |
2037 | new) | |
2038 | (cdr varval))) | |
2039 | (setcdr rules (cons (list (vector nil old) | |
2040 | (list (list 'same 0 1) | |
2041 | (list 'done new nil)) | |
2042 | nil nil) | |
bf77c646 | 2043 | (cdr rules))))))) |
136211a9 | 2044 | |
bf77c646 | 2045 | ;;; calc-rewr.el ends here |