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3132f345 | 1 | ;;; calc-arith.el --- arithmetic functions for Calc |
a1506d29 | 2 | |
58ba2f8f | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
8b72699e | 4 | ;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc. |
3132f345 CW |
5 | |
6 | ;; Author: David Gillespie <daveg@synaptics.com> | |
e8fff8ed | 7 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 EZ |
8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
7c671b23 GM |
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 | |
075969b4 | 13 | ;; the Free Software Foundation; either version 3, or (at your option) |
7c671b23 GM |
14 | ;; any later version. |
15 | ||
136211a9 | 16 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
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. | |
20 | ||
21 | ;; You should have received a copy of the GNU General Public License | |
22 | ;; along with GNU Emacs; see the file COPYING. If not, write to the | |
23 | ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, | |
24 | ;; Boston, MA 02110-1301, USA. | |
136211a9 | 25 | |
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
136211a9 EZ |
29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 31 | |
5e30155b | 32 | (require 'calc-ext) |
136211a9 EZ |
33 | (require 'calc-macs) |
34 | ||
67549a85 JB |
35 | ;;; The following lists are not exhaustive. |
36 | (defvar math-scalar-functions '(calcFunc-det | |
37 | calcFunc-cnorm calcFunc-rnorm | |
38 | calcFunc-vlen calcFunc-vcount | |
39 | calcFunc-vsum calcFunc-vprod | |
40 | calcFunc-vmin calcFunc-vmax)) | |
41 | ||
42 | (defvar math-nonscalar-functions '(vec calcFunc-idn calcFunc-diag | |
43 | calcFunc-cvec calcFunc-index | |
44 | calcFunc-trn | |
45 | | calcFunc-append | |
46 | calcFunc-cons calcFunc-rcons | |
47 | calcFunc-tail calcFunc-rhead)) | |
48 | ||
49 | (defvar math-scalar-if-args-functions '(+ - * / neg)) | |
50 | ||
51 | (defvar math-real-functions '(calcFunc-arg | |
52 | calcFunc-re calcFunc-im | |
53 | calcFunc-floor calcFunc-ceil | |
54 | calcFunc-trunc calcFunc-round | |
55 | calcFunc-rounde calcFunc-roundu | |
56 | calcFunc-ffloor calcFunc-fceil | |
57 | calcFunc-ftrunc calcFunc-fround | |
58 | calcFunc-frounde calcFunc-froundu)) | |
59 | ||
60 | (defvar math-positive-functions '()) | |
61 | ||
62 | (defvar math-nonnegative-functions '(calcFunc-cnorm calcFunc-rnorm | |
63 | calcFunc-vlen calcFunc-vcount)) | |
64 | ||
65 | (defvar math-real-scalar-functions '(% calcFunc-idiv calcFunc-abs | |
66 | calcFunc-choose calcFunc-perm | |
67 | calcFunc-eq calcFunc-neq | |
68 | calcFunc-lt calcFunc-gt | |
69 | calcFunc-leq calcFunc-geq | |
70 | calcFunc-lnot | |
71 | calcFunc-max calcFunc-min)) | |
72 | ||
73 | (defvar math-real-if-arg-functions '(calcFunc-sin calcFunc-cos | |
e3e6f095 JB |
74 | calcFunc-tan calcFunc-sec |
75 | calcFunc-csc calcFunc-cot | |
76 | calcFunc-arctan | |
67549a85 | 77 | calcFunc-sinh calcFunc-cosh |
e3e6f095 JB |
78 | calcFunc-tanh calcFunc-sech |
79 | calcFunc-csch calcFunc-coth | |
80 | calcFunc-exp | |
67549a85 JB |
81 | calcFunc-gamma calcFunc-fact)) |
82 | ||
83 | (defvar math-integer-functions '(calcFunc-idiv | |
84 | calcFunc-isqrt calcFunc-ilog | |
85 | calcFunc-vlen calcFunc-vcount)) | |
86 | ||
87 | (defvar math-num-integer-functions '()) | |
88 | ||
89 | (defvar math-rounding-functions '(calcFunc-floor | |
90 | calcFunc-ceil | |
91 | calcFunc-round calcFunc-trunc | |
92 | calcFunc-rounde calcFunc-roundu)) | |
93 | ||
94 | (defvar math-float-rounding-functions '(calcFunc-ffloor | |
95 | calcFunc-fceil | |
96 | calcFunc-fround calcFunc-ftrunc | |
97 | calcFunc-frounde calcFunc-froundu)) | |
98 | ||
99 | (defvar math-integer-if-args-functions '(+ - * % neg calcFunc-abs | |
100 | calcFunc-min calcFunc-max | |
101 | calcFunc-choose calcFunc-perm)) | |
102 | ||
136211a9 EZ |
103 | |
104 | ;;; Arithmetic. | |
105 | ||
106 | (defun calc-min (arg) | |
107 | (interactive "P") | |
108 | (calc-slow-wrapper | |
898ea5c0 | 109 | (calc-binary-op "min" 'calcFunc-min arg '(var inf var-inf)))) |
136211a9 EZ |
110 | |
111 | (defun calc-max (arg) | |
112 | (interactive "P") | |
113 | (calc-slow-wrapper | |
898ea5c0 | 114 | (calc-binary-op "max" 'calcFunc-max arg '(neg (var inf var-inf))))) |
136211a9 EZ |
115 | |
116 | (defun calc-abs (arg) | |
117 | (interactive "P") | |
118 | (calc-slow-wrapper | |
898ea5c0 | 119 | (calc-unary-op "abs" 'calcFunc-abs arg))) |
136211a9 EZ |
120 | |
121 | ||
122 | (defun calc-idiv (arg) | |
123 | (interactive "P") | |
124 | (calc-slow-wrapper | |
898ea5c0 | 125 | (calc-binary-op "\\" 'calcFunc-idiv arg 1))) |
136211a9 EZ |
126 | |
127 | ||
128 | (defun calc-floor (arg) | |
129 | (interactive "P") | |
130 | (calc-slow-wrapper | |
131 | (if (calc-is-inverse) | |
132 | (if (calc-is-hyperbolic) | |
133 | (calc-unary-op "ceil" 'calcFunc-fceil arg) | |
134 | (calc-unary-op "ceil" 'calcFunc-ceil arg)) | |
135 | (if (calc-is-hyperbolic) | |
136 | (calc-unary-op "flor" 'calcFunc-ffloor arg) | |
898ea5c0 | 137 | (calc-unary-op "flor" 'calcFunc-floor arg))))) |
136211a9 EZ |
138 | |
139 | (defun calc-ceiling (arg) | |
140 | (interactive "P") | |
141 | (calc-invert-func) | |
898ea5c0 | 142 | (calc-floor arg)) |
136211a9 EZ |
143 | |
144 | (defun calc-round (arg) | |
145 | (interactive "P") | |
146 | (calc-slow-wrapper | |
147 | (if (calc-is-inverse) | |
148 | (if (calc-is-hyperbolic) | |
149 | (calc-unary-op "trnc" 'calcFunc-ftrunc arg) | |
150 | (calc-unary-op "trnc" 'calcFunc-trunc arg)) | |
151 | (if (calc-is-hyperbolic) | |
152 | (calc-unary-op "rond" 'calcFunc-fround arg) | |
898ea5c0 | 153 | (calc-unary-op "rond" 'calcFunc-round arg))))) |
136211a9 EZ |
154 | |
155 | (defun calc-trunc (arg) | |
156 | (interactive "P") | |
157 | (calc-invert-func) | |
898ea5c0 | 158 | (calc-round arg)) |
136211a9 EZ |
159 | |
160 | (defun calc-mant-part (arg) | |
161 | (interactive "P") | |
162 | (calc-slow-wrapper | |
898ea5c0 | 163 | (calc-unary-op "mant" 'calcFunc-mant arg))) |
136211a9 EZ |
164 | |
165 | (defun calc-xpon-part (arg) | |
166 | (interactive "P") | |
167 | (calc-slow-wrapper | |
898ea5c0 | 168 | (calc-unary-op "xpon" 'calcFunc-xpon arg))) |
136211a9 EZ |
169 | |
170 | (defun calc-scale-float (arg) | |
171 | (interactive "P") | |
172 | (calc-slow-wrapper | |
898ea5c0 | 173 | (calc-binary-op "scal" 'calcFunc-scf arg))) |
136211a9 EZ |
174 | |
175 | (defun calc-abssqr (arg) | |
176 | (interactive "P") | |
177 | (calc-slow-wrapper | |
898ea5c0 | 178 | (calc-unary-op "absq" 'calcFunc-abssqr arg))) |
136211a9 EZ |
179 | |
180 | (defun calc-sign (arg) | |
181 | (interactive "P") | |
182 | (calc-slow-wrapper | |
898ea5c0 | 183 | (calc-unary-op "sign" 'calcFunc-sign arg))) |
136211a9 EZ |
184 | |
185 | (defun calc-increment (arg) | |
186 | (interactive "p") | |
187 | (calc-wrapper | |
898ea5c0 | 188 | (calc-enter-result 1 "incr" (list 'calcFunc-incr (calc-top-n 1) arg)))) |
136211a9 EZ |
189 | |
190 | (defun calc-decrement (arg) | |
191 | (interactive "p") | |
192 | (calc-wrapper | |
898ea5c0 | 193 | (calc-enter-result 1 "decr" (list 'calcFunc-decr (calc-top-n 1) arg)))) |
136211a9 EZ |
194 | |
195 | ||
196 | (defun math-abs-approx (a) | |
197 | (cond ((Math-negp a) | |
198 | (math-neg a)) | |
199 | ((Math-anglep a) | |
200 | a) | |
201 | ((eq (car a) 'cplx) | |
202 | (math-add (math-abs (nth 1 a)) (math-abs (nth 2 a)))) | |
203 | ((eq (car a) 'polar) | |
204 | (nth 1 a)) | |
205 | ((eq (car a) 'sdev) | |
206 | (math-abs-approx (nth 1 a))) | |
207 | ((eq (car a) 'intv) | |
208 | (math-max (math-abs (nth 2 a)) (math-abs (nth 3 a)))) | |
209 | ((eq (car a) 'date) | |
210 | a) | |
211 | ((eq (car a) 'vec) | |
212 | (math-reduce-vec 'math-add-abs-approx a)) | |
213 | ((eq (car a) 'calcFunc-abs) | |
214 | (car a)) | |
898ea5c0 | 215 | (t a))) |
136211a9 EZ |
216 | |
217 | (defun math-add-abs-approx (a b) | |
898ea5c0 | 218 | (math-add (math-abs-approx a) (math-abs-approx b))) |
136211a9 EZ |
219 | |
220 | ||
221 | ;;;; Declarations. | |
222 | ||
3132f345 CW |
223 | (defvar math-decls-cache-tag nil) |
224 | (defvar math-decls-cache nil) | |
225 | (defvar math-decls-all nil) | |
136211a9 EZ |
226 | |
227 | ;;; Math-decls-cache is an a-list where each entry is a list of the form: | |
228 | ;;; (VAR TYPES RANGE) | |
229 | ;;; where VAR is a variable name (with var- prefix) or function name; | |
230 | ;;; TYPES is a list of type symbols (any, int, frac, ...) | |
231 | ;;; RANGE is a sorted vector of intervals describing the range. | |
232 | ||
67549a85 JB |
233 | (defvar math-super-types |
234 | '((int numint rat real number) | |
235 | (numint real number) | |
236 | (frac rat real number) | |
237 | (rat real number) | |
238 | (float real number) | |
239 | (real number) | |
240 | (number) | |
241 | (scalar) | |
3208fa65 | 242 | (sqmatrix matrix vector) |
67549a85 JB |
243 | (matrix vector) |
244 | (vector) | |
245 | (const))) | |
246 | ||
136211a9 EZ |
247 | (defun math-setup-declarations () |
248 | (or (eq math-decls-cache-tag (calc-var-value 'var-Decls)) | |
249 | (let ((p (calc-var-value 'var-Decls)) | |
250 | vec type range) | |
251 | (setq math-decls-cache-tag p | |
252 | math-decls-cache nil) | |
253 | (and (eq (car-safe p) 'vec) | |
254 | (while (setq p (cdr p)) | |
255 | (and (eq (car-safe (car p)) 'vec) | |
256 | (setq vec (nth 2 (car p))) | |
257 | (condition-case err | |
258 | (let ((v (nth 1 (car p)))) | |
259 | (setq type nil range nil) | |
260 | (or (eq (car-safe vec) 'vec) | |
261 | (setq vec (list 'vec vec))) | |
262 | (while (and (setq vec (cdr vec)) | |
263 | (not (Math-objectp (car vec)))) | |
264 | (and (eq (car-safe (car vec)) 'var) | |
265 | (let ((st (assq (nth 1 (car vec)) | |
266 | math-super-types))) | |
267 | (cond (st (setq type (append type st))) | |
268 | ((eq (nth 1 (car vec)) 'pos) | |
269 | (setq type (append type | |
270 | '(real number)) | |
271 | range | |
272 | '(intv 1 0 (var inf var-inf)))) | |
273 | ((eq (nth 1 (car vec)) 'nonneg) | |
274 | (setq type (append type | |
275 | '(real number)) | |
276 | range | |
277 | '(intv 3 0 | |
278 | (var inf var-inf)))))))) | |
279 | (if vec | |
280 | (setq type (append type '(real number)) | |
281 | range (math-prepare-set (cons 'vec vec)))) | |
282 | (setq type (list type range)) | |
283 | (or (eq (car-safe v) 'vec) | |
284 | (setq v (list 'vec v))) | |
285 | (while (setq v (cdr v)) | |
286 | (if (or (eq (car-safe (car v)) 'var) | |
287 | (not (Math-primp (car v)))) | |
288 | (setq math-decls-cache | |
289 | (cons (cons (if (eq (car (car v)) 'var) | |
290 | (nth 2 (car v)) | |
291 | (car (car v))) | |
292 | type) | |
293 | math-decls-cache))))) | |
294 | (error nil))))) | |
898ea5c0 | 295 | (setq math-decls-all (assq 'var-All math-decls-cache))))) |
136211a9 | 296 | |
136211a9 EZ |
297 | (defun math-known-scalarp (a &optional assume-scalar) |
298 | (math-setup-declarations) | |
299 | (if (if calc-matrix-mode | |
300 | (eq calc-matrix-mode 'scalar) | |
301 | assume-scalar) | |
302 | (not (math-check-known-matrixp a)) | |
898ea5c0 | 303 | (math-check-known-scalarp a))) |
136211a9 EZ |
304 | |
305 | (defun math-known-matrixp (a) | |
306 | (and (not (Math-scalarp a)) | |
898ea5c0 | 307 | (not (math-known-scalarp a t)))) |
136211a9 | 308 | |
05d28205 | 309 | (defun math-known-square-matrixp (a) |
3208fa65 JB |
310 | (and (math-known-matrixp a) |
311 | (math-check-known-square-matrixp a))) | |
312 | ||
136211a9 EZ |
313 | ;;; Try to prove that A is a scalar (i.e., a non-vector). |
314 | (defun math-check-known-scalarp (a) | |
315 | (cond ((Math-objectp a) t) | |
316 | ((memq (car a) math-scalar-functions) | |
317 | t) | |
318 | ((memq (car a) math-real-scalar-functions) | |
319 | t) | |
320 | ((memq (car a) math-scalar-if-args-functions) | |
321 | (while (and (setq a (cdr a)) | |
322 | (math-check-known-scalarp (car a)))) | |
323 | (null a)) | |
324 | ((eq (car a) '^) | |
325 | (math-check-known-scalarp (nth 1 a))) | |
326 | ((math-const-var a) t) | |
327 | (t | |
328 | (let ((decl (if (eq (car a) 'var) | |
329 | (or (assq (nth 2 a) math-decls-cache) | |
330 | math-decls-all) | |
3208fa65 JB |
331 | (assq (car a) math-decls-cache))) |
332 | val) | |
333 | (cond | |
334 | ((memq 'scalar (nth 1 decl)) | |
335 | t) | |
336 | ((and (eq (car a) 'var) | |
eb90d844 | 337 | (symbolp (nth 2 a)) |
3208fa65 JB |
338 | (boundp (nth 2 a)) |
339 | (setq val (symbol-value (nth 2 a)))) | |
340 | (math-check-known-scalarp val)) | |
341 | (t | |
342 | nil)))))) | |
136211a9 EZ |
343 | |
344 | ;;; Try to prove that A is *not* a scalar. | |
345 | (defun math-check-known-matrixp (a) | |
346 | (cond ((Math-objectp a) nil) | |
347 | ((memq (car a) math-nonscalar-functions) | |
348 | t) | |
349 | ((memq (car a) math-scalar-if-args-functions) | |
350 | (while (and (setq a (cdr a)) | |
351 | (not (math-check-known-matrixp (car a))))) | |
352 | a) | |
353 | ((eq (car a) '^) | |
354 | (math-check-known-matrixp (nth 1 a))) | |
355 | ((math-const-var a) nil) | |
356 | (t | |
357 | (let ((decl (if (eq (car a) 'var) | |
358 | (or (assq (nth 2 a) math-decls-cache) | |
359 | math-decls-all) | |
3208fa65 JB |
360 | (assq (car a) math-decls-cache))) |
361 | val) | |
362 | (cond | |
363 | ((memq 'matrix (nth 1 decl)) | |
364 | t) | |
365 | ((and (eq (car a) 'var) | |
c3a1b861 | 366 | (symbolp (nth 2 a)) |
3208fa65 JB |
367 | (boundp (nth 2 a)) |
368 | (setq val (symbol-value (nth 2 a)))) | |
369 | (math-check-known-matrixp val)) | |
370 | (t | |
371 | nil)))))) | |
372 | ||
373 | ;;; Given that A is a matrix, try to prove that it is a square matrix. | |
374 | (defun math-check-known-square-matrixp (a) | |
375 | (cond ((math-square-matrixp a) | |
376 | t) | |
377 | ((eq (car-safe a) '^) | |
378 | (math-check-known-square-matrixp (nth 1 a))) | |
2f884e83 JB |
379 | ((or |
380 | (eq (car-safe a) '*) | |
381 | (eq (car-safe a) '+) | |
382 | (eq (car-safe a) '-)) | |
383 | (and | |
384 | (math-check-known-square-matrixp (nth 1 a)) | |
385 | (math-check-known-square-matrixp (nth 2 a)))) | |
3208fa65 JB |
386 | (t |
387 | (let ((decl (if (eq (car a) 'var) | |
388 | (or (assq (nth 2 a) math-decls-cache) | |
389 | math-decls-all) | |
390 | (assq (car a) math-decls-cache))) | |
391 | val) | |
392 | (cond | |
393 | ((memq 'sqmatrix (nth 1 decl)) | |
394 | t) | |
3208fa65 JB |
395 | ((and (eq (car a) 'var) |
396 | (boundp (nth 2 a)) | |
397 | (setq val (symbol-value (nth 2 a)))) | |
398 | (math-check-known-square-matrixp val)) | |
399 | ((and (or | |
400 | (integerp calc-matrix-mode) | |
401 | (eq calc-matrix-mode 'sqmatrix)) | |
402 | (eq (car-safe a) 'var)) | |
403 | t) | |
16d66184 JB |
404 | ((memq 'matrix (nth 1 decl)) |
405 | nil) | |
3208fa65 JB |
406 | (t |
407 | nil)))))) | |
136211a9 EZ |
408 | |
409 | ;;; Try to prove that A is a real (i.e., not complex). | |
410 | (defun math-known-realp (a) | |
898ea5c0 | 411 | (< (math-possible-signs a) 8)) |
136211a9 EZ |
412 | |
413 | ;;; Try to prove that A is real and positive. | |
414 | (defun math-known-posp (a) | |
898ea5c0 | 415 | (eq (math-possible-signs a) 4)) |
136211a9 EZ |
416 | |
417 | ;;; Try to prove that A is real and negative. | |
418 | (defun math-known-negp (a) | |
898ea5c0 | 419 | (eq (math-possible-signs a) 1)) |
136211a9 EZ |
420 | |
421 | ;;; Try to prove that A is real and nonnegative. | |
422 | (defun math-known-nonnegp (a) | |
898ea5c0 | 423 | (memq (math-possible-signs a) '(2 4 6))) |
136211a9 EZ |
424 | |
425 | ;;; Try to prove that A is real and nonpositive. | |
426 | (defun math-known-nonposp (a) | |
898ea5c0 | 427 | (memq (math-possible-signs a) '(1 2 3))) |
136211a9 EZ |
428 | |
429 | ;;; Try to prove that A is nonzero. | |
430 | (defun math-known-nonzerop (a) | |
898ea5c0 | 431 | (memq (math-possible-signs a) '(1 4 5 8 9 12 13))) |
136211a9 EZ |
432 | |
433 | ;;; Return true if A is negative, or looks negative but we don't know. | |
434 | (defun math-guess-if-neg (a) | |
435 | (let ((sgn (math-possible-signs a))) | |
436 | (if (memq sgn '(1 3)) | |
437 | t | |
438 | (if (memq sgn '(2 4 6)) | |
439 | nil | |
898ea5c0 | 440 | (math-looks-negp a))))) |
136211a9 EZ |
441 | |
442 | ;;; Find the possible signs of A, assuming A is a number of some kind. | |
443 | ;;; Returns an integer with bits: 1 may be negative, | |
444 | ;;; 2 may be zero, | |
445 | ;;; 4 may be positive, | |
446 | ;;; 8 may be nonreal. | |
447 | ||
448 | (defun math-possible-signs (a &optional origin) | |
449 | (cond ((Math-objectp a) | |
450 | (if origin (setq a (math-sub a origin))) | |
451 | (cond ((Math-posp a) 4) | |
452 | ((Math-negp a) 1) | |
453 | ((Math-zerop a) 2) | |
454 | ((eq (car a) 'intv) | |
773a144d JB |
455 | (cond |
456 | ((math-known-posp (nth 2 a)) 4) | |
457 | ((math-known-negp (nth 3 a)) 1) | |
458 | ((Math-zerop (nth 2 a)) 6) | |
459 | ((Math-zerop (nth 3 a)) 3) | |
460 | (t 7))) | |
136211a9 EZ |
461 | ((eq (car a) 'sdev) |
462 | (if (math-known-realp (nth 1 a)) 7 15)) | |
463 | (t 8))) | |
464 | ((memq (car a) '(+ -)) | |
465 | (cond ((Math-realp (nth 1 a)) | |
466 | (if (eq (car a) '-) | |
467 | (math-neg-signs | |
468 | (math-possible-signs (nth 2 a) | |
469 | (if origin | |
470 | (math-add origin (nth 1 a)) | |
471 | (nth 1 a)))) | |
472 | (math-possible-signs (nth 2 a) | |
473 | (if origin | |
474 | (math-sub origin (nth 1 a)) | |
475 | (math-neg (nth 1 a)))))) | |
476 | ((Math-realp (nth 2 a)) | |
477 | (let ((org (if (eq (car a) '-) | |
478 | (nth 2 a) | |
479 | (math-neg (nth 2 a))))) | |
480 | (math-possible-signs (nth 1 a) | |
481 | (if origin | |
482 | (math-add origin org) | |
483 | org)))) | |
484 | (t | |
485 | (let ((s1 (math-possible-signs (nth 1 a) origin)) | |
486 | (s2 (math-possible-signs (nth 2 a)))) | |
487 | (if (eq (car a) '-) (setq s2 (math-neg-signs s2))) | |
488 | (cond ((eq s1 s2) s1) | |
489 | ((eq s1 2) s2) | |
490 | ((eq s2 2) s1) | |
491 | ((>= s1 8) 15) | |
492 | ((>= s2 8) 15) | |
493 | ((and (eq s1 4) (eq s2 6)) 4) | |
494 | ((and (eq s2 4) (eq s1 6)) 4) | |
495 | ((and (eq s1 1) (eq s2 3)) 1) | |
496 | ((and (eq s2 1) (eq s1 3)) 1) | |
497 | (t 7)))))) | |
498 | ((eq (car a) 'neg) | |
499 | (math-neg-signs (math-possible-signs | |
500 | (nth 1 a) | |
501 | (and origin (math-neg origin))))) | |
502 | ((and origin (Math-zerop origin) (setq origin nil) | |
503 | nil)) | |
504 | ((and (or (eq (car a) '*) | |
505 | (and (eq (car a) '/) origin)) | |
506 | (Math-realp (nth 1 a))) | |
507 | (let ((s (if (eq (car a) '*) | |
508 | (if (Math-zerop (nth 1 a)) | |
509 | (math-possible-signs 0 origin) | |
510 | (math-possible-signs (nth 2 a) | |
511 | (math-div (or origin 0) | |
512 | (nth 1 a)))) | |
513 | (math-neg-signs | |
514 | (math-possible-signs (nth 2 a) | |
515 | (math-div (nth 1 a) | |
516 | origin)))))) | |
517 | (if (Math-negp (nth 1 a)) (math-neg-signs s) s))) | |
518 | ((and (memq (car a) '(* /)) (Math-realp (nth 2 a))) | |
519 | (let ((s (math-possible-signs (nth 1 a) | |
520 | (if (eq (car a) '*) | |
521 | (math-mul (or origin 0) (nth 2 a)) | |
522 | (math-div (or origin 0) (nth 2 a)))))) | |
523 | (if (Math-negp (nth 2 a)) (math-neg-signs s) s))) | |
524 | ((eq (car a) 'vec) | |
525 | (let ((signs 0)) | |
526 | (while (and (setq a (cdr a)) (< signs 15)) | |
527 | (setq signs (logior signs (math-possible-signs | |
528 | (car a) origin)))) | |
529 | signs)) | |
530 | (t (let ((sign | |
531 | (cond | |
532 | ((memq (car a) '(* /)) | |
533 | (let ((s1 (math-possible-signs (nth 1 a))) | |
534 | (s2 (math-possible-signs (nth 2 a)))) | |
535 | (cond ((>= s1 8) 15) | |
536 | ((>= s2 8) 15) | |
537 | ((and (eq (car a) '/) (memq s2 '(2 3 6 7))) 15) | |
538 | (t | |
539 | (logior (if (memq s1 '(4 5 6 7)) s2 0) | |
540 | (if (memq s1 '(2 3 6 7)) 2 0) | |
541 | (if (memq s1 '(1 3 5 7)) | |
542 | (math-neg-signs s2) 0)))))) | |
543 | ((eq (car a) '^) | |
544 | (let ((s1 (math-possible-signs (nth 1 a))) | |
545 | (s2 (math-possible-signs (nth 2 a)))) | |
546 | (cond ((>= s1 8) 15) | |
547 | ((>= s2 8) 15) | |
548 | ((eq s1 4) 4) | |
549 | ((eq s1 2) (if (eq s2 4) 2 15)) | |
550 | ((eq s2 2) (if (memq s1 '(1 5)) 2 15)) | |
551 | ((Math-integerp (nth 2 a)) | |
552 | (if (math-evenp (nth 2 a)) | |
553 | (if (memq s1 '(3 6 7)) 6 4) | |
554 | s1)) | |
555 | ((eq s1 6) (if (eq s2 4) 6 15)) | |
556 | (t 7)))) | |
557 | ((eq (car a) '%) | |
558 | (let ((s2 (math-possible-signs (nth 2 a)))) | |
559 | (cond ((>= s2 8) 7) | |
560 | ((eq s2 2) 2) | |
561 | ((memq s2 '(4 6)) 6) | |
562 | ((memq s2 '(1 3)) 3) | |
563 | (t 7)))) | |
564 | ((and (memq (car a) '(calcFunc-abs calcFunc-abssqr)) | |
565 | (= (length a) 2)) | |
566 | (let ((s1 (math-possible-signs (nth 1 a)))) | |
567 | (cond ((eq s1 2) 2) | |
568 | ((memq s1 '(1 4 5)) 4) | |
569 | (t 6)))) | |
570 | ((and (eq (car a) 'calcFunc-exp) (= (length a) 2)) | |
571 | (let ((s1 (math-possible-signs (nth 1 a)))) | |
572 | (if (>= s1 8) | |
573 | 15 | |
574 | (if (or (not origin) (math-negp origin)) | |
575 | 4 | |
576 | (setq origin (math-sub (or origin 0) 1)) | |
577 | (if (Math-zerop origin) (setq origin nil)) | |
578 | s1)))) | |
579 | ((or (and (memq (car a) '(calcFunc-ln calcFunc-log10)) | |
580 | (= (length a) 2)) | |
581 | (and (eq (car a) 'calcFunc-log) | |
582 | (= (length a) 3) | |
583 | (math-known-posp (nth 2 a)))) | |
584 | (if (math-known-nonnegp (nth 1 a)) | |
585 | (math-possible-signs (nth 1 a) 1) | |
586 | 15)) | |
587 | ((and (eq (car a) 'calcFunc-sqrt) (= (length a) 2)) | |
588 | (let ((s1 (math-possible-signs (nth 1 a)))) | |
589 | (if (memq s1 '(2 4 6)) s1 15))) | |
590 | ((memq (car a) math-nonnegative-functions) 6) | |
591 | ((memq (car a) math-positive-functions) 4) | |
592 | ((memq (car a) math-real-functions) 7) | |
593 | ((memq (car a) math-real-scalar-functions) 7) | |
594 | ((and (memq (car a) math-real-if-arg-functions) | |
595 | (= (length a) 2)) | |
596 | (if (math-known-realp (nth 1 a)) 7 15))))) | |
597 | (cond (sign | |
598 | (if origin | |
599 | (+ (logand sign 8) | |
600 | (if (Math-posp origin) | |
601 | (if (memq sign '(1 2 3 8 9 10 11)) 1 7) | |
602 | (if (memq sign '(2 4 6 8 10 12 14)) 4 7))) | |
603 | sign)) | |
604 | ((math-const-var a) | |
605 | (cond ((eq (nth 2 a) 'var-pi) | |
606 | (if origin | |
607 | (math-possible-signs (math-pi) origin) | |
608 | 4)) | |
609 | ((eq (nth 2 a) 'var-e) | |
610 | (if origin | |
611 | (math-possible-signs (math-e) origin) | |
612 | 4)) | |
613 | ((eq (nth 2 a) 'var-inf) 4) | |
614 | ((eq (nth 2 a) 'var-uinf) 13) | |
615 | ((eq (nth 2 a) 'var-i) 8) | |
616 | (t 15))) | |
617 | (t | |
618 | (math-setup-declarations) | |
619 | (let ((decl (if (eq (car a) 'var) | |
620 | (or (assq (nth 2 a) math-decls-cache) | |
621 | math-decls-all) | |
622 | (assq (car a) math-decls-cache)))) | |
623 | (if (and origin | |
624 | (memq 'int (nth 1 decl)) | |
625 | (not (Math-num-integerp origin))) | |
626 | 5 | |
627 | (if (nth 2 decl) | |
628 | (math-possible-signs (nth 2 decl) origin) | |
629 | (if (memq 'real (nth 1 decl)) | |
630 | 7 | |
898ea5c0 | 631 | 15)))))))))) |
136211a9 EZ |
632 | |
633 | (defun math-neg-signs (s1) | |
634 | (if (>= s1 8) | |
635 | (+ 8 (math-neg-signs (- s1 8))) | |
636 | (+ (if (memq s1 '(1 3 5 7)) 4 0) | |
637 | (if (memq s1 '(2 3 6 7)) 2 0) | |
898ea5c0 | 638 | (if (memq s1 '(4 5 6 7)) 1 0)))) |
136211a9 EZ |
639 | |
640 | ||
641 | ;;; Try to prove that A is an integer. | |
642 | (defun math-known-integerp (a) | |
898ea5c0 | 643 | (eq (math-possible-types a) 1)) |
136211a9 EZ |
644 | |
645 | (defun math-known-num-integerp (a) | |
898ea5c0 | 646 | (<= (math-possible-types a t) 3)) |
136211a9 EZ |
647 | |
648 | (defun math-known-imagp (a) | |
898ea5c0 | 649 | (= (math-possible-types a) 16)) |
136211a9 EZ |
650 | |
651 | ||
652 | ;;; Find the possible types of A. | |
653 | ;;; Returns an integer with bits: 1 may be integer. | |
654 | ;;; 2 may be integer-valued float. | |
655 | ;;; 4 may be fraction. | |
656 | ;;; 8 may be non-integer-valued float. | |
657 | ;;; 16 may be imaginary. | |
658 | ;;; 32 may be non-real, non-imaginary. | |
659 | ;;; Real infinities count as integers for the purposes of this function. | |
660 | (defun math-possible-types (a &optional num) | |
661 | (cond ((Math-objectp a) | |
662 | (cond ((Math-integerp a) (if num 3 1)) | |
663 | ((Math-messy-integerp a) (if num 3 2)) | |
664 | ((eq (car a) 'frac) (if num 12 4)) | |
665 | ((eq (car a) 'float) (if num 12 8)) | |
666 | ((eq (car a) 'intv) | |
667 | (if (equal (nth 2 a) (nth 3 a)) | |
668 | (math-possible-types (nth 2 a)) | |
669 | 15)) | |
670 | ((eq (car a) 'sdev) | |
671 | (if (math-known-realp (nth 1 a)) 15 63)) | |
672 | ((eq (car a) 'cplx) | |
673 | (if (math-zerop (nth 1 a)) 16 32)) | |
674 | ((eq (car a) 'polar) | |
675 | (if (or (Math-equal (nth 2 a) (math-quarter-circle nil)) | |
676 | (Math-equal (nth 2 a) | |
677 | (math-neg (math-quarter-circle nil)))) | |
678 | 16 48)) | |
679 | (t 63))) | |
680 | ((eq (car a) '/) | |
681 | (let* ((t1 (math-possible-types (nth 1 a) num)) | |
682 | (t2 (math-possible-types (nth 2 a) num)) | |
683 | (t12 (logior t1 t2))) | |
684 | (if (< t12 16) | |
685 | (if (> (logand t12 10) 0) | |
686 | 10 | |
687 | (if (or (= t1 4) (= t2 4) calc-prefer-frac) | |
688 | 5 | |
689 | 15)) | |
690 | (if (< t12 32) | |
691 | (if (= t1 16) | |
692 | (if (= t2 16) 15 | |
693 | (if (< t2 16) 16 31)) | |
694 | (if (= t2 16) | |
695 | (if (< t1 16) 16 31) | |
696 | 31)) | |
697 | 63)))) | |
698 | ((memq (car a) '(+ - * %)) | |
699 | (let* ((t1 (math-possible-types (nth 1 a) num)) | |
700 | (t2 (math-possible-types (nth 2 a) num)) | |
701 | (t12 (logior t1 t2))) | |
702 | (if (eq (car a) '%) | |
703 | (setq t1 (logand t1 15) t2 (logand t2 15) t12 (logand t12 15))) | |
704 | (if (< t12 16) | |
705 | (let ((mask (if (<= t12 3) | |
706 | 1 | |
707 | (if (and (or (and (<= t1 3) (= (logand t2 3) 0)) | |
708 | (and (<= t2 3) (= (logand t1 3) 0))) | |
709 | (memq (car a) '(+ -))) | |
710 | 4 | |
711 | 5)))) | |
712 | (if num | |
713 | (* mask 3) | |
714 | (logior (if (and (> (logand t1 5) 0) (> (logand t2 5) 0)) | |
715 | mask 0) | |
716 | (if (> (logand t12 10) 0) | |
717 | (* mask 2) 0)))) | |
718 | (if (< t12 32) | |
719 | (if (eq (car a) '*) | |
720 | (if (= t1 16) | |
721 | (if (= t2 16) 15 | |
722 | (if (< t2 16) 16 31)) | |
723 | (if (= t2 16) | |
724 | (if (< t1 16) 16 31) | |
725 | 31)) | |
726 | (if (= t12 16) 16 | |
727 | (if (or (and (= t1 16) (< t2 16)) | |
728 | (and (= t2 16) (< t1 16))) 32 63))) | |
729 | 63)))) | |
730 | ((eq (car a) 'neg) | |
731 | (math-possible-types (nth 1 a))) | |
732 | ((eq (car a) '^) | |
733 | (let* ((t1 (math-possible-types (nth 1 a) num)) | |
734 | (t2 (math-possible-types (nth 2 a) num)) | |
735 | (t12 (logior t1 t2))) | |
736 | (if (and (<= t2 3) (math-known-nonnegp (nth 2 a)) (< t1 16)) | |
737 | (let ((mask (logior (if (> (logand t1 3) 0) 1 0) | |
738 | (logand t1 4) | |
739 | (if (> (logand t1 12) 0) 5 0)))) | |
740 | (if num | |
741 | (* mask 3) | |
742 | (logior (if (and (> (logand t1 5) 0) (> (logand t2 5) 0)) | |
743 | mask 0) | |
744 | (if (> (logand t12 10) 0) | |
745 | (* mask 2) 0)))) | |
746 | (if (and (math-known-nonnegp (nth 1 a)) | |
747 | (math-known-posp (nth 2 a))) | |
748 | 15 | |
749 | 63)))) | |
750 | ((eq (car a) 'calcFunc-sqrt) | |
751 | (let ((t1 (math-possible-signs (nth 1 a)))) | |
752 | (logior (if (> (logand t1 2) 0) 3 0) | |
753 | (if (> (logand t1 1) 0) 16 0) | |
754 | (if (> (logand t1 4) 0) 15 0) | |
755 | (if (> (logand t1 8) 0) 32 0)))) | |
756 | ((eq (car a) 'vec) | |
757 | (let ((types 0)) | |
758 | (while (and (setq a (cdr a)) (< types 63)) | |
759 | (setq types (logior types (math-possible-types (car a) t)))) | |
760 | types)) | |
761 | ((or (memq (car a) math-integer-functions) | |
762 | (and (memq (car a) math-rounding-functions) | |
763 | (math-known-nonnegp (or (nth 2 a) 0)))) | |
764 | 1) | |
765 | ((or (memq (car a) math-num-integer-functions) | |
766 | (and (memq (car a) math-float-rounding-functions) | |
767 | (math-known-nonnegp (or (nth 2 a) 0)))) | |
768 | 2) | |
769 | ((eq (car a) 'calcFunc-frac) | |
770 | 5) | |
771 | ((and (eq (car a) 'calcFunc-float) (= (length a) 2)) | |
772 | (let ((t1 (math-possible-types (nth 1 a)))) | |
773 | (logior (if (> (logand t1 3) 0) 2 0) | |
774 | (if (> (logand t1 12) 0) 8 0) | |
775 | (logand t1 48)))) | |
776 | ((and (memq (car a) '(calcFunc-abs calcFunc-abssqr)) | |
777 | (= (length a) 2)) | |
778 | (let ((t1 (math-possible-types (nth 1 a)))) | |
779 | (if (>= t1 16) | |
780 | 15 | |
781 | t1))) | |
782 | ((math-const-var a) | |
783 | (cond ((memq (nth 2 a) '(var-e var-pi var-phi var-gamma)) 8) | |
784 | ((eq (nth 2 a) 'var-inf) 1) | |
785 | ((eq (nth 2 a) 'var-i) 16) | |
786 | (t 63))) | |
787 | (t | |
788 | (math-setup-declarations) | |
789 | (let ((decl (if (eq (car a) 'var) | |
790 | (or (assq (nth 2 a) math-decls-cache) | |
791 | math-decls-all) | |
792 | (assq (car a) math-decls-cache)))) | |
793 | (cond ((memq 'int (nth 1 decl)) | |
794 | 1) | |
795 | ((memq 'numint (nth 1 decl)) | |
796 | 3) | |
797 | ((memq 'frac (nth 1 decl)) | |
798 | 4) | |
799 | ((memq 'rat (nth 1 decl)) | |
800 | 5) | |
801 | ((memq 'float (nth 1 decl)) | |
802 | 10) | |
803 | ((nth 2 decl) | |
804 | (math-possible-types (nth 2 decl))) | |
805 | ((memq 'real (nth 1 decl)) | |
806 | 15) | |
898ea5c0 | 807 | (t 63)))))) |
136211a9 EZ |
808 | |
809 | (defun math-known-evenp (a) | |
810 | (cond ((Math-integerp a) | |
811 | (math-evenp a)) | |
812 | ((Math-messy-integerp a) | |
813 | (or (> (nth 2 a) 0) | |
814 | (math-evenp (math-trunc a)))) | |
815 | ((eq (car a) '*) | |
816 | (if (math-known-evenp (nth 1 a)) | |
817 | (math-known-num-integerp (nth 2 a)) | |
818 | (if (math-known-num-integerp (nth 1 a)) | |
819 | (math-known-evenp (nth 2 a))))) | |
820 | ((memq (car a) '(+ -)) | |
821 | (or (and (math-known-evenp (nth 1 a)) | |
822 | (math-known-evenp (nth 2 a))) | |
823 | (and (math-known-oddp (nth 1 a)) | |
824 | (math-known-oddp (nth 2 a))))) | |
825 | ((eq (car a) 'neg) | |
898ea5c0 | 826 | (math-known-evenp (nth 1 a))))) |
136211a9 EZ |
827 | |
828 | (defun math-known-oddp (a) | |
829 | (cond ((Math-integerp a) | |
830 | (math-oddp a)) | |
831 | ((Math-messy-integerp a) | |
832 | (and (<= (nth 2 a) 0) | |
833 | (math-oddp (math-trunc a)))) | |
834 | ((memq (car a) '(+ -)) | |
835 | (or (and (math-known-evenp (nth 1 a)) | |
836 | (math-known-oddp (nth 2 a))) | |
837 | (and (math-known-oddp (nth 1 a)) | |
838 | (math-known-evenp (nth 2 a))))) | |
839 | ((eq (car a) 'neg) | |
898ea5c0 | 840 | (math-known-oddp (nth 1 a))))) |
136211a9 EZ |
841 | |
842 | ||
843 | (defun calcFunc-dreal (expr) | |
844 | (let ((types (math-possible-types expr))) | |
845 | (if (< types 16) 1 | |
846 | (if (= (logand types 15) 0) 0 | |
898ea5c0 | 847 | (math-reject-arg expr 'realp 'quiet))))) |
136211a9 EZ |
848 | |
849 | (defun calcFunc-dimag (expr) | |
850 | (let ((types (math-possible-types expr))) | |
851 | (if (= types 16) 1 | |
852 | (if (= (logand types 16) 0) 0 | |
898ea5c0 | 853 | (math-reject-arg expr "Expected an imaginary number"))))) |
136211a9 EZ |
854 | |
855 | (defun calcFunc-dpos (expr) | |
856 | (let ((signs (math-possible-signs expr))) | |
857 | (if (eq signs 4) 1 | |
858 | (if (memq signs '(1 2 3)) 0 | |
898ea5c0 | 859 | (math-reject-arg expr 'posp 'quiet))))) |
136211a9 EZ |
860 | |
861 | (defun calcFunc-dneg (expr) | |
862 | (let ((signs (math-possible-signs expr))) | |
863 | (if (eq signs 1) 1 | |
864 | (if (memq signs '(2 4 6)) 0 | |
898ea5c0 | 865 | (math-reject-arg expr 'negp 'quiet))))) |
136211a9 EZ |
866 | |
867 | (defun calcFunc-dnonneg (expr) | |
868 | (let ((signs (math-possible-signs expr))) | |
869 | (if (memq signs '(2 4 6)) 1 | |
870 | (if (eq signs 1) 0 | |
898ea5c0 | 871 | (math-reject-arg expr 'posp 'quiet))))) |
136211a9 EZ |
872 | |
873 | (defun calcFunc-dnonzero (expr) | |
874 | (let ((signs (math-possible-signs expr))) | |
875 | (if (memq signs '(1 4 5 8 9 12 13)) 1 | |
876 | (if (eq signs 2) 0 | |
898ea5c0 | 877 | (math-reject-arg expr 'nonzerop 'quiet))))) |
136211a9 EZ |
878 | |
879 | (defun calcFunc-dint (expr) | |
880 | (let ((types (math-possible-types expr))) | |
881 | (if (= types 1) 1 | |
882 | (if (= (logand types 1) 0) 0 | |
898ea5c0 | 883 | (math-reject-arg expr 'integerp 'quiet))))) |
136211a9 EZ |
884 | |
885 | (defun calcFunc-dnumint (expr) | |
886 | (let ((types (math-possible-types expr t))) | |
887 | (if (<= types 3) 1 | |
888 | (if (= (logand types 3) 0) 0 | |
898ea5c0 | 889 | (math-reject-arg expr 'integerp 'quiet))))) |
136211a9 EZ |
890 | |
891 | (defun calcFunc-dnatnum (expr) | |
892 | (let ((res (calcFunc-dint expr))) | |
893 | (if (eq res 1) | |
894 | (calcFunc-dnonneg expr) | |
898ea5c0 | 895 | res))) |
136211a9 EZ |
896 | |
897 | (defun calcFunc-deven (expr) | |
898 | (if (math-known-evenp expr) | |
899 | 1 | |
900 | (if (or (math-known-oddp expr) | |
901 | (= (logand (math-possible-types expr) 3) 0)) | |
902 | 0 | |
898ea5c0 | 903 | (math-reject-arg expr "Can't tell if expression is odd or even")))) |
136211a9 EZ |
904 | |
905 | (defun calcFunc-dodd (expr) | |
906 | (if (math-known-oddp expr) | |
907 | 1 | |
908 | (if (or (math-known-evenp expr) | |
909 | (= (logand (math-possible-types expr) 3) 0)) | |
910 | 0 | |
898ea5c0 | 911 | (math-reject-arg expr "Can't tell if expression is odd or even")))) |
136211a9 EZ |
912 | |
913 | (defun calcFunc-drat (expr) | |
914 | (let ((types (math-possible-types expr))) | |
915 | (if (memq types '(1 4 5)) 1 | |
916 | (if (= (logand types 5) 0) 0 | |
898ea5c0 | 917 | (math-reject-arg expr "Rational number expected"))))) |
136211a9 EZ |
918 | |
919 | (defun calcFunc-drange (expr) | |
920 | (math-setup-declarations) | |
921 | (let (range) | |
922 | (if (Math-realp expr) | |
923 | (list 'vec expr) | |
924 | (if (eq (car-safe expr) 'intv) | |
925 | expr | |
926 | (if (eq (car-safe expr) 'var) | |
927 | (setq range (nth 2 (or (assq (nth 2 expr) math-decls-cache) | |
928 | math-decls-all))) | |
929 | (setq range (nth 2 (assq (car-safe expr) math-decls-cache)))) | |
930 | (if range | |
931 | (math-clean-set (copy-sequence range)) | |
932 | (setq range (math-possible-signs expr)) | |
933 | (if (< range 8) | |
934 | (aref [(vec) | |
935 | (intv 2 (neg (var inf var-inf)) 0) | |
936 | (vec 0) | |
937 | (intv 3 (neg (var inf var-inf)) 0) | |
938 | (intv 1 0 (var inf var-inf)) | |
939 | (vec (intv 2 (neg (var inf var-inf)) 0) | |
940 | (intv 1 0 (var inf var-inf))) | |
941 | (intv 3 0 (var inf var-inf)) | |
942 | (intv 3 (neg (var inf var-inf)) (var inf var-inf))] range) | |
898ea5c0 | 943 | (math-reject-arg expr 'realp 'quiet))))))) |
136211a9 EZ |
944 | |
945 | (defun calcFunc-dscalar (a) | |
946 | (if (math-known-scalarp a) 1 | |
947 | (if (math-known-matrixp a) 0 | |
898ea5c0 | 948 | (math-reject-arg a 'objectp 'quiet)))) |
136211a9 EZ |
949 | |
950 | ||
136211a9 EZ |
951 | ;;;; Arithmetic. |
952 | ||
3132f345 | 953 | (defsubst calcFunc-neg (a) |
898ea5c0 | 954 | (math-normalize (list 'neg a))) |
136211a9 EZ |
955 | |
956 | (defun math-neg-fancy (a) | |
957 | (cond ((eq (car a) 'polar) | |
958 | (list 'polar | |
959 | (nth 1 a) | |
960 | (if (math-posp (nth 2 a)) | |
961 | (math-sub (nth 2 a) (math-half-circle nil)) | |
962 | (math-add (nth 2 a) (math-half-circle nil))))) | |
963 | ((eq (car a) 'mod) | |
964 | (if (math-zerop (nth 1 a)) | |
965 | a | |
966 | (list 'mod (math-sub (nth 2 a) (nth 1 a)) (nth 2 a)))) | |
967 | ((eq (car a) 'sdev) | |
968 | (list 'sdev (math-neg (nth 1 a)) (nth 2 a))) | |
969 | ((eq (car a) 'intv) | |
970 | (math-make-intv (aref [0 2 1 3] (nth 1 a)) | |
971 | (math-neg (nth 3 a)) | |
972 | (math-neg (nth 2 a)))) | |
973 | ((and math-simplify-only | |
974 | (not (equal a math-simplify-only))) | |
975 | (list 'neg a)) | |
976 | ((eq (car a) '+) | |
977 | (math-sub (math-neg (nth 1 a)) (nth 2 a))) | |
978 | ((eq (car a) '-) | |
979 | (math-sub (nth 2 a) (nth 1 a))) | |
980 | ((and (memq (car a) '(* /)) | |
981 | (math-okay-neg (nth 1 a))) | |
982 | (list (car a) (math-neg (nth 1 a)) (nth 2 a))) | |
983 | ((and (memq (car a) '(* /)) | |
984 | (math-okay-neg (nth 2 a))) | |
985 | (list (car a) (nth 1 a) (math-neg (nth 2 a)))) | |
986 | ((and (memq (car a) '(* /)) | |
987 | (or (math-objectp (nth 1 a)) | |
988 | (and (eq (car (nth 1 a)) '*) | |
989 | (math-objectp (nth 1 (nth 1 a)))))) | |
990 | (list (car a) (math-neg (nth 1 a)) (nth 2 a))) | |
991 | ((and (eq (car a) '/) | |
992 | (or (math-objectp (nth 2 a)) | |
993 | (and (eq (car (nth 2 a)) '*) | |
994 | (math-objectp (nth 1 (nth 2 a)))))) | |
995 | (list (car a) (nth 1 a) (math-neg (nth 2 a)))) | |
996 | ((and (eq (car a) 'var) (memq (nth 2 a) '(var-uinf var-nan))) | |
997 | a) | |
998 | ((eq (car a) 'neg) | |
999 | (nth 1 a)) | |
898ea5c0 | 1000 | (t (list 'neg a)))) |
136211a9 EZ |
1001 | |
1002 | (defun math-okay-neg (a) | |
1003 | (or (math-looks-negp a) | |
898ea5c0 | 1004 | (eq (car-safe a) '-))) |
136211a9 EZ |
1005 | |
1006 | (defun math-neg-float (a) | |
898ea5c0 | 1007 | (list 'float (Math-integer-neg (nth 1 a)) (nth 2 a))) |
136211a9 EZ |
1008 | |
1009 | ||
1010 | (defun calcFunc-add (&rest rest) | |
1011 | (if rest | |
1012 | (let ((a (car rest))) | |
1013 | (while (setq rest (cdr rest)) | |
1014 | (setq a (list '+ a (car rest)))) | |
1015 | (math-normalize a)) | |
898ea5c0 | 1016 | 0)) |
136211a9 EZ |
1017 | |
1018 | (defun calcFunc-sub (&rest rest) | |
1019 | (if rest | |
1020 | (let ((a (car rest))) | |
1021 | (while (setq rest (cdr rest)) | |
1022 | (setq a (list '- a (car rest)))) | |
1023 | (math-normalize a)) | |
898ea5c0 | 1024 | 0)) |
136211a9 EZ |
1025 | |
1026 | (defun math-add-objects-fancy (a b) | |
1027 | (cond ((and (Math-numberp a) (Math-numberp b)) | |
1028 | (let ((aa (math-complex a)) | |
1029 | (bb (math-complex b))) | |
1030 | (math-normalize | |
1031 | (let ((res (list 'cplx | |
1032 | (math-add (nth 1 aa) (nth 1 bb)) | |
1033 | (math-add (nth 2 aa) (nth 2 bb))))) | |
1034 | (if (math-want-polar a b) | |
1035 | (math-polar res) | |
1036 | res))))) | |
1037 | ((or (Math-vectorp a) (Math-vectorp b)) | |
1038 | (math-map-vec-2 'math-add a b)) | |
1039 | ((eq (car-safe a) 'sdev) | |
1040 | (if (eq (car-safe b) 'sdev) | |
1041 | (math-make-sdev (math-add (nth 1 a) (nth 1 b)) | |
1042 | (math-hypot (nth 2 a) (nth 2 b))) | |
1043 | (and (or (Math-scalarp b) | |
1044 | (not (Math-objvecp b))) | |
1045 | (math-make-sdev (math-add (nth 1 a) b) (nth 2 a))))) | |
1046 | ((and (eq (car-safe b) 'sdev) | |
1047 | (or (Math-scalarp a) | |
1048 | (not (Math-objvecp a)))) | |
1049 | (math-make-sdev (math-add a (nth 1 b)) (nth 2 b))) | |
1050 | ((eq (car-safe a) 'intv) | |
1051 | (if (eq (car-safe b) 'intv) | |
1052 | (math-make-intv (logior (logand (nth 1 a) (nth 1 b)) | |
1053 | (if (equal (nth 2 a) | |
1054 | '(neg (var inf var-inf))) | |
1055 | (logand (nth 1 a) 2) 0) | |
1056 | (if (equal (nth 2 b) | |
1057 | '(neg (var inf var-inf))) | |
1058 | (logand (nth 1 b) 2) 0) | |
1059 | (if (equal (nth 3 a) '(var inf var-inf)) | |
1060 | (logand (nth 1 a) 1) 0) | |
1061 | (if (equal (nth 3 b) '(var inf var-inf)) | |
1062 | (logand (nth 1 b) 1) 0)) | |
1063 | (math-add (nth 2 a) (nth 2 b)) | |
1064 | (math-add (nth 3 a) (nth 3 b))) | |
1065 | (and (or (Math-anglep b) | |
1066 | (eq (car b) 'date) | |
1067 | (not (Math-objvecp b))) | |
1068 | (math-make-intv (nth 1 a) | |
1069 | (math-add (nth 2 a) b) | |
1070 | (math-add (nth 3 a) b))))) | |
1071 | ((and (eq (car-safe b) 'intv) | |
1072 | (or (Math-anglep a) | |
1073 | (eq (car a) 'date) | |
1074 | (not (Math-objvecp a)))) | |
1075 | (math-make-intv (nth 1 b) | |
1076 | (math-add a (nth 2 b)) | |
1077 | (math-add a (nth 3 b)))) | |
1078 | ((eq (car-safe a) 'date) | |
1079 | (cond ((eq (car-safe b) 'date) | |
1080 | (math-add (nth 1 a) (nth 1 b))) | |
1081 | ((eq (car-safe b) 'hms) | |
1082 | (let ((parts (math-date-parts (nth 1 a)))) | |
1083 | (list 'date | |
1084 | (math-add (car parts) ; this minimizes roundoff | |
1085 | (math-div (math-add | |
1086 | (math-add (nth 1 parts) | |
1087 | (nth 2 parts)) | |
1088 | (math-add | |
1089 | (math-mul (nth 1 b) 3600) | |
1090 | (math-add (math-mul (nth 2 b) 60) | |
1091 | (nth 3 b)))) | |
1092 | 86400))))) | |
1093 | ((Math-realp b) | |
1094 | (list 'date (math-add (nth 1 a) b))) | |
1095 | (t nil))) | |
1096 | ((eq (car-safe b) 'date) | |
1097 | (math-add-objects-fancy b a)) | |
1098 | ((and (eq (car-safe a) 'mod) | |
1099 | (eq (car-safe b) 'mod) | |
1100 | (equal (nth 2 a) (nth 2 b))) | |
1101 | (math-make-mod (math-add (nth 1 a) (nth 1 b)) (nth 2 a))) | |
1102 | ((and (eq (car-safe a) 'mod) | |
1103 | (Math-anglep b)) | |
1104 | (math-make-mod (math-add (nth 1 a) b) (nth 2 a))) | |
1105 | ((and (eq (car-safe b) 'mod) | |
1106 | (Math-anglep a)) | |
1107 | (math-make-mod (math-add a (nth 1 b)) (nth 2 b))) | |
1108 | ((and (or (eq (car-safe a) 'hms) (eq (car-safe b) 'hms)) | |
1109 | (and (Math-anglep a) (Math-anglep b))) | |
1110 | (or (eq (car-safe a) 'hms) (setq a (math-to-hms a))) | |
1111 | (or (eq (car-safe b) 'hms) (setq b (math-to-hms b))) | |
1112 | (math-normalize | |
1113 | (if (math-negp a) | |
1114 | (math-neg (math-add (math-neg a) (math-neg b))) | |
1115 | (if (math-negp b) | |
1116 | (let* ((s (math-add (nth 3 a) (nth 3 b))) | |
1117 | (m (math-add (nth 2 a) (nth 2 b))) | |
1118 | (h (math-add (nth 1 a) (nth 1 b)))) | |
1119 | (if (math-negp s) | |
1120 | (setq s (math-add s 60) | |
1121 | m (math-add m -1))) | |
1122 | (if (math-negp m) | |
1123 | (setq m (math-add m 60) | |
1124 | h (math-add h -1))) | |
1125 | (if (math-negp h) | |
1126 | (math-add b a) | |
1127 | (list 'hms h m s))) | |
1128 | (let* ((s (math-add (nth 3 a) (nth 3 b))) | |
1129 | (m (math-add (nth 2 a) (nth 2 b))) | |
1130 | (h (math-add (nth 1 a) (nth 1 b)))) | |
1131 | (list 'hms h m s)))))) | |
898ea5c0 | 1132 | (t (calc-record-why "*Incompatible arguments for +" a b)))) |
136211a9 EZ |
1133 | |
1134 | (defun math-add-symb-fancy (a b) | |
1135 | (or (and math-simplify-only | |
1136 | (not (equal a math-simplify-only)) | |
1137 | (list '+ a b)) | |
1138 | (and (eq (car-safe b) '+) | |
1139 | (math-add (math-add a (nth 1 b)) | |
1140 | (nth 2 b))) | |
1141 | (and (eq (car-safe b) '-) | |
1142 | (math-sub (math-add a (nth 1 b)) | |
1143 | (nth 2 b))) | |
1144 | (and (eq (car-safe b) 'neg) | |
1145 | (eq (car-safe (nth 1 b)) '+) | |
1146 | (math-sub (math-sub a (nth 1 (nth 1 b))) | |
1147 | (nth 2 (nth 1 b)))) | |
1148 | (and (or (and (Math-vectorp a) (math-known-scalarp b)) | |
1149 | (and (Math-vectorp b) (math-known-scalarp a))) | |
1150 | (math-map-vec-2 'math-add a b)) | |
1151 | (let ((inf (math-infinitep a))) | |
1152 | (cond | |
1153 | (inf | |
1154 | (let ((inf2 (math-infinitep b))) | |
1155 | (if inf2 | |
1156 | (if (or (memq (nth 2 inf) '(var-uinf var-nan)) | |
1157 | (memq (nth 2 inf2) '(var-uinf var-nan))) | |
1158 | '(var nan var-nan) | |
1159 | (let ((dir (math-infinite-dir a inf)) | |
1160 | (dir2 (math-infinite-dir b inf2))) | |
1161 | (if (and (Math-objectp dir) (Math-objectp dir2)) | |
1162 | (if (Math-equal dir dir2) | |
1163 | a | |
1164 | '(var nan var-nan))))) | |
1165 | (if (and (equal a '(var inf var-inf)) | |
1166 | (eq (car-safe b) 'intv) | |
1167 | (memq (nth 1 b) '(2 3)) | |
1168 | (equal (nth 2 b) '(neg (var inf var-inf)))) | |
1169 | (list 'intv 3 (nth 2 b) a) | |
1170 | (if (and (equal a '(neg (var inf var-inf))) | |
1171 | (eq (car-safe b) 'intv) | |
1172 | (memq (nth 1 b) '(1 3)) | |
1173 | (equal (nth 3 b) '(var inf var-inf))) | |
1174 | (list 'intv 3 a (nth 3 b)) | |
1175 | a))))) | |
1176 | ((math-infinitep b) | |
1177 | (if (eq (car-safe a) 'intv) | |
1178 | (math-add b a) | |
1179 | b)) | |
1180 | ((eq (car-safe a) '+) | |
1181 | (let ((temp (math-combine-sum (nth 2 a) b nil nil t))) | |
1182 | (and temp | |
1183 | (math-add (nth 1 a) temp)))) | |
1184 | ((eq (car-safe a) '-) | |
1185 | (let ((temp (math-combine-sum (nth 2 a) b t nil t))) | |
1186 | (and temp | |
1187 | (math-add (nth 1 a) temp)))) | |
1188 | ((and (Math-objectp a) (Math-objectp b)) | |
1189 | nil) | |
1190 | (t | |
1191 | (math-combine-sum a b nil nil nil)))) | |
1192 | (and (Math-looks-negp b) | |
1193 | (list '- a (math-neg b))) | |
1194 | (and (Math-looks-negp a) | |
1195 | (list '- b (math-neg a))) | |
1196 | (and (eq (car-safe a) 'calcFunc-idn) | |
1197 | (= (length a) 2) | |
1198 | (or (and (eq (car-safe b) 'calcFunc-idn) | |
1199 | (= (length b) 2) | |
1200 | (list 'calcFunc-idn (math-add (nth 1 a) (nth 1 b)))) | |
1201 | (and (math-square-matrixp b) | |
1202 | (math-add (math-mimic-ident (nth 1 a) b) b)) | |
1203 | (and (math-known-scalarp b) | |
1204 | (math-add (nth 1 a) b)))) | |
1205 | (and (eq (car-safe b) 'calcFunc-idn) | |
6a056c5d | 1206 | (= (length b) 2) |
136211a9 EZ |
1207 | (or (and (math-square-matrixp a) |
1208 | (math-add a (math-mimic-ident (nth 1 b) a))) | |
1209 | (and (math-known-scalarp a) | |
1210 | (math-add a (nth 1 b))))) | |
898ea5c0 | 1211 | (list '+ a b))) |
136211a9 EZ |
1212 | |
1213 | ||
1214 | (defun calcFunc-mul (&rest rest) | |
1215 | (if rest | |
1216 | (let ((a (car rest))) | |
1217 | (while (setq rest (cdr rest)) | |
1218 | (setq a (list '* a (car rest)))) | |
1219 | (math-normalize a)) | |
898ea5c0 | 1220 | 1)) |
136211a9 EZ |
1221 | |
1222 | (defun math-mul-objects-fancy (a b) | |
1223 | (cond ((and (Math-numberp a) (Math-numberp b)) | |
1224 | (math-normalize | |
1225 | (if (math-want-polar a b) | |
1226 | (let ((a (math-polar a)) | |
1227 | (b (math-polar b))) | |
1228 | (list 'polar | |
1229 | (math-mul (nth 1 a) (nth 1 b)) | |
1230 | (math-fix-circular (math-add (nth 2 a) (nth 2 b))))) | |
1231 | (setq a (math-complex a) | |
1232 | b (math-complex b)) | |
1233 | (list 'cplx | |
1234 | (math-sub (math-mul (nth 1 a) (nth 1 b)) | |
1235 | (math-mul (nth 2 a) (nth 2 b))) | |
1236 | (math-add (math-mul (nth 1 a) (nth 2 b)) | |
1237 | (math-mul (nth 2 a) (nth 1 b))))))) | |
1238 | ((Math-vectorp a) | |
1239 | (if (Math-vectorp b) | |
1240 | (if (math-matrixp a) | |
1241 | (if (math-matrixp b) | |
1242 | (if (= (length (nth 1 a)) (length b)) | |
1243 | (math-mul-mats a b) | |
1244 | (math-dimension-error)) | |
1245 | (if (= (length (nth 1 a)) 2) | |
1246 | (if (= (length a) (length b)) | |
1247 | (math-mul-mats a (list 'vec b)) | |
1248 | (math-dimension-error)) | |
1249 | (if (= (length (nth 1 a)) (length b)) | |
1250 | (math-mul-mat-vec a b) | |
1251 | (math-dimension-error)))) | |
1252 | (if (math-matrixp b) | |
1253 | (if (= (length a) (length b)) | |
1254 | (nth 1 (math-mul-mats (list 'vec a) b)) | |
1255 | (math-dimension-error)) | |
1256 | (if (= (length a) (length b)) | |
1257 | (math-dot-product a b) | |
1258 | (math-dimension-error)))) | |
1259 | (math-map-vec-2 'math-mul a b))) | |
1260 | ((Math-vectorp b) | |
1261 | (math-map-vec-2 'math-mul a b)) | |
1262 | ((eq (car-safe a) 'sdev) | |
1263 | (if (eq (car-safe b) 'sdev) | |
1264 | (math-make-sdev (math-mul (nth 1 a) (nth 1 b)) | |
1265 | (math-hypot (math-mul (nth 2 a) (nth 1 b)) | |
1266 | (math-mul (nth 2 b) (nth 1 a)))) | |
1267 | (and (or (Math-scalarp b) | |
1268 | (not (Math-objvecp b))) | |
1269 | (math-make-sdev (math-mul (nth 1 a) b) | |
1270 | (math-mul (nth 2 a) b))))) | |
1271 | ((and (eq (car-safe b) 'sdev) | |
1272 | (or (Math-scalarp a) | |
1273 | (not (Math-objvecp a)))) | |
1274 | (math-make-sdev (math-mul a (nth 1 b)) (math-mul a (nth 2 b)))) | |
1275 | ((and (eq (car-safe a) 'intv) (Math-anglep b)) | |
1276 | (if (Math-negp b) | |
1277 | (math-neg (math-mul a (math-neg b))) | |
1278 | (math-make-intv (nth 1 a) | |
1279 | (math-mul (nth 2 a) b) | |
1280 | (math-mul (nth 3 a) b)))) | |
1281 | ((and (eq (car-safe b) 'intv) (Math-anglep a)) | |
1282 | (math-mul b a)) | |
1283 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) | |
1284 | (eq (car-safe b) 'intv) (math-intv-constp b)) | |
1285 | (let ((lo (math-mul a (nth 2 b))) | |
1286 | (hi (math-mul a (nth 3 b)))) | |
1287 | (or (eq (car-safe lo) 'intv) | |
1288 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) lo lo))) | |
1289 | (or (eq (car-safe hi) 'intv) | |
1290 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) hi hi))) | |
1291 | (math-combine-intervals | |
1292 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) | |
1293 | (math-infinitep (nth 2 lo))) | |
1294 | (memq (nth 1 lo) '(2 3))) | |
1295 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) | |
1296 | (math-infinitep (nth 3 lo))) | |
1297 | (memq (nth 1 lo) '(1 3))) | |
1298 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) | |
1299 | (math-infinitep (nth 2 hi))) | |
1300 | (memq (nth 1 hi) '(2 3))) | |
1301 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) | |
1302 | (math-infinitep (nth 3 hi))) | |
1303 | (memq (nth 1 hi) '(1 3)))))) | |
1304 | ((and (eq (car-safe a) 'mod) | |
1305 | (eq (car-safe b) 'mod) | |
1306 | (equal (nth 2 a) (nth 2 b))) | |
1307 | (math-make-mod (math-mul (nth 1 a) (nth 1 b)) (nth 2 a))) | |
1308 | ((and (eq (car-safe a) 'mod) | |
1309 | (Math-anglep b)) | |
1310 | (math-make-mod (math-mul (nth 1 a) b) (nth 2 a))) | |
1311 | ((and (eq (car-safe b) 'mod) | |
1312 | (Math-anglep a)) | |
1313 | (math-make-mod (math-mul a (nth 1 b)) (nth 2 b))) | |
1314 | ((and (eq (car-safe a) 'hms) (Math-realp b)) | |
1315 | (math-with-extra-prec 2 | |
1316 | (math-to-hms (math-mul (math-from-hms a 'deg) b) 'deg))) | |
1317 | ((and (eq (car-safe b) 'hms) (Math-realp a)) | |
1318 | (math-mul b a)) | |
898ea5c0 | 1319 | (t (calc-record-why "*Incompatible arguments for *" a b)))) |
136211a9 EZ |
1320 | |
1321 | ;;; Fast function to multiply floating-point numbers. | |
1322 | (defun math-mul-float (a b) ; [F F F] | |
1323 | (math-make-float (math-mul (nth 1 a) (nth 1 b)) | |
898ea5c0 | 1324 | (+ (nth 2 a) (nth 2 b)))) |
136211a9 EZ |
1325 | |
1326 | (defun math-sqr-float (a) ; [F F] | |
1327 | (math-make-float (math-mul (nth 1 a) (nth 1 a)) | |
898ea5c0 | 1328 | (+ (nth 2 a) (nth 2 a)))) |
136211a9 EZ |
1329 | |
1330 | (defun math-intv-constp (a &optional finite) | |
1331 | (and (or (Math-anglep (nth 2 a)) | |
1332 | (and (equal (nth 2 a) '(neg (var inf var-inf))) | |
1333 | (or (not finite) | |
1334 | (memq (nth 1 a) '(0 1))))) | |
1335 | (or (Math-anglep (nth 3 a)) | |
1336 | (and (equal (nth 3 a) '(var inf var-inf)) | |
1337 | (or (not finite) | |
898ea5c0 | 1338 | (memq (nth 1 a) '(0 2))))))) |
136211a9 EZ |
1339 | |
1340 | (defun math-mul-zero (a b) | |
1341 | (if (math-known-matrixp b) | |
1342 | (if (math-vectorp b) | |
1343 | (math-map-vec-2 'math-mul a b) | |
1344 | (math-mimic-ident 0 b)) | |
1345 | (if (math-infinitep b) | |
1346 | '(var nan var-nan) | |
1347 | (let ((aa nil) (bb nil)) | |
1348 | (if (and (eq (car-safe b) 'intv) | |
1349 | (progn | |
1350 | (and (equal (nth 2 b) '(neg (var inf var-inf))) | |
1351 | (memq (nth 1 b) '(2 3)) | |
1352 | (setq aa (nth 2 b))) | |
1353 | (and (equal (nth 3 b) '(var inf var-inf)) | |
1354 | (memq (nth 1 b) '(1 3)) | |
1355 | (setq bb (nth 3 b))) | |
1356 | (or aa bb))) | |
1357 | (if (or (math-posp a) | |
1358 | (and (math-zerop a) | |
1359 | (or (memq calc-infinite-mode '(-1 1)) | |
1360 | (setq aa '(neg (var inf var-inf)) | |
1361 | bb '(var inf var-inf))))) | |
1362 | (list 'intv 3 (or aa 0) (or bb 0)) | |
1363 | (if (math-negp a) | |
1364 | (math-neg (list 'intv 3 (or aa 0) (or bb 0))) | |
1365 | '(var nan var-nan))) | |
898ea5c0 | 1366 | (if (or (math-floatp a) (math-floatp b)) '(float 0 0) 0)))))) |
136211a9 EZ |
1367 | |
1368 | ||
1369 | (defun math-mul-symb-fancy (a b) | |
1370 | (or (and math-simplify-only | |
1371 | (not (equal a math-simplify-only)) | |
1372 | (list '* a b)) | |
1373 | (and (Math-equal-int a 1) | |
1374 | b) | |
1375 | (and (Math-equal-int a -1) | |
1376 | (math-neg b)) | |
1377 | (and (or (and (Math-vectorp a) (math-known-scalarp b)) | |
1378 | (and (Math-vectorp b) (math-known-scalarp a))) | |
1379 | (math-map-vec-2 'math-mul a b)) | |
1380 | (and (Math-objectp b) (not (Math-objectp a)) | |
1381 | (math-mul b a)) | |
1382 | (and (eq (car-safe a) 'neg) | |
1383 | (math-neg (math-mul (nth 1 a) b))) | |
1384 | (and (eq (car-safe b) 'neg) | |
1385 | (math-neg (math-mul a (nth 1 b)))) | |
1386 | (and (eq (car-safe a) '*) | |
1387 | (math-mul (nth 1 a) | |
1388 | (math-mul (nth 2 a) b))) | |
1389 | (and (eq (car-safe a) '^) | |
1390 | (Math-looks-negp (nth 2 a)) | |
1391 | (not (and (eq (car-safe b) '^) (Math-looks-negp (nth 2 b)))) | |
1392 | (math-known-scalarp b t) | |
1393 | (math-div b (math-normalize | |
1394 | (list '^ (nth 1 a) (math-neg (nth 2 a)))))) | |
1395 | (and (eq (car-safe b) '^) | |
1396 | (Math-looks-negp (nth 2 b)) | |
1397 | (not (and (eq (car-safe a) '^) (Math-looks-negp (nth 2 a)))) | |
7199ddd2 | 1398 | (not (math-known-matrixp (nth 1 b))) |
136211a9 EZ |
1399 | (math-div a (math-normalize |
1400 | (list '^ (nth 1 b) (math-neg (nth 2 b)))))) | |
1401 | (and (eq (car-safe a) '/) | |
1402 | (or (math-known-scalarp a t) (math-known-scalarp b t)) | |
1403 | (let ((temp (math-combine-prod (nth 2 a) b t nil t))) | |
1404 | (if temp | |
1405 | (math-mul (nth 1 a) temp) | |
1406 | (math-div (math-mul (nth 1 a) b) (nth 2 a))))) | |
1407 | (and (eq (car-safe b) '/) | |
1408 | (math-div (math-mul a (nth 1 b)) (nth 2 b))) | |
1409 | (and (eq (car-safe b) '+) | |
1410 | (Math-numberp a) | |
1411 | (or (Math-numberp (nth 1 b)) | |
1412 | (Math-numberp (nth 2 b))) | |
1413 | (math-add (math-mul a (nth 1 b)) | |
1414 | (math-mul a (nth 2 b)))) | |
1415 | (and (eq (car-safe b) '-) | |
1416 | (Math-numberp a) | |
1417 | (or (Math-numberp (nth 1 b)) | |
1418 | (Math-numberp (nth 2 b))) | |
1419 | (math-sub (math-mul a (nth 1 b)) | |
1420 | (math-mul a (nth 2 b)))) | |
1421 | (and (eq (car-safe b) '*) | |
1422 | (Math-numberp (nth 1 b)) | |
1423 | (not (Math-numberp a)) | |
1424 | (math-mul (nth 1 b) (math-mul a (nth 2 b)))) | |
1425 | (and (eq (car-safe a) 'calcFunc-idn) | |
1426 | (= (length a) 2) | |
1427 | (or (and (eq (car-safe b) 'calcFunc-idn) | |
1428 | (= (length b) 2) | |
1429 | (list 'calcFunc-idn (math-mul (nth 1 a) (nth 1 b)))) | |
1430 | (and (math-known-scalarp b) | |
1431 | (list 'calcFunc-idn (math-mul (nth 1 a) b))) | |
1432 | (and (math-known-matrixp b) | |
1433 | (math-mul (nth 1 a) b)))) | |
1434 | (and (eq (car-safe b) 'calcFunc-idn) | |
1435 | (= (length b) 2) | |
1436 | (or (and (math-known-scalarp a) | |
1437 | (list 'calcFunc-idn (math-mul a (nth 1 b)))) | |
1438 | (and (math-known-matrixp a) | |
1439 | (math-mul a (nth 1 b))))) | |
7199ddd2 JB |
1440 | (and (math-identity-matrix-p a t) |
1441 | (or (and (eq (car-safe b) 'calcFunc-idn) | |
1442 | (= (length b) 2) | |
1443 | (list 'calcFunc-idn (math-mul | |
1444 | (nth 1 (nth 1 a)) | |
1445 | (nth 1 b)) | |
1446 | (1- (length a)))) | |
1447 | (and (math-known-scalarp b) | |
1448 | (list 'calcFunc-idn (math-mul | |
1449 | (nth 1 (nth 1 a)) b) | |
1450 | (1- (length a)))) | |
1451 | (and (math-known-matrixp b) | |
1452 | (math-mul (nth 1 (nth 1 a)) b)))) | |
1453 | (and (math-identity-matrix-p b t) | |
1454 | (or (and (eq (car-safe a) 'calcFunc-idn) | |
1455 | (= (length a) 2) | |
1456 | (list 'calcFunc-idn (math-mul (nth 1 a) | |
1457 | (nth 1 (nth 1 b))) | |
1458 | (1- (length b)))) | |
1459 | (and (math-known-scalarp a) | |
1460 | (list 'calcFunc-idn (math-mul a (nth 1 (nth 1 b))) | |
1461 | (1- (length b)))) | |
1462 | (and (math-known-matrixp a) | |
1463 | (math-mul a (nth 1 (nth 1 b)))))) | |
136211a9 EZ |
1464 | (and (math-looks-negp b) |
1465 | (math-mul (math-neg a) (math-neg b))) | |
1466 | (and (eq (car-safe b) '-) | |
1467 | (math-looks-negp a) | |
1468 | (math-mul (math-neg a) (math-neg b))) | |
1469 | (cond | |
1470 | ((eq (car-safe b) '*) | |
1471 | (let ((temp (math-combine-prod a (nth 1 b) nil nil t))) | |
1472 | (and temp | |
1473 | (math-mul temp (nth 2 b))))) | |
1474 | (t | |
1475 | (math-combine-prod a b nil nil nil))) | |
1476 | (and (equal a '(var nan var-nan)) | |
1477 | a) | |
1478 | (and (equal b '(var nan var-nan)) | |
1479 | b) | |
1480 | (and (equal a '(var uinf var-uinf)) | |
1481 | a) | |
1482 | (and (equal b '(var uinf var-uinf)) | |
1483 | b) | |
1484 | (and (equal b '(var inf var-inf)) | |
1485 | (let ((s1 (math-possible-signs a))) | |
1486 | (cond ((eq s1 4) | |
1487 | b) | |
1488 | ((eq s1 6) | |
1489 | '(intv 3 0 (var inf var-inf))) | |
1490 | ((eq s1 1) | |
1491 | (math-neg b)) | |
1492 | ((eq s1 3) | |
1493 | '(intv 3 (neg (var inf var-inf)) 0)) | |
1494 | ((and (eq (car a) 'intv) (math-intv-constp a)) | |
1495 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf))) | |
1496 | ((and (eq (car a) 'cplx) | |
1497 | (math-zerop (nth 1 a))) | |
1498 | (list '* (list 'cplx 0 (calcFunc-sign (nth 2 a))) b)) | |
1499 | ((eq (car a) 'polar) | |
1500 | (list '* (list 'polar 1 (nth 2 a)) b))))) | |
1501 | (and (equal a '(var inf var-inf)) | |
1502 | (math-mul b a)) | |
898ea5c0 | 1503 | (list '* a b))) |
136211a9 EZ |
1504 | |
1505 | ||
1506 | (defun calcFunc-div (a &rest rest) | |
1507 | (while rest | |
1508 | (setq a (list '/ a (car rest)) | |
1509 | rest (cdr rest))) | |
898ea5c0 | 1510 | (math-normalize a)) |
136211a9 EZ |
1511 | |
1512 | (defun math-div-objects-fancy (a b) | |
1513 | (cond ((and (Math-numberp a) (Math-numberp b)) | |
1514 | (math-normalize | |
1515 | (cond ((math-want-polar a b) | |
1516 | (let ((a (math-polar a)) | |
1517 | (b (math-polar b))) | |
1518 | (list 'polar | |
1519 | (math-div (nth 1 a) (nth 1 b)) | |
1520 | (math-fix-circular (math-sub (nth 2 a) | |
1521 | (nth 2 b)))))) | |
1522 | ((Math-realp b) | |
1523 | (setq a (math-complex a)) | |
1524 | (list 'cplx (math-div (nth 1 a) b) | |
1525 | (math-div (nth 2 a) b))) | |
1526 | (t | |
1527 | (setq a (math-complex a) | |
1528 | b (math-complex b)) | |
1529 | (math-div | |
1530 | (list 'cplx | |
1531 | (math-add (math-mul (nth 1 a) (nth 1 b)) | |
1532 | (math-mul (nth 2 a) (nth 2 b))) | |
1533 | (math-sub (math-mul (nth 2 a) (nth 1 b)) | |
1534 | (math-mul (nth 1 a) (nth 2 b)))) | |
1535 | (math-add (math-sqr (nth 1 b)) | |
1536 | (math-sqr (nth 2 b)))))))) | |
1537 | ((math-matrixp b) | |
1538 | (if (math-square-matrixp b) | |
1539 | (let ((n1 (length b))) | |
1540 | (if (Math-vectorp a) | |
1541 | (if (math-matrixp a) | |
1542 | (if (= (length a) n1) | |
1543 | (math-lud-solve (math-matrix-lud b) a b) | |
1544 | (if (= (length (nth 1 a)) n1) | |
1545 | (math-transpose | |
1546 | (math-lud-solve (math-matrix-lud | |
1547 | (math-transpose b)) | |
1548 | (math-transpose a) b)) | |
1549 | (math-dimension-error))) | |
1550 | (if (= (length a) n1) | |
1551 | (math-mat-col (math-lud-solve (math-matrix-lud b) | |
1552 | (math-col-matrix a) b) | |
1553 | 1) | |
1554 | (math-dimension-error))) | |
1555 | (if (Math-equal-int a 1) | |
1556 | (calcFunc-inv b) | |
1557 | (math-mul a (calcFunc-inv b))))) | |
1558 | (math-reject-arg b 'square-matrixp))) | |
1559 | ((and (Math-vectorp a) (Math-objectp b)) | |
1560 | (math-map-vec-2 'math-div a b)) | |
1561 | ((eq (car-safe a) 'sdev) | |
1562 | (if (eq (car-safe b) 'sdev) | |
1563 | (let ((x (math-div (nth 1 a) (nth 1 b)))) | |
1564 | (math-make-sdev x | |
1565 | (math-div (math-hypot (nth 2 a) | |
1566 | (math-mul (nth 2 b) x)) | |
1567 | (nth 1 b)))) | |
1568 | (if (or (Math-scalarp b) | |
1569 | (not (Math-objvecp b))) | |
1570 | (math-make-sdev (math-div (nth 1 a) b) (math-div (nth 2 a) b)) | |
1571 | (math-reject-arg 'realp b)))) | |
1572 | ((and (eq (car-safe b) 'sdev) | |
1573 | (or (Math-scalarp a) | |
1574 | (not (Math-objvecp a)))) | |
1575 | (let ((x (math-div a (nth 1 b)))) | |
1576 | (math-make-sdev x | |
1577 | (math-div (math-mul (nth 2 b) x) (nth 1 b))))) | |
1578 | ((and (eq (car-safe a) 'intv) (Math-anglep b)) | |
1579 | (if (Math-negp b) | |
1580 | (math-neg (math-div a (math-neg b))) | |
1581 | (math-make-intv (nth 1 a) | |
1582 | (math-div (nth 2 a) b) | |
1583 | (math-div (nth 3 a) b)))) | |
1584 | ((and (eq (car-safe b) 'intv) (Math-anglep a)) | |
1585 | (if (or (Math-posp (nth 2 b)) | |
1586 | (and (Math-zerop (nth 2 b)) (or (memq (nth 1 b) '(0 1)) | |
1587 | calc-infinite-mode))) | |
1588 | (if (Math-negp a) | |
1589 | (math-neg (math-div (math-neg a) b)) | |
1590 | (let ((calc-infinite-mode 1)) | |
1591 | (math-make-intv (aref [0 2 1 3] (nth 1 b)) | |
1592 | (math-div a (nth 3 b)) | |
1593 | (math-div a (nth 2 b))))) | |
1594 | (if (or (Math-negp (nth 3 b)) | |
1595 | (and (Math-zerop (nth 3 b)) (or (memq (nth 1 b) '(0 2)) | |
1596 | calc-infinite-mode))) | |
1597 | (math-neg (math-div a (math-neg b))) | |
1598 | (if calc-infinite-mode | |
1599 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) | |
1600 | (math-reject-arg b "*Division by zero"))))) | |
1601 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) | |
1602 | (eq (car-safe b) 'intv) (math-intv-constp b)) | |
1603 | (if (or (Math-posp (nth 2 b)) | |
1604 | (and (Math-zerop (nth 2 b)) (or (memq (nth 1 b) '(0 1)) | |
1605 | calc-infinite-mode))) | |
1606 | (let* ((calc-infinite-mode 1) | |
1607 | (lo (math-div a (nth 2 b))) | |
1608 | (hi (math-div a (nth 3 b)))) | |
1609 | (or (eq (car-safe lo) 'intv) | |
1610 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) | |
1611 | lo lo))) | |
1612 | (or (eq (car-safe hi) 'intv) | |
1613 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) | |
1614 | hi hi))) | |
1615 | (math-combine-intervals | |
1616 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) | |
1617 | (and (math-infinitep (nth 2 lo)) | |
1618 | (not (math-zerop (nth 2 b))))) | |
1619 | (memq (nth 1 lo) '(2 3))) | |
1620 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) | |
1621 | (and (math-infinitep (nth 3 lo)) | |
1622 | (not (math-zerop (nth 2 b))))) | |
1623 | (memq (nth 1 lo) '(1 3))) | |
1624 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) | |
1625 | (and (math-infinitep (nth 2 hi)) | |
1626 | (not (math-zerop (nth 3 b))))) | |
1627 | (memq (nth 1 hi) '(2 3))) | |
1628 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) | |
1629 | (and (math-infinitep (nth 3 hi)) | |
1630 | (not (math-zerop (nth 3 b))))) | |
1631 | (memq (nth 1 hi) '(1 3))))) | |
1632 | (if (or (Math-negp (nth 3 b)) | |
1633 | (and (Math-zerop (nth 3 b)) (or (memq (nth 1 b) '(0 2)) | |
1634 | calc-infinite-mode))) | |
1635 | (math-neg (math-div a (math-neg b))) | |
1636 | (if calc-infinite-mode | |
1637 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) | |
1638 | (math-reject-arg b "*Division by zero"))))) | |
1639 | ((and (eq (car-safe a) 'mod) | |
1640 | (eq (car-safe b) 'mod) | |
1641 | (equal (nth 2 a) (nth 2 b))) | |
1642 | (math-make-mod (math-div-mod (nth 1 a) (nth 1 b) (nth 2 a)) | |
1643 | (nth 2 a))) | |
1644 | ((and (eq (car-safe a) 'mod) | |
1645 | (Math-anglep b)) | |
1646 | (math-make-mod (math-div-mod (nth 1 a) b (nth 2 a)) (nth 2 a))) | |
1647 | ((and (eq (car-safe b) 'mod) | |
1648 | (Math-anglep a)) | |
1649 | (math-make-mod (math-div-mod a (nth 1 b) (nth 2 b)) (nth 2 b))) | |
1650 | ((eq (car-safe a) 'hms) | |
1651 | (if (eq (car-safe b) 'hms) | |
1652 | (math-with-extra-prec 1 | |
1653 | (math-div (math-from-hms a 'deg) | |
1654 | (math-from-hms b 'deg))) | |
1655 | (math-with-extra-prec 2 | |
1656 | (math-to-hms (math-div (math-from-hms a 'deg) b) 'deg)))) | |
898ea5c0 | 1657 | (t (calc-record-why "*Incompatible arguments for /" a b)))) |
136211a9 EZ |
1658 | |
1659 | (defun math-div-by-zero (a b) | |
1660 | (if (math-infinitep a) | |
1661 | (if (or (equal a '(var nan var-nan)) | |
1662 | (equal b '(var uinf var-uinf)) | |
1663 | (memq calc-infinite-mode '(-1 1))) | |
1664 | a | |
1665 | '(var uinf var-uinf)) | |
1666 | (if calc-infinite-mode | |
1667 | (if (math-zerop a) | |
1668 | '(var nan var-nan) | |
1669 | (if (eq calc-infinite-mode 1) | |
1670 | (math-mul a '(var inf var-inf)) | |
1671 | (if (eq calc-infinite-mode -1) | |
1672 | (math-mul a '(neg (var inf var-inf))) | |
1673 | (if (eq (car-safe a) 'intv) | |
1674 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) | |
1675 | '(var uinf var-uinf))))) | |
898ea5c0 | 1676 | (math-reject-arg a "*Division by zero")))) |
136211a9 EZ |
1677 | |
1678 | (defun math-div-zero (a b) | |
1679 | (if (math-known-matrixp b) | |
1680 | (if (math-vectorp b) | |
1681 | (math-map-vec-2 'math-div a b) | |
1682 | (math-mimic-ident 0 b)) | |
1683 | (if (equal b '(var nan var-nan)) | |
1684 | b | |
1685 | (if (and (eq (car-safe b) 'intv) (math-intv-constp b) | |
1686 | (not (math-posp b)) (not (math-negp b))) | |
1687 | (if calc-infinite-mode | |
1688 | (list 'intv 3 | |
1689 | (if (and (math-zerop (nth 2 b)) | |
1690 | (memq calc-infinite-mode '(1 -1))) | |
1691 | (nth 2 b) '(neg (var inf var-inf))) | |
1692 | (if (and (math-zerop (nth 3 b)) | |
1693 | (memq calc-infinite-mode '(1 -1))) | |
1694 | (nth 3 b) '(var inf var-inf))) | |
1695 | (math-reject-arg b "*Division by zero")) | |
898ea5c0 | 1696 | a)))) |
136211a9 | 1697 | |
7db3d0d5 JB |
1698 | ;; For math-div-symb-fancy |
1699 | (defvar math-trig-inverses | |
1700 | '((calcFunc-sin . calcFunc-csc) | |
1701 | (calcFunc-cos . calcFunc-sec) | |
1702 | (calcFunc-tan . calcFunc-cot) | |
1703 | (calcFunc-sec . calcFunc-cos) | |
1704 | (calcFunc-csc . calcFunc-sin) | |
1705 | (calcFunc-cot . calcFunc-tan) | |
1706 | (calcFunc-sinh . calcFunc-csch) | |
1707 | (calcFunc-cosh . calcFunc-sech) | |
1708 | (calcFunc-tanh . calcFunc-coth) | |
1709 | (calcFunc-sech . calcFunc-cosh) | |
1710 | (calcFunc-csch . calcFunc-sinh) | |
1711 | (calcFunc-coth . calcFunc-tanh))) | |
1712 | ||
1713 | (defvar math-div-trig) | |
1714 | (defvar math-div-non-trig) | |
1715 | ||
1716 | (defun math-div-new-trig (tr) | |
1717 | (if math-div-trig | |
1718 | (setq math-div-trig | |
1719 | (list '* tr math-div-trig)) | |
1720 | (setq math-div-trig tr))) | |
1721 | ||
1722 | (defun math-div-new-non-trig (ntr) | |
1723 | (if math-div-non-trig | |
1724 | (setq math-div-non-trig | |
1725 | (list '* ntr math-div-non-trig)) | |
1726 | (setq math-div-non-trig ntr))) | |
1727 | ||
1728 | (defun math-div-isolate-trig (expr) | |
1729 | (if (eq (car-safe expr) '*) | |
1730 | (progn | |
1731 | (math-div-isolate-trig-term (nth 1 expr)) | |
1732 | (math-div-isolate-trig (nth 2 expr))) | |
1733 | (math-div-isolate-trig-term expr))) | |
1734 | ||
1735 | (defun math-div-isolate-trig-term (term) | |
1736 | (let ((fn (assoc (car-safe term) math-trig-inverses))) | |
1737 | (if fn | |
1738 | (math-div-new-trig | |
1739 | (cons (cdr fn) (cdr term))) | |
1740 | (math-div-new-non-trig term)))) | |
1741 | ||
136211a9 | 1742 | (defun math-div-symb-fancy (a b) |
7199ddd2 JB |
1743 | (or (and (math-known-matrixp b) |
1744 | (math-mul a (math-pow b -1))) | |
1745 | (and math-simplify-only | |
136211a9 EZ |
1746 | (not (equal a math-simplify-only)) |
1747 | (list '/ a b)) | |
1748 | (and (Math-equal-int b 1) a) | |
1749 | (and (Math-equal-int b -1) (math-neg a)) | |
1750 | (and (Math-vectorp a) (math-known-scalarp b) | |
1751 | (math-map-vec-2 'math-div a b)) | |
1752 | (and (eq (car-safe b) '^) | |
1753 | (or (Math-looks-negp (nth 2 b)) (Math-equal-int a 1)) | |
1754 | (math-mul a (math-normalize | |
1755 | (list '^ (nth 1 b) (math-neg (nth 2 b)))))) | |
1756 | (and (eq (car-safe a) 'neg) | |
1757 | (math-neg (math-div (nth 1 a) b))) | |
1758 | (and (eq (car-safe b) 'neg) | |
1759 | (math-neg (math-div a (nth 1 b)))) | |
1760 | (and (eq (car-safe a) '/) | |
1761 | (math-div (nth 1 a) (math-mul (nth 2 a) b))) | |
1762 | (and (eq (car-safe b) '/) | |
1763 | (or (math-known-scalarp (nth 1 b) t) | |
1764 | (math-known-scalarp (nth 2 b) t)) | |
1765 | (math-div (math-mul a (nth 2 b)) (nth 1 b))) | |
1766 | (and (eq (car-safe b) 'frac) | |
1767 | (math-mul (math-make-frac (nth 2 b) (nth 1 b)) a)) | |
1768 | (and (eq (car-safe a) '+) | |
1769 | (or (Math-numberp (nth 1 a)) | |
1770 | (Math-numberp (nth 2 a))) | |
1771 | (Math-numberp b) | |
1772 | (math-add (math-div (nth 1 a) b) | |
1773 | (math-div (nth 2 a) b))) | |
1774 | (and (eq (car-safe a) '-) | |
1775 | (or (Math-numberp (nth 1 a)) | |
1776 | (Math-numberp (nth 2 a))) | |
1777 | (Math-numberp b) | |
1778 | (math-sub (math-div (nth 1 a) b) | |
1779 | (math-div (nth 2 a) b))) | |
1780 | (and (or (eq (car-safe a) '-) | |
1781 | (math-looks-negp a)) | |
1782 | (math-looks-negp b) | |
1783 | (math-div (math-neg a) (math-neg b))) | |
1784 | (and (eq (car-safe b) '-) | |
1785 | (math-looks-negp a) | |
1786 | (math-div (math-neg a) (math-neg b))) | |
1787 | (and (eq (car-safe a) 'calcFunc-idn) | |
1788 | (= (length a) 2) | |
1789 | (or (and (eq (car-safe b) 'calcFunc-idn) | |
1790 | (= (length b) 2) | |
1791 | (list 'calcFunc-idn (math-div (nth 1 a) (nth 1 b)))) | |
1792 | (and (math-known-scalarp b) | |
1793 | (list 'calcFunc-idn (math-div (nth 1 a) b))) | |
1794 | (and (math-known-matrixp b) | |
1795 | (math-div (nth 1 a) b)))) | |
1796 | (and (eq (car-safe b) 'calcFunc-idn) | |
1797 | (= (length b) 2) | |
1798 | (or (and (math-known-scalarp a) | |
1799 | (list 'calcFunc-idn (math-div a (nth 1 b)))) | |
1800 | (and (math-known-matrixp a) | |
1801 | (math-div a (nth 1 b))))) | |
7db3d0d5 JB |
1802 | (and math-simplifying |
1803 | (let ((math-div-trig nil) | |
1804 | (math-div-non-trig nil)) | |
1805 | (math-div-isolate-trig b) | |
1806 | (if math-div-trig | |
1807 | (if math-div-non-trig | |
1808 | (math-div (math-mul a math-div-trig) math-div-non-trig) | |
1809 | (math-mul a math-div-trig)) | |
1810 | nil))) | |
136211a9 EZ |
1811 | (if (and calc-matrix-mode |
1812 | (or (math-known-matrixp a) (math-known-matrixp b))) | |
1813 | (math-combine-prod a b nil t nil) | |
1814 | (if (eq (car-safe a) '*) | |
1815 | (if (eq (car-safe b) '*) | |
1816 | (let ((c (math-combine-prod (nth 1 a) (nth 1 b) nil t t))) | |
1817 | (and c | |
1818 | (math-div (math-mul c (nth 2 a)) (nth 2 b)))) | |
1819 | (let ((c (math-combine-prod (nth 1 a) b nil t t))) | |
1820 | (and c | |
1821 | (math-mul c (nth 2 a))))) | |
1822 | (if (eq (car-safe b) '*) | |
1823 | (let ((c (math-combine-prod a (nth 1 b) nil t t))) | |
1824 | (and c | |
1825 | (math-div c (nth 2 b)))) | |
1826 | (math-combine-prod a b nil t nil)))) | |
1827 | (and (math-infinitep a) | |
1828 | (if (math-infinitep b) | |
1829 | '(var nan var-nan) | |
1830 | (if (or (equal a '(var nan var-nan)) | |
1831 | (equal a '(var uinf var-uinf))) | |
1832 | a | |
1833 | (if (equal a '(var inf var-inf)) | |
1834 | (if (or (math-posp b) | |
1835 | (and (eq (car-safe b) 'intv) | |
1836 | (math-zerop (nth 2 b)))) | |
1837 | (if (and (eq (car-safe b) 'intv) | |
1838 | (not (math-intv-constp b t))) | |
1839 | '(intv 3 0 (var inf var-inf)) | |
1840 | a) | |
1841 | (if (or (math-negp b) | |
1842 | (and (eq (car-safe b) 'intv) | |
1843 | (math-zerop (nth 3 b)))) | |
1844 | (if (and (eq (car-safe b) 'intv) | |
1845 | (not (math-intv-constp b t))) | |
1846 | '(intv 3 (neg (var inf var-inf)) 0) | |
1847 | (math-neg a)) | |
1848 | (if (and (eq (car-safe b) 'intv) | |
1849 | (math-negp (nth 2 b)) (math-posp (nth 3 b))) | |
1850 | '(intv 3 (neg (var inf var-inf)) | |
1851 | (var inf var-inf))))))))) | |
1852 | (and (math-infinitep b) | |
1853 | (if (equal b '(var nan var-nan)) | |
1854 | b | |
1855 | (let ((calc-infinite-mode 1)) | |
1856 | (math-mul-zero b a)))) | |
898ea5c0 | 1857 | (list '/ a b))) |
136211a9 | 1858 | |
d883348d JB |
1859 | ;;; Division from the left. |
1860 | (defun calcFunc-ldiv (a b) | |
d0158f73 JB |
1861 | (if (math-known-scalarp a) |
1862 | (math-div b a) | |
1863 | (math-mul (math-pow a -1) b))) | |
136211a9 EZ |
1864 | |
1865 | (defun calcFunc-mod (a b) | |
898ea5c0 | 1866 | (math-normalize (list '% a b))) |
136211a9 EZ |
1867 | |
1868 | (defun math-mod-fancy (a b) | |
1869 | (cond ((equal b '(var inf var-inf)) | |
1870 | (if (or (math-posp a) (math-zerop a)) | |
1871 | a | |
1872 | (if (math-negp a) | |
1873 | b | |
1874 | (if (eq (car-safe a) 'intv) | |
1875 | (if (math-negp (nth 2 a)) | |
1876 | '(intv 3 0 (var inf var-inf)) | |
1877 | a) | |
1878 | (list '% a b))))) | |
1879 | ((and (eq (car-safe a) 'mod) (Math-realp b) (math-posp b)) | |
1880 | (math-make-mod (nth 1 a) b)) | |
1881 | ((and (eq (car-safe a) 'intv) (math-intv-constp a t) (math-posp b)) | |
1882 | (math-mod-intv a b)) | |
1883 | (t | |
1884 | (if (Math-anglep a) | |
1885 | (calc-record-why 'anglep b) | |
1886 | (calc-record-why 'anglep a)) | |
898ea5c0 | 1887 | (list '% a b)))) |
136211a9 EZ |
1888 | |
1889 | ||
1890 | (defun calcFunc-pow (a b) | |
898ea5c0 | 1891 | (math-normalize (list '^ a b))) |
136211a9 EZ |
1892 | |
1893 | (defun math-pow-of-zero (a b) | |
6adaed78 JB |
1894 | "Raise A to the power of B, where A is a form of zero." |
1895 | (if (math-floatp b) (setq a (math-float a))) | |
1896 | (cond | |
1897 | ;; 0^0 = 1 | |
1898 | ((eq b 0) | |
1899 | 1) | |
1900 | ;; 0^0.0, etc., are undetermined | |
1901 | ((Math-zerop b) | |
1902 | (if calc-infinite-mode | |
1903 | '(var nan var-nan) | |
1904 | (math-reject-arg (list '^ a b) "*Indeterminate form"))) | |
1905 | ;; 0^positive = 0 | |
773a144d | 1906 | ((math-known-posp b) |
6adaed78 JB |
1907 | a) |
1908 | ;; 0^negative is undefined (let math-div handle it) | |
773a144d | 1909 | ((math-known-negp b) |
6adaed78 JB |
1910 | (math-div 1 a)) |
1911 | ;; 0^infinity is undefined | |
1912 | ((math-infinitep b) | |
1913 | '(var nan var-nan)) | |
1914 | ;; Some intervals | |
1915 | ((and (eq (car b) 'intv) | |
1916 | calc-infinite-mode | |
1917 | (math-negp (nth 2 b)) | |
1918 | (math-posp (nth 3 b))) | |
1919 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf))) | |
1920 | ;; If none of the above, leave it alone. | |
1921 | (t | |
1922 | (list '^ a b)))) | |
136211a9 EZ |
1923 | |
1924 | (defun math-pow-zero (a b) | |
1925 | (if (eq (car-safe a) 'mod) | |
1926 | (math-make-mod 1 (nth 2 a)) | |
1927 | (if (math-known-matrixp a) | |
1928 | (math-mimic-ident 1 a) | |
1929 | (if (math-infinitep a) | |
1930 | '(var nan var-nan) | |
1931 | (if (and (eq (car a) 'intv) (math-intv-constp a) | |
1932 | (or (and (not (math-posp a)) (not (math-negp a))) | |
1933 | (not (math-intv-constp a t)))) | |
1934 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) | |
1935 | (if (or (math-floatp a) (math-floatp b)) | |
898ea5c0 | 1936 | '(float 1 0) 1)))))) |
136211a9 EZ |
1937 | |
1938 | (defun math-pow-fancy (a b) | |
1939 | (cond ((and (Math-numberp a) (Math-numberp b)) | |
1940 | (or (if (memq (math-quarter-integer b) '(1 2 3)) | |
1941 | (let ((sqrt (math-sqrt (if (math-floatp b) | |
1942 | (math-float a) a)))) | |
1943 | (and (Math-numberp sqrt) | |
1944 | (math-pow sqrt (math-mul 2 b)))) | |
1945 | (and (eq (car b) 'frac) | |
1946 | (integerp (nth 2 b)) | |
1947 | (<= (nth 2 b) 10) | |
1948 | (let ((root (math-nth-root a (nth 2 b)))) | |
1949 | (and root (math-ipow root (nth 1 b)))))) | |
1950 | (and (or (eq a 10) (equal a '(float 1 1))) | |
1951 | (math-num-integerp b) | |
1952 | (calcFunc-scf '(float 1 0) b)) | |
1953 | (and calc-symbolic-mode | |
1954 | (list '^ a b)) | |
1955 | (math-with-extra-prec 2 | |
1956 | (math-exp-raw | |
1957 | (math-float (math-mul b (math-ln-raw (math-float a)))))))) | |
1958 | ((or (not (Math-objvecp a)) | |
1959 | (not (Math-objectp b))) | |
1960 | (let (temp) | |
1961 | (cond ((and math-simplify-only | |
1962 | (not (equal a math-simplify-only))) | |
1963 | (list '^ a b)) | |
05d28205 JB |
1964 | ((and (eq (car-safe a) '*) |
1965 | (or | |
1966 | (and | |
1967 | (math-known-matrixp (nth 1 a)) | |
1968 | (math-known-matrixp (nth 2 a))) | |
1969 | (and | |
1970 | calc-matrix-mode | |
1971 | (not (eq calc-matrix-mode 'scalar)) | |
1972 | (and (not (math-known-scalarp (nth 1 a))) | |
1973 | (not (math-known-scalarp (nth 2 a))))))) | |
1974 | (if (and (= b -1) | |
1975 | (math-known-square-matrixp (nth 1 a)) | |
1976 | (math-known-square-matrixp (nth 2 a))) | |
2f884e83 JB |
1977 | (math-mul (math-pow-fancy (nth 2 a) -1) |
1978 | (math-pow-fancy (nth 1 a) -1)) | |
05d28205 | 1979 | (list '^ a b))) |
136211a9 EZ |
1980 | ((and (eq (car-safe a) '*) |
1981 | (or (math-known-num-integerp b) | |
1982 | (math-known-nonnegp (nth 1 a)) | |
1983 | (math-known-nonnegp (nth 2 a)))) | |
1984 | (math-mul (math-pow (nth 1 a) b) | |
1985 | (math-pow (nth 2 a) b))) | |
1986 | ((and (eq (car-safe a) '/) | |
1987 | (or (math-known-num-integerp b) | |
1988 | (math-known-nonnegp (nth 2 a)))) | |
1989 | (math-div (math-pow (nth 1 a) b) | |
1990 | (math-pow (nth 2 a) b))) | |
1991 | ((and (eq (car-safe a) '/) | |
1992 | (math-known-nonnegp (nth 1 a)) | |
1993 | (not (math-equal-int (nth 1 a) 1))) | |
1994 | (math-mul (math-pow (nth 1 a) b) | |
1995 | (math-pow (math-div 1 (nth 2 a)) b))) | |
1996 | ((and (eq (car-safe a) '^) | |
1997 | (or (math-known-num-integerp b) | |
1998 | (math-known-nonnegp (nth 1 a)))) | |
1999 | (math-pow (nth 1 a) (math-mul (nth 2 a) b))) | |
2000 | ((and (eq (car-safe a) 'calcFunc-sqrt) | |
2001 | (or (math-known-num-integerp b) | |
2002 | (math-known-nonnegp (nth 1 a)))) | |
2003 | (math-pow (nth 1 a) (math-div b 2))) | |
2004 | ((and (eq (car-safe a) '^) | |
2005 | (math-known-evenp (nth 2 a)) | |
2006 | (memq (math-quarter-integer b) '(1 2 3)) | |
2007 | (math-known-realp (nth 1 a))) | |
2008 | (math-abs (math-pow (nth 1 a) (math-mul (nth 2 a) b)))) | |
2009 | ((and (math-looks-negp a) | |
2010 | (math-known-integerp b) | |
2011 | (setq temp (or (and (math-known-evenp b) | |
2012 | (math-pow (math-neg a) b)) | |
2013 | (and (math-known-oddp b) | |
2014 | (math-neg (math-pow (math-neg a) | |
2015 | b)))))) | |
2016 | temp) | |
2017 | ((and (eq (car-safe a) 'calcFunc-abs) | |
2018 | (math-known-realp (nth 1 a)) | |
2019 | (math-known-evenp b)) | |
2020 | (math-pow (nth 1 a) b)) | |
2021 | ((math-infinitep a) | |
2022 | (cond ((equal a '(var nan var-nan)) | |
2023 | a) | |
2024 | ((eq (car a) 'neg) | |
2025 | (math-mul (math-pow -1 b) (math-pow (nth 1 a) b))) | |
2026 | ((math-posp b) | |
2027 | a) | |
2028 | ((math-negp b) | |
2029 | (if (math-floatp b) '(float 0 0) 0)) | |
2030 | ((and (eq (car-safe b) 'intv) | |
2031 | (math-intv-constp b)) | |
2032 | '(intv 3 0 (var inf var-inf))) | |
2033 | (t | |
2034 | '(var nan var-nan)))) | |
2035 | ((math-infinitep b) | |
2036 | (let (scale) | |
2037 | (cond ((math-negp b) | |
2038 | (math-pow (math-div 1 a) (math-neg b))) | |
2039 | ((not (math-posp b)) | |
2040 | '(var nan var-nan)) | |
2041 | ((math-equal-int (setq scale (calcFunc-abssqr a)) 1) | |
2042 | '(var nan var-nan)) | |
2043 | ((Math-lessp scale 1) | |
2044 | (if (math-floatp a) '(float 0 0) 0)) | |
2045 | ((Math-lessp 1 a) | |
2046 | b) | |
2047 | ((Math-lessp a -1) | |
2048 | '(var uinf var-uinf)) | |
2049 | ((and (eq (car a) 'intv) | |
2050 | (math-intv-constp a)) | |
2051 | (if (Math-lessp -1 a) | |
2052 | (if (math-equal-int (nth 3 a) 1) | |
2053 | '(intv 3 0 1) | |
2054 | '(intv 3 0 (var inf var-inf))) | |
2055 | '(intv 3 (neg (var inf var-inf)) | |
2056 | (var inf var-inf)))) | |
2057 | (t (list '^ a b))))) | |
2058 | ((and (eq (car-safe a) 'calcFunc-idn) | |
2059 | (= (length a) 2) | |
2060 | (math-known-num-integerp b)) | |
2061 | (list 'calcFunc-idn (math-pow (nth 1 a) b))) | |
2062 | (t (if (Math-objectp a) | |
2063 | (calc-record-why 'objectp b) | |
2064 | (calc-record-why 'objectp a)) | |
2065 | (list '^ a b))))) | |
2066 | ((and (eq (car-safe a) 'sdev) (eq (car-safe b) 'sdev)) | |
2067 | (if (and (math-constp a) (math-constp b)) | |
2068 | (math-with-extra-prec 2 | |
2069 | (let* ((ln (math-ln-raw (math-float (nth 1 a)))) | |
2070 | (pow (math-exp-raw | |
2071 | (math-float (math-mul (nth 1 b) ln))))) | |
2072 | (math-make-sdev | |
2073 | pow | |
2074 | (math-mul | |
2075 | pow | |
2076 | (math-hypot (math-mul (nth 2 a) | |
2077 | (math-div (nth 1 b) (nth 1 a))) | |
2078 | (math-mul (nth 2 b) ln)))))) | |
2079 | (let ((pow (math-pow (nth 1 a) (nth 1 b)))) | |
2080 | (math-make-sdev | |
2081 | pow | |
2082 | (math-mul pow | |
2083 | (math-hypot (math-mul (nth 2 a) | |
2084 | (math-div (nth 1 b) (nth 1 a))) | |
2085 | (math-mul (nth 2 b) (calcFunc-ln | |
2086 | (nth 1 a))))))))) | |
2087 | ((and (eq (car-safe a) 'sdev) (Math-numberp b)) | |
2088 | (if (math-constp a) | |
2089 | (math-with-extra-prec 2 | |
2090 | (let ((pow (math-pow (nth 1 a) (math-sub b 1)))) | |
2091 | (math-make-sdev (math-mul pow (nth 1 a)) | |
2092 | (math-mul pow (math-mul (nth 2 a) b))))) | |
2093 | (math-make-sdev (math-pow (nth 1 a) b) | |
2094 | (math-mul (math-pow (nth 1 a) (math-add b -1)) | |
2095 | (math-mul (nth 2 a) b))))) | |
2096 | ((and (eq (car-safe b) 'sdev) (Math-numberp a)) | |
2097 | (math-with-extra-prec 2 | |
2098 | (let* ((ln (math-ln-raw (math-float a))) | |
2099 | (pow (calcFunc-exp (math-mul (nth 1 b) ln)))) | |
2100 | (math-make-sdev pow (math-mul pow (math-mul (nth 2 b) ln)))))) | |
2101 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) | |
2102 | (Math-realp b) | |
2103 | (or (Math-natnump b) | |
2104 | (Math-posp (nth 2 a)) | |
2105 | (and (math-zerop (nth 2 a)) | |
2106 | (or (Math-posp b) | |
2107 | (and (Math-integerp b) calc-infinite-mode))) | |
2108 | (Math-negp (nth 3 a)) | |
2109 | (and (math-zerop (nth 3 a)) | |
2110 | (or (Math-posp b) | |
2111 | (and (Math-integerp b) calc-infinite-mode))))) | |
2112 | (if (math-evenp b) | |
2113 | (setq a (math-abs a))) | |
2114 | (let ((calc-infinite-mode (if (math-zerop (nth 3 a)) -1 1))) | |
2115 | (math-sort-intv (nth 1 a) | |
2116 | (math-pow (nth 2 a) b) | |
2117 | (math-pow (nth 3 a) b)))) | |
2118 | ((and (eq (car-safe b) 'intv) (math-intv-constp b) | |
2119 | (Math-realp a) (Math-posp a)) | |
2120 | (math-sort-intv (nth 1 b) | |
2121 | (math-pow a (nth 2 b)) | |
2122 | (math-pow a (nth 3 b)))) | |
2123 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) | |
2124 | (eq (car-safe b) 'intv) (math-intv-constp b) | |
2125 | (or (and (not (Math-negp (nth 2 a))) | |
2126 | (not (Math-negp (nth 2 b)))) | |
2127 | (and (Math-posp (nth 2 a)) | |
2128 | (not (Math-posp (nth 3 b)))))) | |
2129 | (let ((lo (math-pow a (nth 2 b))) | |
2130 | (hi (math-pow a (nth 3 b)))) | |
2131 | (or (eq (car-safe lo) 'intv) | |
2132 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) lo lo))) | |
2133 | (or (eq (car-safe hi) 'intv) | |
2134 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) hi hi))) | |
2135 | (math-combine-intervals | |
2136 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) | |
2137 | (math-infinitep (nth 2 lo))) | |
2138 | (memq (nth 1 lo) '(2 3))) | |
2139 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) | |
2140 | (math-infinitep (nth 3 lo))) | |
2141 | (memq (nth 1 lo) '(1 3))) | |
2142 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) | |
2143 | (math-infinitep (nth 2 hi))) | |
2144 | (memq (nth 1 hi) '(2 3))) | |
2145 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) | |
2146 | (math-infinitep (nth 3 hi))) | |
2147 | (memq (nth 1 hi) '(1 3)))))) | |
2148 | ((and (eq (car-safe a) 'mod) (eq (car-safe b) 'mod) | |
2149 | (equal (nth 2 a) (nth 2 b))) | |
2150 | (math-make-mod (math-pow-mod (nth 1 a) (nth 1 b) (nth 2 a)) | |
2151 | (nth 2 a))) | |
2152 | ((and (eq (car-safe a) 'mod) (Math-anglep b)) | |
2153 | (math-make-mod (math-pow-mod (nth 1 a) b (nth 2 a)) (nth 2 a))) | |
2154 | ((and (eq (car-safe b) 'mod) (Math-anglep a)) | |
2155 | (math-make-mod (math-pow-mod a (nth 1 b) (nth 2 b)) (nth 2 b))) | |
2156 | ((not (Math-numberp a)) | |
2157 | (math-reject-arg a 'numberp)) | |
2158 | (t | |
898ea5c0 | 2159 | (math-reject-arg b 'numberp)))) |
136211a9 EZ |
2160 | |
2161 | (defun math-quarter-integer (x) | |
2162 | (if (Math-integerp x) | |
2163 | 0 | |
2164 | (if (math-negp x) | |
2165 | (progn | |
2166 | (setq x (math-quarter-integer (math-neg x))) | |
2167 | (and x (- 4 x))) | |
2168 | (if (eq (car x) 'frac) | |
2169 | (if (eq (nth 2 x) 2) | |
2170 | 2 | |
2171 | (and (eq (nth 2 x) 4) | |
2172 | (progn | |
2173 | (setq x (nth 1 x)) | |
2174 | (% (if (consp x) (nth 1 x) x) 4)))) | |
2175 | (if (eq (car x) 'float) | |
2176 | (if (>= (nth 2 x) 0) | |
2177 | 0 | |
2178 | (if (= (nth 2 x) -1) | |
2179 | (progn | |
2180 | (setq x (nth 1 x)) | |
2181 | (and (= (% (if (consp x) (nth 1 x) x) 10) 5) 2)) | |
2182 | (if (= (nth 2 x) -2) | |
2183 | (progn | |
2184 | (setq x (nth 1 x) | |
2185 | x (% (if (consp x) (nth 1 x) x) 100)) | |
2186 | (if (= x 25) 1 | |
898ea5c0 | 2187 | (if (= x 75) 3))))))))))) |
136211a9 EZ |
2188 | |
2189 | ;;; This assumes A < M and M > 0. | |
2190 | (defun math-pow-mod (a b m) ; [R R R R] | |
2191 | (if (and (Math-integerp a) (Math-integerp b) (Math-integerp m)) | |
2192 | (if (Math-negp b) | |
2193 | (math-div-mod 1 (math-pow-mod a (Math-integer-neg b) m) m) | |
2194 | (if (eq m 1) | |
2195 | 0 | |
2196 | (math-pow-mod-step a b m))) | |
898ea5c0 | 2197 | (math-mod (math-pow a b) m))) |
136211a9 EZ |
2198 | |
2199 | (defun math-pow-mod-step (a n m) ; [I I I I] | |
2200 | (math-working "pow" a) | |
2201 | (let ((val (cond | |
2202 | ((eq n 0) 1) | |
2203 | ((eq n 1) a) | |
2204 | (t | |
2205 | (let ((rest (math-pow-mod-step | |
2206 | (math-imod (math-mul a a) m) | |
2207 | (math-div2 n) | |
2208 | m))) | |
2209 | (if (math-evenp n) | |
2210 | rest | |
2211 | (math-mod (math-mul a rest) m))))))) | |
2212 | (math-working "pow" val) | |
898ea5c0 | 2213 | val)) |
136211a9 EZ |
2214 | |
2215 | ||
2216 | ;;; Compute the minimum of two real numbers. [R R R] [Public] | |
2217 | (defun math-min (a b) | |
2218 | (if (and (consp a) (eq (car a) 'intv)) | |
2219 | (if (and (consp b) (eq (car b) 'intv)) | |
2220 | (let ((lo (nth 2 a)) | |
2221 | (lom (memq (nth 1 a) '(2 3))) | |
2222 | (hi (nth 3 a)) | |
2223 | (him (memq (nth 1 a) '(1 3))) | |
2224 | res) | |
2225 | (if (= (setq res (math-compare (nth 2 b) lo)) -1) | |
2226 | (setq lo (nth 2 b) lom (memq (nth 1 b) '(2 3))) | |
2227 | (if (= res 0) | |
2228 | (setq lom (or lom (memq (nth 1 b) '(2 3)))))) | |
2229 | (if (= (setq res (math-compare (nth 3 b) hi)) -1) | |
2230 | (setq hi (nth 3 b) him (memq (nth 1 b) '(1 3))) | |
2231 | (if (= res 0) | |
2232 | (setq him (or him (memq (nth 1 b) '(1 3)))))) | |
2233 | (math-make-intv (+ (if lom 2 0) (if him 1 0)) lo hi)) | |
2234 | (math-min a (list 'intv 3 b b))) | |
2235 | (if (and (consp b) (eq (car b) 'intv)) | |
2236 | (math-min (list 'intv 3 a a) b) | |
2237 | (let ((res (math-compare a b))) | |
2238 | (if (= res 1) | |
2239 | b | |
2240 | (if (= res 2) | |
2241 | '(var nan var-nan) | |
898ea5c0 | 2242 | a)))))) |
136211a9 EZ |
2243 | |
2244 | (defun calcFunc-min (&optional a &rest b) | |
2245 | (if (not a) | |
2246 | '(var inf var-inf) | |
2247 | (if (not (or (Math-anglep a) (eq (car a) 'date) | |
2248 | (and (eq (car a) 'intv) (math-intv-constp a)) | |
2249 | (math-infinitep a))) | |
2250 | (math-reject-arg a 'anglep)) | |
898ea5c0 | 2251 | (math-min-list a b))) |
136211a9 EZ |
2252 | |
2253 | (defun math-min-list (a b) | |
2254 | (if b | |
2255 | (if (or (Math-anglep (car b)) (eq (car b) 'date) | |
2256 | (and (eq (car (car b)) 'intv) (math-intv-constp (car b))) | |
2257 | (math-infinitep (car b))) | |
2258 | (math-min-list (math-min a (car b)) (cdr b)) | |
2259 | (math-reject-arg (car b) 'anglep)) | |
898ea5c0 | 2260 | a)) |
136211a9 EZ |
2261 | |
2262 | ;;; Compute the maximum of two real numbers. [R R R] [Public] | |
2263 | (defun math-max (a b) | |
2264 | (if (or (and (consp a) (eq (car a) 'intv)) | |
2265 | (and (consp b) (eq (car b) 'intv))) | |
2266 | (math-neg (math-min (math-neg a) (math-neg b))) | |
2267 | (let ((res (math-compare a b))) | |
2268 | (if (= res -1) | |
2269 | b | |
2270 | (if (= res 2) | |
2271 | '(var nan var-nan) | |
898ea5c0 | 2272 | a))))) |
136211a9 EZ |
2273 | |
2274 | (defun calcFunc-max (&optional a &rest b) | |
2275 | (if (not a) | |
2276 | '(neg (var inf var-inf)) | |
2277 | (if (not (or (Math-anglep a) (eq (car a) 'date) | |
2278 | (and (eq (car a) 'intv) (math-intv-constp a)) | |
2279 | (math-infinitep a))) | |
2280 | (math-reject-arg a 'anglep)) | |
898ea5c0 | 2281 | (math-max-list a b))) |
136211a9 EZ |
2282 | |
2283 | (defun math-max-list (a b) | |
2284 | (if b | |
2285 | (if (or (Math-anglep (car b)) (eq (car b) 'date) | |
2286 | (and (eq (car (car b)) 'intv) (math-intv-constp (car b))) | |
2287 | (math-infinitep (car b))) | |
2288 | (math-max-list (math-max a (car b)) (cdr b)) | |
2289 | (math-reject-arg (car b) 'anglep)) | |
898ea5c0 | 2290 | a)) |
136211a9 EZ |
2291 | |
2292 | ||
2293 | ;;; Compute the absolute value of A. [O O; r r] [Public] | |
2294 | (defun math-abs (a) | |
2295 | (cond ((Math-negp a) | |
2296 | (math-neg a)) | |
2297 | ((Math-anglep a) | |
2298 | a) | |
2299 | ((eq (car a) 'cplx) | |
2300 | (math-hypot (nth 1 a) (nth 2 a))) | |
2301 | ((eq (car a) 'polar) | |
2302 | (nth 1 a)) | |
2303 | ((eq (car a) 'vec) | |
2304 | (if (cdr (cdr (cdr a))) | |
2305 | (math-sqrt (calcFunc-abssqr a)) | |
2306 | (if (cdr (cdr a)) | |
2307 | (math-hypot (nth 1 a) (nth 2 a)) | |
2308 | (if (cdr a) | |
2309 | (math-abs (nth 1 a)) | |
2310 | a)))) | |
2311 | ((eq (car a) 'sdev) | |
2312 | (list 'sdev (math-abs (nth 1 a)) (nth 2 a))) | |
2313 | ((and (eq (car a) 'intv) (math-intv-constp a)) | |
2314 | (if (Math-posp a) | |
2315 | a | |
2316 | (let* ((nlo (math-neg (nth 2 a))) | |
2317 | (res (math-compare nlo (nth 3 a)))) | |
2318 | (cond ((= res 1) | |
2319 | (math-make-intv (if (memq (nth 1 a) '(0 1)) 2 3) 0 nlo)) | |
2320 | ((= res 0) | |
2321 | (math-make-intv (if (eq (nth 1 a) 0) 2 3) 0 nlo)) | |
2322 | (t | |
2323 | (math-make-intv (if (memq (nth 1 a) '(0 2)) 2 3) | |
2324 | 0 (nth 3 a))))))) | |
2325 | ((math-looks-negp a) | |
2326 | (list 'calcFunc-abs (math-neg a))) | |
2327 | ((let ((signs (math-possible-signs a))) | |
2328 | (or (and (memq signs '(2 4 6)) a) | |
2329 | (and (memq signs '(1 3)) (math-neg a))))) | |
2330 | ((let ((inf (math-infinitep a))) | |
2331 | (and inf | |
2332 | (if (equal inf '(var nan var-nan)) | |
2333 | inf | |
2334 | '(var inf var-inf))))) | |
2335 | (t (calc-record-why 'numvecp a) | |
898ea5c0 | 2336 | (list 'calcFunc-abs a)))) |
136211a9 | 2337 | |
898ea5c0 | 2338 | (defalias 'calcFunc-abs 'math-abs) |
136211a9 EZ |
2339 | |
2340 | (defun math-float-fancy (a) | |
2341 | (cond ((eq (car a) 'intv) | |
2342 | (cons (car a) (cons (nth 1 a) (mapcar 'math-float (nthcdr 2 a))))) | |
2343 | ((and (memq (car a) '(* /)) | |
2344 | (math-numberp (nth 1 a))) | |
2345 | (list (car a) (math-float (nth 1 a)) | |
2346 | (list 'calcFunc-float (nth 2 a)))) | |
2347 | ((and (eq (car a) '/) | |
2348 | (eq (car (nth 1 a)) '*) | |
2349 | (math-numberp (nth 1 (nth 1 a)))) | |
2350 | (list '* (math-float (nth 1 (nth 1 a))) | |
2351 | (list 'calcFunc-float (list '/ (nth 2 (nth 1 a)) (nth 2 a))))) | |
2352 | ((math-infinitep a) a) | |
2353 | ((eq (car a) 'calcFunc-float) a) | |
2354 | ((let ((func (assq (car a) '((calcFunc-floor . calcFunc-ffloor) | |
2355 | (calcFunc-ceil . calcFunc-fceil) | |
2356 | (calcFunc-trunc . calcFunc-ftrunc) | |
2357 | (calcFunc-round . calcFunc-fround) | |
2358 | (calcFunc-rounde . calcFunc-frounde) | |
2359 | (calcFunc-roundu . calcFunc-froundu))))) | |
2360 | (and func (cons (cdr func) (cdr a))))) | |
898ea5c0 | 2361 | (t (math-reject-arg a 'objectp)))) |
136211a9 | 2362 | |
898ea5c0 | 2363 | (defalias 'calcFunc-float 'math-float) |
136211a9 | 2364 | |
67549a85 JB |
2365 | ;; The variable math-trunc-prec is local to math-trunc in calc-misc.el, |
2366 | ;; but used by math-trunc-fancy which is called by math-trunc. | |
2367 | (defvar math-trunc-prec) | |
2368 | ||
136211a9 EZ |
2369 | (defun math-trunc-fancy (a) |
2370 | (cond ((eq (car a) 'frac) (math-quotient (nth 1 a) (nth 2 a))) | |
2371 | ((eq (car a) 'cplx) (math-trunc (nth 1 a))) | |
2372 | ((eq (car a) 'polar) (math-trunc (math-complex a))) | |
2373 | ((eq (car a) 'hms) (list 'hms (nth 1 a) 0 0)) | |
2374 | ((eq (car a) 'date) (list 'date (math-trunc (nth 1 a)))) | |
2375 | ((eq (car a) 'mod) | |
2376 | (if (math-messy-integerp (nth 2 a)) | |
2377 | (math-trunc (math-make-mod (nth 1 a) (math-trunc (nth 2 a)))) | |
2378 | (math-make-mod (math-trunc (nth 1 a)) (nth 2 a)))) | |
2379 | ((eq (car a) 'intv) | |
2380 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) | |
2381 | (memq (nth 1 a) '(0 1))) | |
2382 | 0 2) | |
2383 | (if (and (equal (nth 3 a) '(var inf var-inf)) | |
2384 | (memq (nth 1 a) '(0 2))) | |
2385 | 0 1)) | |
2386 | (if (and (Math-negp (nth 2 a)) | |
2387 | (Math-num-integerp (nth 2 a)) | |
2388 | (memq (nth 1 a) '(0 1))) | |
2389 | (math-add (math-trunc (nth 2 a)) 1) | |
2390 | (math-trunc (nth 2 a))) | |
2391 | (if (and (Math-posp (nth 3 a)) | |
2392 | (Math-num-integerp (nth 3 a)) | |
2393 | (memq (nth 1 a) '(0 2))) | |
2394 | (math-add (math-trunc (nth 3 a)) -1) | |
2395 | (math-trunc (nth 3 a))))) | |
2396 | ((math-provably-integerp a) a) | |
2397 | ((Math-vectorp a) | |
67549a85 | 2398 | (math-map-vec (function (lambda (x) (math-trunc x math-trunc-prec))) a)) |
136211a9 EZ |
2399 | ((math-infinitep a) |
2400 | (if (or (math-posp a) (math-negp a)) | |
2401 | a | |
2402 | '(var nan var-nan))) | |
2403 | ((math-to-integer a)) | |
898ea5c0 | 2404 | (t (math-reject-arg a 'numberp)))) |
136211a9 EZ |
2405 | |
2406 | (defun math-trunc-special (a prec) | |
2407 | (if (Math-messy-integerp prec) | |
2408 | (setq prec (math-trunc prec))) | |
2409 | (or (integerp prec) | |
2410 | (math-reject-arg prec 'fixnump)) | |
2411 | (if (and (<= prec 0) | |
2412 | (math-provably-integerp a)) | |
2413 | a | |
2414 | (calcFunc-scf (math-trunc (let ((calc-prefer-frac t)) | |
2415 | (calcFunc-scf a prec))) | |
898ea5c0 | 2416 | (- prec)))) |
136211a9 EZ |
2417 | |
2418 | (defun math-to-integer (a) | |
2419 | (let ((func (assq (car-safe a) '((calcFunc-ffloor . calcFunc-floor) | |
2420 | (calcFunc-fceil . calcFunc-ceil) | |
2421 | (calcFunc-ftrunc . calcFunc-trunc) | |
2422 | (calcFunc-fround . calcFunc-round) | |
2423 | (calcFunc-frounde . calcFunc-rounde) | |
2424 | (calcFunc-froundu . calcFunc-roundu))))) | |
2425 | (and func (= (length a) 2) | |
898ea5c0 | 2426 | (cons (cdr func) (cdr a))))) |
136211a9 EZ |
2427 | |
2428 | (defun calcFunc-ftrunc (a &optional prec) | |
2429 | (if (and (Math-messy-integerp a) | |
2430 | (or (not prec) (and (integerp prec) | |
2431 | (<= prec 0)))) | |
2432 | a | |
898ea5c0 | 2433 | (math-float (math-trunc a prec)))) |
136211a9 | 2434 | |
67549a85 JB |
2435 | ;; The variable math-floor-prec is local to math-floor in calc-misc.el, |
2436 | ;; but used by math-floor-fancy which is called by math-floor. | |
2437 | (defvar math-floor-prec) | |
2438 | ||
136211a9 EZ |
2439 | (defun math-floor-fancy (a) |
2440 | (cond ((math-provably-integerp a) a) | |
2441 | ((eq (car a) 'hms) | |
2442 | (if (or (math-posp a) | |
2443 | (and (math-zerop (nth 2 a)) | |
2444 | (math-zerop (nth 3 a)))) | |
2445 | (math-trunc a) | |
2446 | (math-add (math-trunc a) -1))) | |
2447 | ((eq (car a) 'date) (list 'date (math-floor (nth 1 a)))) | |
2448 | ((eq (car a) 'intv) | |
2449 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) | |
2450 | (memq (nth 1 a) '(0 1))) | |
2451 | 0 2) | |
2452 | (if (and (equal (nth 3 a) '(var inf var-inf)) | |
2453 | (memq (nth 1 a) '(0 2))) | |
2454 | 0 1)) | |
2455 | (math-floor (nth 2 a)) | |
2456 | (if (and (Math-num-integerp (nth 3 a)) | |
2457 | (memq (nth 1 a) '(0 2))) | |
2458 | (math-add (math-floor (nth 3 a)) -1) | |
2459 | (math-floor (nth 3 a))))) | |
2460 | ((Math-vectorp a) | |
95d91710 | 2461 | (math-map-vec (function (lambda (x) (math-floor x math-floor-prec))) a)) |
136211a9 EZ |
2462 | ((math-infinitep a) |
2463 | (if (or (math-posp a) (math-negp a)) | |
2464 | a | |
2465 | '(var nan var-nan))) | |
2466 | ((math-to-integer a)) | |
898ea5c0 | 2467 | (t (math-reject-arg a 'anglep)))) |
136211a9 EZ |
2468 | |
2469 | (defun math-floor-special (a prec) | |
2470 | (if (Math-messy-integerp prec) | |
2471 | (setq prec (math-trunc prec))) | |
2472 | (or (integerp prec) | |
2473 | (math-reject-arg prec 'fixnump)) | |
2474 | (if (and (<= prec 0) | |
2475 | (math-provably-integerp a)) | |
2476 | a | |
2477 | (calcFunc-scf (math-floor (let ((calc-prefer-frac t)) | |
2478 | (calcFunc-scf a prec))) | |
898ea5c0 | 2479 | (- prec)))) |
136211a9 EZ |
2480 | |
2481 | (defun calcFunc-ffloor (a &optional prec) | |
2482 | (if (and (Math-messy-integerp a) | |
2483 | (or (not prec) (and (integerp prec) | |
2484 | (<= prec 0)))) | |
2485 | a | |
898ea5c0 | 2486 | (math-float (math-floor a prec)))) |
136211a9 EZ |
2487 | |
2488 | ;;; Coerce A to be an integer (by truncation toward plus infinity). [I N] | |
2489 | (defun math-ceiling (a &optional prec) ; [Public] | |
2490 | (cond (prec | |
2491 | (if (Math-messy-integerp prec) | |
2492 | (setq prec (math-trunc prec))) | |
2493 | (or (integerp prec) | |
2494 | (math-reject-arg prec 'fixnump)) | |
2495 | (if (and (<= prec 0) | |
2496 | (math-provably-integerp a)) | |
2497 | a | |
2498 | (calcFunc-scf (math-ceiling (let ((calc-prefer-frac t)) | |
2499 | (calcFunc-scf a prec))) | |
2500 | (- prec)))) | |
2501 | ((Math-integerp a) a) | |
2502 | ((Math-messy-integerp a) (math-trunc a)) | |
2503 | ((Math-realp a) | |
2504 | (if (Math-posp a) | |
2505 | (math-add (math-trunc a) 1) | |
2506 | (math-trunc a))) | |
2507 | ((math-provably-integerp a) a) | |
2508 | ((eq (car a) 'hms) | |
2509 | (if (or (math-negp a) | |
2510 | (and (math-zerop (nth 2 a)) | |
2511 | (math-zerop (nth 3 a)))) | |
2512 | (math-trunc a) | |
2513 | (math-add (math-trunc a) 1))) | |
2514 | ((eq (car a) 'date) (list 'date (math-ceiling (nth 1 a)))) | |
2515 | ((eq (car a) 'intv) | |
2516 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) | |
2517 | (memq (nth 1 a) '(0 1))) | |
2518 | 0 2) | |
2519 | (if (and (equal (nth 3 a) '(var inf var-inf)) | |
2520 | (memq (nth 1 a) '(0 2))) | |
2521 | 0 1)) | |
2522 | (if (and (Math-num-integerp (nth 2 a)) | |
2523 | (memq (nth 1 a) '(0 1))) | |
2524 | (math-add (math-floor (nth 2 a)) 1) | |
2525 | (math-ceiling (nth 2 a))) | |
2526 | (math-ceiling (nth 3 a)))) | |
2527 | ((Math-vectorp a) | |
2528 | (math-map-vec (function (lambda (x) (math-ceiling x prec))) a)) | |
2529 | ((math-infinitep a) | |
2530 | (if (or (math-posp a) (math-negp a)) | |
2531 | a | |
2532 | '(var nan var-nan))) | |
2533 | ((math-to-integer a)) | |
898ea5c0 CW |
2534 | (t (math-reject-arg a 'anglep)))) |
2535 | ||
2536 | (defalias 'calcFunc-ceil 'math-ceiling) | |
136211a9 EZ |
2537 | |
2538 | (defun calcFunc-fceil (a &optional prec) | |
2539 | (if (and (Math-messy-integerp a) | |
2540 | (or (not prec) (and (integerp prec) | |
2541 | (<= prec 0)))) | |
2542 | a | |
898ea5c0 | 2543 | (math-float (math-ceiling a prec)))) |
136211a9 | 2544 | |
3132f345 | 2545 | (defvar math-rounding-mode nil) |
136211a9 EZ |
2546 | |
2547 | ;;; Coerce A to be an integer (by rounding to nearest integer). [I N] [Public] | |
2548 | (defun math-round (a &optional prec) | |
2549 | (cond (prec | |
2550 | (if (Math-messy-integerp prec) | |
2551 | (setq prec (math-trunc prec))) | |
2552 | (or (integerp prec) | |
2553 | (math-reject-arg prec 'fixnump)) | |
2554 | (if (and (<= prec 0) | |
2555 | (math-provably-integerp a)) | |
2556 | a | |
2557 | (calcFunc-scf (math-round (let ((calc-prefer-frac t)) | |
2558 | (calcFunc-scf a prec))) | |
2559 | (- prec)))) | |
2560 | ((Math-anglep a) | |
2561 | (if (Math-num-integerp a) | |
2562 | (math-trunc a) | |
2563 | (if (and (Math-negp a) (not (eq math-rounding-mode 'up))) | |
2564 | (math-neg (math-round (math-neg a))) | |
2565 | (setq a (let ((calc-angle-mode 'deg)) ; in case of HMS forms | |
2566 | (math-add a (if (Math-ratp a) | |
2567 | '(frac 1 2) | |
2568 | '(float 5 -1))))) | |
2569 | (if (and (Math-num-integerp a) (eq math-rounding-mode 'even)) | |
2570 | (progn | |
2571 | (setq a (math-floor a)) | |
2572 | (or (math-evenp a) | |
2573 | (setq a (math-sub a 1))) | |
2574 | a) | |
2575 | (math-floor a))))) | |
2576 | ((math-provably-integerp a) a) | |
2577 | ((eq (car a) 'date) (list 'date (math-round (nth 1 a)))) | |
2578 | ((eq (car a) 'intv) | |
2579 | (math-floor (math-add a '(frac 1 2)))) | |
2580 | ((Math-vectorp a) | |
2581 | (math-map-vec (function (lambda (x) (math-round x prec))) a)) | |
2582 | ((math-infinitep a) | |
2583 | (if (or (math-posp a) (math-negp a)) | |
2584 | a | |
2585 | '(var nan var-nan))) | |
2586 | ((math-to-integer a)) | |
898ea5c0 | 2587 | (t (math-reject-arg a 'anglep)))) |
136211a9 | 2588 | |
898ea5c0 CW |
2589 | (defalias 'calcFunc-round 'math-round) |
2590 | ||
2591 | (defsubst calcFunc-rounde (a &optional prec) | |
136211a9 | 2592 | (let ((math-rounding-mode 'even)) |
898ea5c0 | 2593 | (math-round a prec))) |
136211a9 | 2594 | |
898ea5c0 | 2595 | (defsubst calcFunc-roundu (a &optional prec) |
136211a9 | 2596 | (let ((math-rounding-mode 'up)) |
898ea5c0 | 2597 | (math-round a prec))) |
136211a9 EZ |
2598 | |
2599 | (defun calcFunc-fround (a &optional prec) | |
2600 | (if (and (Math-messy-integerp a) | |
2601 | (or (not prec) (and (integerp prec) | |
2602 | (<= prec 0)))) | |
2603 | a | |
898ea5c0 | 2604 | (math-float (math-round a prec)))) |
136211a9 | 2605 | |
898ea5c0 | 2606 | (defsubst calcFunc-frounde (a &optional prec) |
136211a9 | 2607 | (let ((math-rounding-mode 'even)) |
898ea5c0 | 2608 | (calcFunc-fround a prec))) |
136211a9 | 2609 | |
898ea5c0 | 2610 | (defsubst calcFunc-froundu (a &optional prec) |
136211a9 | 2611 | (let ((math-rounding-mode 'up)) |
898ea5c0 | 2612 | (calcFunc-fround a prec))) |
136211a9 EZ |
2613 | |
2614 | ;;; Pull floating-point values apart into mantissa and exponent. | |
2615 | (defun calcFunc-mant (x) | |
2616 | (if (Math-realp x) | |
2617 | (if (or (Math-ratp x) | |
2618 | (eq (nth 1 x) 0)) | |
2619 | x | |
2620 | (list 'float (nth 1 x) (- 1 (math-numdigs (nth 1 x))))) | |
2621 | (calc-record-why 'realp x) | |
898ea5c0 | 2622 | (list 'calcFunc-mant x))) |
136211a9 EZ |
2623 | |
2624 | (defun calcFunc-xpon (x) | |
2625 | (if (Math-realp x) | |
2626 | (if (or (Math-ratp x) | |
2627 | (eq (nth 1 x) 0)) | |
2628 | 0 | |
2629 | (math-normalize (+ (nth 2 x) (1- (math-numdigs (nth 1 x)))))) | |
2630 | (calc-record-why 'realp x) | |
898ea5c0 | 2631 | (list 'calcFunc-xpon x))) |
136211a9 EZ |
2632 | |
2633 | (defun calcFunc-scf (x n) | |
2634 | (if (integerp n) | |
2635 | (cond ((eq n 0) | |
2636 | x) | |
2637 | ((Math-integerp x) | |
2638 | (if (> n 0) | |
2639 | (math-scale-int x n) | |
2640 | (math-div x (math-scale-int 1 (- n))))) | |
2641 | ((eq (car x) 'frac) | |
2642 | (if (> n 0) | |
2643 | (math-make-frac (math-scale-int (nth 1 x) n) (nth 2 x)) | |
2644 | (math-make-frac (nth 1 x) (math-scale-int (nth 2 x) (- n))))) | |
2645 | ((eq (car x) 'float) | |
2646 | (math-make-float (nth 1 x) (+ (nth 2 x) n))) | |
2647 | ((memq (car x) '(cplx sdev)) | |
2648 | (math-normalize | |
2649 | (list (car x) | |
2650 | (calcFunc-scf (nth 1 x) n) | |
2651 | (calcFunc-scf (nth 2 x) n)))) | |
2652 | ((memq (car x) '(polar mod)) | |
2653 | (math-normalize | |
2654 | (list (car x) | |
2655 | (calcFunc-scf (nth 1 x) n) | |
2656 | (nth 2 x)))) | |
2657 | ((eq (car x) 'intv) | |
2658 | (math-normalize | |
2659 | (list (car x) | |
2660 | (nth 1 x) | |
2661 | (calcFunc-scf (nth 2 x) n) | |
2662 | (calcFunc-scf (nth 3 x) n)))) | |
2663 | ((eq (car x) 'vec) | |
2664 | (math-map-vec (function (lambda (x) (calcFunc-scf x n))) x)) | |
2665 | ((math-infinitep x) | |
2666 | x) | |
2667 | (t | |
2668 | (calc-record-why 'realp x) | |
2669 | (list 'calcFunc-scf x n))) | |
2670 | (if (math-messy-integerp n) | |
2671 | (if (< (nth 2 n) 10) | |
2672 | (calcFunc-scf x (math-trunc n)) | |
2673 | (math-overflow n)) | |
2674 | (if (math-integerp n) | |
2675 | (math-overflow n) | |
2676 | (calc-record-why 'integerp n) | |
898ea5c0 | 2677 | (list 'calcFunc-scf x n))))) |
136211a9 EZ |
2678 | |
2679 | ||
2680 | (defun calcFunc-incr (x &optional step relative-to) | |
2681 | (or step (setq step 1)) | |
2682 | (cond ((not (Math-integerp step)) | |
2683 | (math-reject-arg step 'integerp)) | |
2684 | ((Math-integerp x) | |
2685 | (math-add x step)) | |
2686 | ((eq (car x) 'float) | |
2687 | (if (and (math-zerop x) | |
2688 | (eq (car-safe relative-to) 'float)) | |
2689 | (math-mul step | |
2690 | (calcFunc-scf relative-to (- 1 calc-internal-prec))) | |
2691 | (math-add-float x (math-make-float | |
2692 | step | |
2693 | (+ (nth 2 x) | |
2694 | (- (math-numdigs (nth 1 x)) | |
2695 | calc-internal-prec)))))) | |
2696 | ((eq (car x) 'date) | |
2697 | (if (Math-integerp (nth 1 x)) | |
2698 | (math-add x step) | |
2699 | (math-add x (list 'hms 0 0 step)))) | |
2700 | (t | |
898ea5c0 | 2701 | (math-reject-arg x 'realp)))) |
136211a9 | 2702 | |
898ea5c0 CW |
2703 | (defsubst calcFunc-decr (x &optional step relative-to) |
2704 | (calcFunc-incr x (math-neg (or step 1)) relative-to)) | |
136211a9 EZ |
2705 | |
2706 | (defun calcFunc-percent (x) | |
2707 | (if (math-objectp x) | |
2708 | (let ((calc-prefer-frac nil)) | |
2709 | (math-div x 100)) | |
898ea5c0 | 2710 | (list 'calcFunc-percent x))) |
136211a9 EZ |
2711 | |
2712 | (defun calcFunc-relch (x y) | |
2713 | (if (and (math-objectp x) (math-objectp y)) | |
2714 | (math-div (math-sub y x) x) | |
898ea5c0 | 2715 | (list 'calcFunc-relch x y))) |
136211a9 EZ |
2716 | |
2717 | ;;; Compute the absolute value squared of A. [F N] [Public] | |
2718 | (defun calcFunc-abssqr (a) | |
2719 | (cond ((Math-realp a) | |
2720 | (math-mul a a)) | |
2721 | ((eq (car a) 'cplx) | |
2722 | (math-add (math-sqr (nth 1 a)) | |
2723 | (math-sqr (nth 2 a)))) | |
2724 | ((eq (car a) 'polar) | |
2725 | (math-sqr (nth 1 a))) | |
2726 | ((and (memq (car a) '(sdev intv)) (math-constp a)) | |
2727 | (math-sqr (math-abs a))) | |
2728 | ((eq (car a) 'vec) | |
2729 | (math-reduce-vec 'math-add (math-map-vec 'calcFunc-abssqr a))) | |
2730 | ((math-known-realp a) | |
2731 | (math-pow a 2)) | |
2732 | ((let ((inf (math-infinitep a))) | |
2733 | (and inf | |
2734 | (math-mul (calcFunc-abssqr (math-infinite-dir a inf)) inf)))) | |
2735 | (t (calc-record-why 'numvecp a) | |
898ea5c0 | 2736 | (list 'calcFunc-abssqr a)))) |
136211a9 | 2737 | |
898ea5c0 CW |
2738 | (defsubst math-sqr (a) |
2739 | (math-mul a a)) | |
136211a9 EZ |
2740 | |
2741 | ;;;; Number theory. | |
2742 | ||
2743 | (defun calcFunc-idiv (a b) ; [I I I] [Public] | |
2744 | (cond ((and (Math-natnump a) (Math-natnump b) (not (eq b 0))) | |
2745 | (math-quotient a b)) | |
2746 | ((Math-realp a) | |
2747 | (if (Math-realp b) | |
2748 | (let ((calc-prefer-frac t)) | |
2749 | (math-floor (math-div a b))) | |
2750 | (math-reject-arg b 'realp))) | |
2751 | ((eq (car-safe a) 'hms) | |
2752 | (if (eq (car-safe b) 'hms) | |
2753 | (let ((calc-prefer-frac t)) | |
2754 | (math-floor (math-div a b))) | |
2755 | (math-reject-arg b 'hmsp))) | |
2756 | ((and (or (eq (car-safe a) 'intv) (Math-realp a)) | |
2757 | (or (eq (car-safe b) 'intv) (Math-realp b))) | |
2758 | (math-floor (math-div a b))) | |
2759 | ((or (math-infinitep a) | |
2760 | (math-infinitep b)) | |
2761 | (math-div a b)) | |
898ea5c0 | 2762 | (t (math-reject-arg a 'anglep)))) |
136211a9 EZ |
2763 | |
2764 | ||
2765 | ;;; Combine two terms being added, if possible. | |
2766 | (defun math-combine-sum (a b nega negb scalar-okay) | |
2767 | (if (and scalar-okay (Math-objvecp a) (Math-objvecp b)) | |
2768 | (math-add-or-sub a b nega negb) | |
2769 | (let ((amult 1) (bmult 1)) | |
2770 | (and (consp a) | |
2771 | (cond ((and (eq (car a) '*) | |
2772 | (Math-objectp (nth 1 a))) | |
2773 | (setq amult (nth 1 a) | |
2774 | a (nth 2 a))) | |
2775 | ((and (eq (car a) '/) | |
2776 | (Math-objectp (nth 2 a))) | |
2777 | (setq amult (if (Math-integerp (nth 2 a)) | |
2778 | (list 'frac 1 (nth 2 a)) | |
2779 | (math-div 1 (nth 2 a))) | |
2780 | a (nth 1 a))) | |
2781 | ((eq (car a) 'neg) | |
2782 | (setq amult -1 | |
2783 | a (nth 1 a))))) | |
2784 | (and (consp b) | |
2785 | (cond ((and (eq (car b) '*) | |
2786 | (Math-objectp (nth 1 b))) | |
2787 | (setq bmult (nth 1 b) | |
2788 | b (nth 2 b))) | |
2789 | ((and (eq (car b) '/) | |
2790 | (Math-objectp (nth 2 b))) | |
2791 | (setq bmult (if (Math-integerp (nth 2 b)) | |
2792 | (list 'frac 1 (nth 2 b)) | |
2793 | (math-div 1 (nth 2 b))) | |
2794 | b (nth 1 b))) | |
2795 | ((eq (car b) 'neg) | |
2796 | (setq bmult -1 | |
2797 | b (nth 1 b))))) | |
2798 | (and (if math-simplifying | |
2799 | (Math-equal a b) | |
2800 | (equal a b)) | |
2801 | (progn | |
2802 | (if nega (setq amult (math-neg amult))) | |
2803 | (if negb (setq bmult (math-neg bmult))) | |
2804 | (setq amult (math-add amult bmult)) | |
898ea5c0 | 2805 | (math-mul amult a)))))) |
136211a9 EZ |
2806 | |
2807 | (defun math-add-or-sub (a b aneg bneg) | |
2808 | (if aneg (setq a (math-neg a))) | |
2809 | (if bneg (setq b (math-neg b))) | |
2810 | (if (or (Math-vectorp a) (Math-vectorp b)) | |
2811 | (math-normalize (list '+ a b)) | |
898ea5c0 | 2812 | (math-add a b))) |
136211a9 | 2813 | |
3132f345 CW |
2814 | (defvar math-combine-prod-e '(var e var-e)) |
2815 | ||
136211a9 | 2816 | ;;; The following is expanded out four ways for speed. |
67549a85 JB |
2817 | |
2818 | ;; math-unit-prefixes is defined in calc-units.el, | |
2819 | ;; but used here. | |
2820 | (defvar math-unit-prefixes) | |
2821 | ||
136211a9 EZ |
2822 | (defun math-combine-prod (a b inva invb scalar-okay) |
2823 | (cond | |
2824 | ((or (and inva (Math-zerop a)) | |
2825 | (and invb (Math-zerop b))) | |
2826 | nil) | |
2827 | ((and scalar-okay (Math-objvecp a) (Math-objvecp b)) | |
2828 | (setq a (math-mul-or-div a b inva invb)) | |
2829 | (and (Math-objvecp a) | |
2830 | a)) | |
2831 | ((and (eq (car-safe a) '^) | |
2832 | inva | |
2833 | (math-looks-negp (nth 2 a))) | |
2834 | (math-mul (math-pow (nth 1 a) (math-neg (nth 2 a))) b)) | |
2835 | ((and (eq (car-safe b) '^) | |
2836 | invb | |
2837 | (math-looks-negp (nth 2 b))) | |
2838 | (math-mul a (math-pow (nth 1 b) (math-neg (nth 2 b))))) | |
7db3d0d5 JB |
2839 | ((and math-simplifying |
2840 | (math-combine-prod-trig a b))) | |
136211a9 EZ |
2841 | (t (let ((apow 1) (bpow 1)) |
2842 | (and (consp a) | |
2843 | (cond ((and (eq (car a) '^) | |
2844 | (or math-simplifying | |
2845 | (Math-numberp (nth 2 a)))) | |
2846 | (setq apow (nth 2 a) | |
2847 | a (nth 1 a))) | |
2848 | ((eq (car a) 'calcFunc-sqrt) | |
2849 | (setq apow '(frac 1 2) | |
2850 | a (nth 1 a))) | |
2851 | ((and (eq (car a) 'calcFunc-exp) | |
2852 | (or math-simplifying | |
2853 | (Math-numberp (nth 1 a)))) | |
2854 | (setq apow (nth 1 a) | |
2855 | a math-combine-prod-e)))) | |
2856 | (and (consp a) (eq (car a) 'frac) | |
2857 | (Math-lessp (nth 1 a) (nth 2 a)) | |
2858 | (setq a (math-div 1 a) apow (math-neg apow))) | |
2859 | (and (consp b) | |
2860 | (cond ((and (eq (car b) '^) | |
2861 | (or math-simplifying | |
2862 | (Math-numberp (nth 2 b)))) | |
2863 | (setq bpow (nth 2 b) | |
2864 | b (nth 1 b))) | |
2865 | ((eq (car b) 'calcFunc-sqrt) | |
2866 | (setq bpow '(frac 1 2) | |
2867 | b (nth 1 b))) | |
2868 | ((and (eq (car b) 'calcFunc-exp) | |
2869 | (or math-simplifying | |
2870 | (Math-numberp (nth 1 b)))) | |
2871 | (setq bpow (nth 1 b) | |
2872 | b math-combine-prod-e)))) | |
2873 | (and (consp b) (eq (car b) 'frac) | |
2874 | (Math-lessp (nth 1 b) (nth 2 b)) | |
2875 | (setq b (math-div 1 b) bpow (math-neg bpow))) | |
2876 | (if inva (setq apow (math-neg apow))) | |
2877 | (if invb (setq bpow (math-neg bpow))) | |
2878 | (or (and (if math-simplifying | |
2879 | (math-commutative-equal a b) | |
2880 | (equal a b)) | |
2881 | (let ((sumpow (math-add apow bpow))) | |
2882 | (and (or (not (Math-integerp a)) | |
2883 | (Math-zerop sumpow) | |
2884 | (eq (eq (car-safe apow) 'frac) | |
2885 | (eq (car-safe bpow) 'frac))) | |
2886 | (progn | |
2887 | (and (math-looks-negp sumpow) | |
2888 | (Math-ratp a) (Math-posp a) | |
2889 | (setq a (math-div 1 a) | |
2890 | sumpow (math-neg sumpow))) | |
2891 | (cond ((equal sumpow '(frac 1 2)) | |
2892 | (list 'calcFunc-sqrt a)) | |
2893 | ((equal sumpow '(frac -1 2)) | |
2894 | (math-div 1 (list 'calcFunc-sqrt a))) | |
2895 | ((and (eq a math-combine-prod-e) | |
2896 | (eq a b)) | |
2897 | (list 'calcFunc-exp sumpow)) | |
2898 | (t | |
2899 | (condition-case err | |
2900 | (math-pow a sumpow) | |
2901 | (inexact-result (list '^ a sumpow))))))))) | |
2902 | (and math-simplifying-units | |
2903 | math-combining-units | |
2904 | (let* ((ua (math-check-unit-name a)) | |
2905 | ub) | |
2906 | (and ua | |
2907 | (eq ua (setq ub (math-check-unit-name b))) | |
2908 | (progn | |
2909 | (setq ua (if (eq (nth 1 a) (car ua)) | |
2910 | 1 | |
2911 | (nth 1 (assq (aref (symbol-name (nth 1 a)) | |
2912 | 0) | |
2913 | math-unit-prefixes))) | |
2914 | ub (if (eq (nth 1 b) (car ub)) | |
2915 | 1 | |
2916 | (nth 1 (assq (aref (symbol-name (nth 1 b)) | |
2917 | 0) | |
2918 | math-unit-prefixes)))) | |
2919 | (if (Math-lessp ua ub) | |
2920 | (let (temp) | |
2921 | (setq temp a a b b temp | |
2922 | temp ua ua ub ub temp | |
2923 | temp apow apow bpow bpow temp))) | |
2924 | (math-mul (math-pow (math-div ua ub) apow) | |
2925 | (math-pow b (math-add apow bpow))))))) | |
2926 | (and (equal apow bpow) | |
2927 | (Math-natnump a) (Math-natnump b) | |
2928 | (cond ((equal apow '(frac 1 2)) | |
2929 | (list 'calcFunc-sqrt (math-mul a b))) | |
2930 | ((equal apow '(frac -1 2)) | |
2931 | (math-div 1 (list 'calcFunc-sqrt (math-mul a b)))) | |
2932 | (t | |
2933 | (setq a (math-mul a b)) | |
2934 | (condition-case err | |
2935 | (math-pow a apow) | |
898ea5c0 | 2936 | (inexact-result (list '^ a apow))))))))))) |
136211a9 | 2937 | |
7db3d0d5 JB |
2938 | (defun math-combine-prod-trig (a b) |
2939 | (cond | |
2940 | ((and (eq (car-safe a) 'calcFunc-sin) | |
2941 | (eq (car-safe b) 'calcFunc-csc) | |
2942 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2943 | 1) | |
2944 | ((and (eq (car-safe a) 'calcFunc-sin) | |
2945 | (eq (car-safe b) 'calcFunc-sec) | |
2946 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2947 | (cons 'calcFunc-tan (cdr a))) | |
2948 | ((and (eq (car-safe a) 'calcFunc-sin) | |
2949 | (eq (car-safe b) 'calcFunc-cot) | |
2950 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2951 | (cons 'calcFunc-cos (cdr a))) | |
2952 | ((and (eq (car-safe a) 'calcFunc-cos) | |
2953 | (eq (car-safe b) 'calcFunc-sec) | |
2954 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2955 | 1) | |
2956 | ((and (eq (car-safe a) 'calcFunc-cos) | |
2957 | (eq (car-safe b) 'calcFunc-csc) | |
2958 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2959 | (cons 'calcFunc-cot (cdr a))) | |
2960 | ((and (eq (car-safe a) 'calcFunc-cos) | |
2961 | (eq (car-safe b) 'calcFunc-tan) | |
2962 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2963 | (cons 'calcFunc-sin (cdr a))) | |
2964 | ((and (eq (car-safe a) 'calcFunc-tan) | |
2965 | (eq (car-safe b) 'calcFunc-cot) | |
2966 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2967 | 1) | |
2968 | ((and (eq (car-safe a) 'calcFunc-tan) | |
2969 | (eq (car-safe b) 'calcFunc-csc) | |
2970 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2971 | (cons 'calcFunc-sec (cdr a))) | |
2972 | ((and (eq (car-safe a) 'calcFunc-sec) | |
2973 | (eq (car-safe b) 'calcFunc-cot) | |
2974 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2975 | (cons 'calcFunc-csc (cdr a))) | |
2976 | ((and (eq (car-safe a) 'calcFunc-sinh) | |
2977 | (eq (car-safe b) 'calcFunc-csch) | |
2978 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2979 | 1) | |
2980 | ((and (eq (car-safe a) 'calcFunc-sinh) | |
2981 | (eq (car-safe b) 'calcFunc-sech) | |
2982 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2983 | (cons 'calcFunc-tanh (cdr a))) | |
2984 | ((and (eq (car-safe a) 'calcFunc-sinh) | |
2985 | (eq (car-safe b) 'calcFunc-coth) | |
2986 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2987 | (cons 'calcFunc-cosh (cdr a))) | |
2988 | ((and (eq (car-safe a) 'calcFunc-cosh) | |
2989 | (eq (car-safe b) 'calcFunc-sech) | |
2990 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2991 | 1) | |
2992 | ((and (eq (car-safe a) 'calcFunc-cosh) | |
2993 | (eq (car-safe b) 'calcFunc-csch) | |
2994 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2995 | (cons 'calcFunc-coth (cdr a))) | |
2996 | ((and (eq (car-safe a) 'calcFunc-cosh) | |
2997 | (eq (car-safe b) 'calcFunc-tanh) | |
2998 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
2999 | (cons 'calcFunc-sinh (cdr a))) | |
3000 | ((and (eq (car-safe a) 'calcFunc-tanh) | |
3001 | (eq (car-safe b) 'calcFunc-coth) | |
3002 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
3003 | 1) | |
3004 | ((and (eq (car-safe a) 'calcFunc-tanh) | |
3005 | (eq (car-safe b) 'calcFunc-csch) | |
3006 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
3007 | (cons 'calcFunc-sech (cdr a))) | |
3008 | ((and (eq (car-safe a) 'calcFunc-sech) | |
3009 | (eq (car-safe b) 'calcFunc-coth) | |
3010 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) | |
3011 | (cons 'calcFunc-csch (cdr a))) | |
3012 | (t | |
3013 | nil))) | |
3014 | ||
136211a9 EZ |
3015 | (defun math-mul-or-div (a b ainv binv) |
3016 | (if (or (Math-vectorp a) (Math-vectorp b)) | |
3017 | (math-normalize | |
3018 | (if ainv | |
3019 | (if binv | |
3020 | (list '/ (math-div 1 a) b) | |
3021 | (list '/ b a)) | |
3022 | (if binv | |
3023 | (list '/ a b) | |
3024 | (list '* a b)))) | |
3025 | (if ainv | |
3026 | (if binv | |
3027 | (math-div (math-div 1 a) b) | |
3028 | (math-div b a)) | |
3029 | (if binv | |
3030 | (math-div a b) | |
898ea5c0 | 3031 | (math-mul a b))))) |
136211a9 | 3032 | |
67549a85 JB |
3033 | ;; The variable math-com-bterms is local to math-commutative-equal, |
3034 | ;; but is used by math-commutative collect, which is called by | |
3035 | ;; math-commutative-equal. | |
3036 | (defvar math-com-bterms) | |
3037 | ||
136211a9 EZ |
3038 | (defun math-commutative-equal (a b) |
3039 | (if (memq (car-safe a) '(+ -)) | |
3040 | (and (memq (car-safe b) '(+ -)) | |
67549a85 | 3041 | (let ((math-com-bterms nil) aterms p) |
136211a9 | 3042 | (math-commutative-collect b nil) |
67549a85 | 3043 | (setq aterms math-com-bterms math-com-bterms nil) |
136211a9 | 3044 | (math-commutative-collect a nil) |
67549a85 | 3045 | (and (= (length aterms) (length math-com-bterms)) |
136211a9 EZ |
3046 | (progn |
3047 | (while (and aterms | |
3048 | (progn | |
67549a85 | 3049 | (setq p math-com-bterms) |
136211a9 EZ |
3050 | (while (and p (not (equal (car aterms) |
3051 | (car p)))) | |
3052 | (setq p (cdr p))) | |
3053 | p)) | |
67549a85 | 3054 | (setq math-com-bterms (delq (car p) math-com-bterms) |
136211a9 EZ |
3055 | aterms (cdr aterms))) |
3056 | (not aterms))))) | |
898ea5c0 | 3057 | (equal a b))) |
136211a9 EZ |
3058 | |
3059 | (defun math-commutative-collect (b neg) | |
3060 | (if (eq (car-safe b) '+) | |
3061 | (progn | |
3062 | (math-commutative-collect (nth 1 b) neg) | |
3063 | (math-commutative-collect (nth 2 b) neg)) | |
3064 | (if (eq (car-safe b) '-) | |
3065 | (progn | |
3066 | (math-commutative-collect (nth 1 b) neg) | |
3067 | (math-commutative-collect (nth 2 b) (not neg))) | |
67549a85 | 3068 | (setq math-com-bterms (cons (if neg (math-neg b) b) math-com-bterms))))) |
136211a9 | 3069 | |
5e30155b JB |
3070 | (provide 'calc-arith) |
3071 | ||
cbee283d | 3072 | ;; arch-tag: 6c396b5b-14c6-40ed-bb2a-7cc2e8111465 |
898ea5c0 | 3073 | ;;; calc-arith.el ends here |