| 1 | ;;; calc-arith.el --- arithmetic functions for Calc |
| 2 | |
| 3 | ;; Copyright (C) 1990-1993, 2001-2012 Free Software Foundation, Inc. |
| 4 | |
| 5 | ;; Author: David Gillespie <daveg@synaptics.com> |
| 6 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
| 7 | |
| 8 | ;; This file is part of GNU Emacs. |
| 9 | |
| 10 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
| 11 | ;; it under the terms of the GNU General Public License as published by |
| 12 | ;; the Free Software Foundation, either version 3 of the License, or |
| 13 | ;; (at your option) any later version. |
| 14 | |
| 15 | ;; GNU Emacs is distributed in the hope that it will be useful, |
| 16 | ;; but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 17 | ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 18 | ;; GNU General Public License for more details. |
| 19 | |
| 20 | ;; You should have received a copy of the GNU General Public License |
| 21 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
| 22 | |
| 23 | ;;; Commentary: |
| 24 | |
| 25 | ;;; Code: |
| 26 | |
| 27 | ;; This file is autoloaded from calc-ext.el. |
| 28 | |
| 29 | (require 'calc-ext) |
| 30 | (require 'calc-macs) |
| 31 | |
| 32 | ;;; The following lists are not exhaustive. |
| 33 | (defvar math-scalar-functions '(calcFunc-det |
| 34 | calcFunc-cnorm calcFunc-rnorm |
| 35 | calcFunc-vlen calcFunc-vcount |
| 36 | calcFunc-vsum calcFunc-vprod |
| 37 | calcFunc-vmin calcFunc-vmax)) |
| 38 | |
| 39 | (defvar math-nonscalar-functions '(vec calcFunc-idn calcFunc-diag |
| 40 | calcFunc-cvec calcFunc-index |
| 41 | calcFunc-trn |
| 42 | | calcFunc-append |
| 43 | calcFunc-cons calcFunc-rcons |
| 44 | calcFunc-tail calcFunc-rhead)) |
| 45 | |
| 46 | (defvar math-scalar-if-args-functions '(+ - * / neg)) |
| 47 | |
| 48 | (defvar math-real-functions '(calcFunc-arg |
| 49 | calcFunc-re calcFunc-im |
| 50 | calcFunc-floor calcFunc-ceil |
| 51 | calcFunc-trunc calcFunc-round |
| 52 | calcFunc-rounde calcFunc-roundu |
| 53 | calcFunc-ffloor calcFunc-fceil |
| 54 | calcFunc-ftrunc calcFunc-fround |
| 55 | calcFunc-frounde calcFunc-froundu)) |
| 56 | |
| 57 | (defvar math-positive-functions '()) |
| 58 | |
| 59 | (defvar math-nonnegative-functions '(calcFunc-cnorm calcFunc-rnorm |
| 60 | calcFunc-vlen calcFunc-vcount)) |
| 61 | |
| 62 | (defvar math-real-scalar-functions '(% calcFunc-idiv calcFunc-abs |
| 63 | calcFunc-choose calcFunc-perm |
| 64 | calcFunc-eq calcFunc-neq |
| 65 | calcFunc-lt calcFunc-gt |
| 66 | calcFunc-leq calcFunc-geq |
| 67 | calcFunc-lnot |
| 68 | calcFunc-max calcFunc-min)) |
| 69 | |
| 70 | (defvar math-real-if-arg-functions '(calcFunc-sin calcFunc-cos |
| 71 | calcFunc-tan calcFunc-sec |
| 72 | calcFunc-csc calcFunc-cot |
| 73 | calcFunc-arctan |
| 74 | calcFunc-sinh calcFunc-cosh |
| 75 | calcFunc-tanh calcFunc-sech |
| 76 | calcFunc-csch calcFunc-coth |
| 77 | calcFunc-exp |
| 78 | calcFunc-gamma calcFunc-fact)) |
| 79 | |
| 80 | (defvar math-integer-functions '(calcFunc-idiv |
| 81 | calcFunc-isqrt calcFunc-ilog |
| 82 | calcFunc-vlen calcFunc-vcount)) |
| 83 | |
| 84 | (defvar math-num-integer-functions '()) |
| 85 | |
| 86 | (defvar math-rounding-functions '(calcFunc-floor |
| 87 | calcFunc-ceil |
| 88 | calcFunc-round calcFunc-trunc |
| 89 | calcFunc-rounde calcFunc-roundu)) |
| 90 | |
| 91 | (defvar math-float-rounding-functions '(calcFunc-ffloor |
| 92 | calcFunc-fceil |
| 93 | calcFunc-fround calcFunc-ftrunc |
| 94 | calcFunc-frounde calcFunc-froundu)) |
| 95 | |
| 96 | (defvar math-integer-if-args-functions '(+ - * % neg calcFunc-abs |
| 97 | calcFunc-min calcFunc-max |
| 98 | calcFunc-choose calcFunc-perm)) |
| 99 | |
| 100 | |
| 101 | ;;; Arithmetic. |
| 102 | |
| 103 | (defun calc-min (arg) |
| 104 | (interactive "P") |
| 105 | (calc-slow-wrapper |
| 106 | (calc-binary-op "min" 'calcFunc-min arg '(var inf var-inf)))) |
| 107 | |
| 108 | (defun calc-max (arg) |
| 109 | (interactive "P") |
| 110 | (calc-slow-wrapper |
| 111 | (calc-binary-op "max" 'calcFunc-max arg '(neg (var inf var-inf))))) |
| 112 | |
| 113 | (defun calc-abs (arg) |
| 114 | (interactive "P") |
| 115 | (calc-slow-wrapper |
| 116 | (calc-unary-op "abs" 'calcFunc-abs arg))) |
| 117 | |
| 118 | |
| 119 | (defun calc-idiv (arg) |
| 120 | (interactive "P") |
| 121 | (calc-slow-wrapper |
| 122 | (calc-binary-op "\\" 'calcFunc-idiv arg 1))) |
| 123 | |
| 124 | |
| 125 | (defun calc-floor (arg) |
| 126 | (interactive "P") |
| 127 | (calc-slow-wrapper |
| 128 | (if (calc-is-inverse) |
| 129 | (if (calc-is-hyperbolic) |
| 130 | (calc-unary-op "ceil" 'calcFunc-fceil arg) |
| 131 | (calc-unary-op "ceil" 'calcFunc-ceil arg)) |
| 132 | (if (calc-is-hyperbolic) |
| 133 | (calc-unary-op "flor" 'calcFunc-ffloor arg) |
| 134 | (calc-unary-op "flor" 'calcFunc-floor arg))))) |
| 135 | |
| 136 | (defun calc-ceiling (arg) |
| 137 | (interactive "P") |
| 138 | (calc-invert-func) |
| 139 | (calc-floor arg)) |
| 140 | |
| 141 | (defun calc-round (arg) |
| 142 | (interactive "P") |
| 143 | (calc-slow-wrapper |
| 144 | (if (calc-is-inverse) |
| 145 | (if (calc-is-hyperbolic) |
| 146 | (calc-unary-op "trnc" 'calcFunc-ftrunc arg) |
| 147 | (calc-unary-op "trnc" 'calcFunc-trunc arg)) |
| 148 | (if (calc-is-hyperbolic) |
| 149 | (calc-unary-op "rond" 'calcFunc-fround arg) |
| 150 | (calc-unary-op "rond" 'calcFunc-round arg))))) |
| 151 | |
| 152 | (defun calc-trunc (arg) |
| 153 | (interactive "P") |
| 154 | (calc-invert-func) |
| 155 | (calc-round arg)) |
| 156 | |
| 157 | (defun calc-mant-part (arg) |
| 158 | (interactive "P") |
| 159 | (calc-slow-wrapper |
| 160 | (calc-unary-op "mant" 'calcFunc-mant arg))) |
| 161 | |
| 162 | (defun calc-xpon-part (arg) |
| 163 | (interactive "P") |
| 164 | (calc-slow-wrapper |
| 165 | (calc-unary-op "xpon" 'calcFunc-xpon arg))) |
| 166 | |
| 167 | (defun calc-scale-float (arg) |
| 168 | (interactive "P") |
| 169 | (calc-slow-wrapper |
| 170 | (calc-binary-op "scal" 'calcFunc-scf arg))) |
| 171 | |
| 172 | (defun calc-abssqr (arg) |
| 173 | (interactive "P") |
| 174 | (calc-slow-wrapper |
| 175 | (calc-unary-op "absq" 'calcFunc-abssqr arg))) |
| 176 | |
| 177 | (defun calc-sign (arg) |
| 178 | (interactive "P") |
| 179 | (calc-slow-wrapper |
| 180 | (calc-unary-op "sign" 'calcFunc-sign arg))) |
| 181 | |
| 182 | (defun calc-increment (arg) |
| 183 | (interactive "p") |
| 184 | (calc-wrapper |
| 185 | (calc-enter-result 1 "incr" (list 'calcFunc-incr (calc-top-n 1) arg)))) |
| 186 | |
| 187 | (defun calc-decrement (arg) |
| 188 | (interactive "p") |
| 189 | (calc-wrapper |
| 190 | (calc-enter-result 1 "decr" (list 'calcFunc-decr (calc-top-n 1) arg)))) |
| 191 | |
| 192 | |
| 193 | (defun math-abs-approx (a) |
| 194 | (cond ((Math-negp a) |
| 195 | (math-neg a)) |
| 196 | ((Math-anglep a) |
| 197 | a) |
| 198 | ((eq (car a) 'cplx) |
| 199 | (math-add (math-abs (nth 1 a)) (math-abs (nth 2 a)))) |
| 200 | ((eq (car a) 'polar) |
| 201 | (nth 1 a)) |
| 202 | ((eq (car a) 'sdev) |
| 203 | (math-abs-approx (nth 1 a))) |
| 204 | ((eq (car a) 'intv) |
| 205 | (math-max (math-abs (nth 2 a)) (math-abs (nth 3 a)))) |
| 206 | ((eq (car a) 'date) |
| 207 | a) |
| 208 | ((eq (car a) 'vec) |
| 209 | (math-reduce-vec 'math-add-abs-approx a)) |
| 210 | ((eq (car a) 'calcFunc-abs) |
| 211 | (car a)) |
| 212 | (t a))) |
| 213 | |
| 214 | (defun math-add-abs-approx (a b) |
| 215 | (math-add (math-abs-approx a) (math-abs-approx b))) |
| 216 | |
| 217 | |
| 218 | ;;;; Declarations. |
| 219 | |
| 220 | (defvar math-decls-cache-tag nil) |
| 221 | (defvar math-decls-cache nil) |
| 222 | (defvar math-decls-all nil) |
| 223 | |
| 224 | ;;; Math-decls-cache is an a-list where each entry is a list of the form: |
| 225 | ;;; (VAR TYPES RANGE) |
| 226 | ;;; where VAR is a variable name (with var- prefix) or function name; |
| 227 | ;;; TYPES is a list of type symbols (any, int, frac, ...) |
| 228 | ;;; RANGE is a sorted vector of intervals describing the range. |
| 229 | |
| 230 | (defvar math-super-types |
| 231 | '((int numint rat real number) |
| 232 | (numint real number) |
| 233 | (frac rat real number) |
| 234 | (rat real number) |
| 235 | (float real number) |
| 236 | (real number) |
| 237 | (number) |
| 238 | (scalar) |
| 239 | (sqmatrix matrix vector) |
| 240 | (matrix vector) |
| 241 | (vector) |
| 242 | (const))) |
| 243 | |
| 244 | (defun math-setup-declarations () |
| 245 | (or (eq math-decls-cache-tag (calc-var-value 'var-Decls)) |
| 246 | (let ((p (calc-var-value 'var-Decls)) |
| 247 | vec type range) |
| 248 | (setq math-decls-cache-tag p |
| 249 | math-decls-cache nil) |
| 250 | (and (eq (car-safe p) 'vec) |
| 251 | (while (setq p (cdr p)) |
| 252 | (and (eq (car-safe (car p)) 'vec) |
| 253 | (setq vec (nth 2 (car p))) |
| 254 | (condition-case err |
| 255 | (let ((v (nth 1 (car p)))) |
| 256 | (setq type nil range nil) |
| 257 | (or (eq (car-safe vec) 'vec) |
| 258 | (setq vec (list 'vec vec))) |
| 259 | (while (and (setq vec (cdr vec)) |
| 260 | (not (Math-objectp (car vec)))) |
| 261 | (and (eq (car-safe (car vec)) 'var) |
| 262 | (let ((st (assq (nth 1 (car vec)) |
| 263 | math-super-types))) |
| 264 | (cond (st (setq type (append type st))) |
| 265 | ((eq (nth 1 (car vec)) 'pos) |
| 266 | (setq type (append type |
| 267 | '(real number)) |
| 268 | range |
| 269 | '(intv 1 0 (var inf var-inf)))) |
| 270 | ((eq (nth 1 (car vec)) 'nonneg) |
| 271 | (setq type (append type |
| 272 | '(real number)) |
| 273 | range |
| 274 | '(intv 3 0 |
| 275 | (var inf var-inf)))))))) |
| 276 | (if vec |
| 277 | (setq type (append type '(real number)) |
| 278 | range (math-prepare-set (cons 'vec vec)))) |
| 279 | (setq type (list type range)) |
| 280 | (or (eq (car-safe v) 'vec) |
| 281 | (setq v (list 'vec v))) |
| 282 | (while (setq v (cdr v)) |
| 283 | (if (or (eq (car-safe (car v)) 'var) |
| 284 | (not (Math-primp (car v)))) |
| 285 | (setq math-decls-cache |
| 286 | (cons (cons (if (eq (car (car v)) 'var) |
| 287 | (nth 2 (car v)) |
| 288 | (car (car v))) |
| 289 | type) |
| 290 | math-decls-cache))))) |
| 291 | (error nil))))) |
| 292 | (setq math-decls-all (assq 'var-All math-decls-cache))))) |
| 293 | |
| 294 | (defun math-known-scalarp (a &optional assume-scalar) |
| 295 | (math-setup-declarations) |
| 296 | (if (if calc-matrix-mode |
| 297 | (eq calc-matrix-mode 'scalar) |
| 298 | assume-scalar) |
| 299 | (not (math-check-known-matrixp a)) |
| 300 | (math-check-known-scalarp a))) |
| 301 | |
| 302 | (defun math-known-matrixp (a) |
| 303 | (and (not (Math-scalarp a)) |
| 304 | (not (math-known-scalarp a t)))) |
| 305 | |
| 306 | (defun math-known-square-matrixp (a) |
| 307 | (and (math-known-matrixp a) |
| 308 | (math-check-known-square-matrixp a))) |
| 309 | |
| 310 | ;;; Try to prove that A is a scalar (i.e., a non-vector). |
| 311 | (defun math-check-known-scalarp (a) |
| 312 | (cond ((Math-objectp a) t) |
| 313 | ((memq (car a) math-scalar-functions) |
| 314 | t) |
| 315 | ((memq (car a) math-real-scalar-functions) |
| 316 | t) |
| 317 | ((memq (car a) math-scalar-if-args-functions) |
| 318 | (while (and (setq a (cdr a)) |
| 319 | (math-check-known-scalarp (car a)))) |
| 320 | (null a)) |
| 321 | ((eq (car a) '^) |
| 322 | (math-check-known-scalarp (nth 1 a))) |
| 323 | ((math-const-var a) t) |
| 324 | (t |
| 325 | (let ((decl (if (eq (car a) 'var) |
| 326 | (or (assq (nth 2 a) math-decls-cache) |
| 327 | math-decls-all) |
| 328 | (assq (car a) math-decls-cache))) |
| 329 | val) |
| 330 | (cond |
| 331 | ((memq 'scalar (nth 1 decl)) |
| 332 | t) |
| 333 | ((and (eq (car a) 'var) |
| 334 | (symbolp (nth 2 a)) |
| 335 | (boundp (nth 2 a)) |
| 336 | (setq val (symbol-value (nth 2 a)))) |
| 337 | (math-check-known-scalarp val)) |
| 338 | (t |
| 339 | nil)))))) |
| 340 | |
| 341 | ;;; Try to prove that A is *not* a scalar. |
| 342 | (defun math-check-known-matrixp (a) |
| 343 | (cond ((Math-objectp a) nil) |
| 344 | ((memq (car a) math-nonscalar-functions) |
| 345 | t) |
| 346 | ((memq (car a) math-scalar-if-args-functions) |
| 347 | (while (and (setq a (cdr a)) |
| 348 | (not (math-check-known-matrixp (car a))))) |
| 349 | a) |
| 350 | ((eq (car a) '^) |
| 351 | (math-check-known-matrixp (nth 1 a))) |
| 352 | ((math-const-var a) nil) |
| 353 | (t |
| 354 | (let ((decl (if (eq (car a) 'var) |
| 355 | (or (assq (nth 2 a) math-decls-cache) |
| 356 | math-decls-all) |
| 357 | (assq (car a) math-decls-cache))) |
| 358 | val) |
| 359 | (cond |
| 360 | ((memq 'matrix (nth 1 decl)) |
| 361 | t) |
| 362 | ((and (eq (car a) 'var) |
| 363 | (symbolp (nth 2 a)) |
| 364 | (boundp (nth 2 a)) |
| 365 | (setq val (symbol-value (nth 2 a)))) |
| 366 | (math-check-known-matrixp val)) |
| 367 | (t |
| 368 | nil)))))) |
| 369 | |
| 370 | ;;; Given that A is a matrix, try to prove that it is a square matrix. |
| 371 | (defun math-check-known-square-matrixp (a) |
| 372 | (cond ((math-square-matrixp a) |
| 373 | t) |
| 374 | ((eq (car-safe a) '^) |
| 375 | (math-check-known-square-matrixp (nth 1 a))) |
| 376 | ((or |
| 377 | (eq (car-safe a) '*) |
| 378 | (eq (car-safe a) '+) |
| 379 | (eq (car-safe a) '-)) |
| 380 | (and |
| 381 | (math-check-known-square-matrixp (nth 1 a)) |
| 382 | (math-check-known-square-matrixp (nth 2 a)))) |
| 383 | (t |
| 384 | (let ((decl (if (eq (car a) 'var) |
| 385 | (or (assq (nth 2 a) math-decls-cache) |
| 386 | math-decls-all) |
| 387 | (assq (car a) math-decls-cache))) |
| 388 | val) |
| 389 | (cond |
| 390 | ((memq 'sqmatrix (nth 1 decl)) |
| 391 | t) |
| 392 | ((and (eq (car a) 'var) |
| 393 | (boundp (nth 2 a)) |
| 394 | (setq val (symbol-value (nth 2 a)))) |
| 395 | (math-check-known-square-matrixp val)) |
| 396 | ((and (or |
| 397 | (integerp calc-matrix-mode) |
| 398 | (eq calc-matrix-mode 'sqmatrix)) |
| 399 | (eq (car-safe a) 'var)) |
| 400 | t) |
| 401 | ((memq 'matrix (nth 1 decl)) |
| 402 | nil) |
| 403 | (t |
| 404 | nil)))))) |
| 405 | |
| 406 | ;;; Try to prove that A is a real (i.e., not complex). |
| 407 | (defun math-known-realp (a) |
| 408 | (< (math-possible-signs a) 8)) |
| 409 | |
| 410 | ;;; Try to prove that A is real and positive. |
| 411 | (defun math-known-posp (a) |
| 412 | (eq (math-possible-signs a) 4)) |
| 413 | |
| 414 | ;;; Try to prove that A is real and negative. |
| 415 | (defun math-known-negp (a) |
| 416 | (eq (math-possible-signs a) 1)) |
| 417 | |
| 418 | ;;; Try to prove that A is real and nonnegative. |
| 419 | (defun math-known-nonnegp (a) |
| 420 | (memq (math-possible-signs a) '(2 4 6))) |
| 421 | |
| 422 | ;;; Try to prove that A is real and nonpositive. |
| 423 | (defun math-known-nonposp (a) |
| 424 | (memq (math-possible-signs a) '(1 2 3))) |
| 425 | |
| 426 | ;;; Try to prove that A is nonzero. |
| 427 | (defun math-known-nonzerop (a) |
| 428 | (memq (math-possible-signs a) '(1 4 5 8 9 12 13))) |
| 429 | |
| 430 | ;;; Return true if A is negative, or looks negative but we don't know. |
| 431 | (defun math-guess-if-neg (a) |
| 432 | (let ((sgn (math-possible-signs a))) |
| 433 | (if (memq sgn '(1 3)) |
| 434 | t |
| 435 | (if (memq sgn '(2 4 6)) |
| 436 | nil |
| 437 | (math-looks-negp a))))) |
| 438 | |
| 439 | ;;; Find the possible signs of A, assuming A is a number of some kind. |
| 440 | ;;; Returns an integer with bits: 1 may be negative, |
| 441 | ;;; 2 may be zero, |
| 442 | ;;; 4 may be positive, |
| 443 | ;;; 8 may be nonreal. |
| 444 | |
| 445 | (defun math-possible-signs (a &optional origin) |
| 446 | (cond ((Math-objectp a) |
| 447 | (if origin (setq a (math-sub a origin))) |
| 448 | (cond ((Math-posp a) 4) |
| 449 | ((Math-negp a) 1) |
| 450 | ((Math-zerop a) 2) |
| 451 | ((eq (car a) 'intv) |
| 452 | (cond |
| 453 | ((math-known-posp (nth 2 a)) 4) |
| 454 | ((math-known-negp (nth 3 a)) 1) |
| 455 | ((Math-zerop (nth 2 a)) 6) |
| 456 | ((Math-zerop (nth 3 a)) 3) |
| 457 | (t 7))) |
| 458 | ((eq (car a) 'sdev) |
| 459 | (if (math-known-realp (nth 1 a)) 7 15)) |
| 460 | (t 8))) |
| 461 | ((memq (car a) '(+ -)) |
| 462 | (cond ((Math-realp (nth 1 a)) |
| 463 | (if (eq (car a) '-) |
| 464 | (math-neg-signs |
| 465 | (math-possible-signs (nth 2 a) |
| 466 | (if origin |
| 467 | (math-add origin (nth 1 a)) |
| 468 | (nth 1 a)))) |
| 469 | (math-possible-signs (nth 2 a) |
| 470 | (if origin |
| 471 | (math-sub origin (nth 1 a)) |
| 472 | (math-neg (nth 1 a)))))) |
| 473 | ((Math-realp (nth 2 a)) |
| 474 | (let ((org (if (eq (car a) '-) |
| 475 | (nth 2 a) |
| 476 | (math-neg (nth 2 a))))) |
| 477 | (math-possible-signs (nth 1 a) |
| 478 | (if origin |
| 479 | (math-add origin org) |
| 480 | org)))) |
| 481 | (t |
| 482 | (let ((s1 (math-possible-signs (nth 1 a) origin)) |
| 483 | (s2 (math-possible-signs (nth 2 a)))) |
| 484 | (if (eq (car a) '-) (setq s2 (math-neg-signs s2))) |
| 485 | (cond ((eq s1 s2) s1) |
| 486 | ((eq s1 2) s2) |
| 487 | ((eq s2 2) s1) |
| 488 | ((>= s1 8) 15) |
| 489 | ((>= s2 8) 15) |
| 490 | ((and (eq s1 4) (eq s2 6)) 4) |
| 491 | ((and (eq s2 4) (eq s1 6)) 4) |
| 492 | ((and (eq s1 1) (eq s2 3)) 1) |
| 493 | ((and (eq s2 1) (eq s1 3)) 1) |
| 494 | (t 7)))))) |
| 495 | ((eq (car a) 'neg) |
| 496 | (math-neg-signs (math-possible-signs |
| 497 | (nth 1 a) |
| 498 | (and origin (math-neg origin))))) |
| 499 | ((and origin (Math-zerop origin) (setq origin nil) |
| 500 | nil)) |
| 501 | ((and (or (eq (car a) '*) |
| 502 | (and (eq (car a) '/) origin)) |
| 503 | (Math-realp (nth 1 a))) |
| 504 | (let ((s (if (eq (car a) '*) |
| 505 | (if (Math-zerop (nth 1 a)) |
| 506 | (math-possible-signs 0 origin) |
| 507 | (math-possible-signs (nth 2 a) |
| 508 | (math-div (or origin 0) |
| 509 | (nth 1 a)))) |
| 510 | (math-neg-signs |
| 511 | (math-possible-signs (nth 2 a) |
| 512 | (math-div (nth 1 a) |
| 513 | origin)))))) |
| 514 | (if (Math-negp (nth 1 a)) (math-neg-signs s) s))) |
| 515 | ((and (memq (car a) '(* /)) (Math-realp (nth 2 a))) |
| 516 | (let ((s (math-possible-signs (nth 1 a) |
| 517 | (if (eq (car a) '*) |
| 518 | (math-mul (or origin 0) (nth 2 a)) |
| 519 | (math-div (or origin 0) (nth 2 a)))))) |
| 520 | (if (Math-negp (nth 2 a)) (math-neg-signs s) s))) |
| 521 | ((eq (car a) 'vec) |
| 522 | (let ((signs 0)) |
| 523 | (while (and (setq a (cdr a)) (< signs 15)) |
| 524 | (setq signs (logior signs (math-possible-signs |
| 525 | (car a) origin)))) |
| 526 | signs)) |
| 527 | (t (let ((sign |
| 528 | (cond |
| 529 | ((memq (car a) '(* /)) |
| 530 | (let ((s1 (math-possible-signs (nth 1 a))) |
| 531 | (s2 (math-possible-signs (nth 2 a)))) |
| 532 | (cond ((>= s1 8) 15) |
| 533 | ((>= s2 8) 15) |
| 534 | ((and (eq (car a) '/) (memq s2 '(2 3 6 7))) 15) |
| 535 | (t |
| 536 | (logior (if (memq s1 '(4 5 6 7)) s2 0) |
| 537 | (if (memq s1 '(2 3 6 7)) 2 0) |
| 538 | (if (memq s1 '(1 3 5 7)) |
| 539 | (math-neg-signs s2) 0)))))) |
| 540 | ((eq (car a) '^) |
| 541 | (let ((s1 (math-possible-signs (nth 1 a))) |
| 542 | (s2 (math-possible-signs (nth 2 a)))) |
| 543 | (cond ((>= s1 8) 15) |
| 544 | ((>= s2 8) 15) |
| 545 | ((eq s1 4) 4) |
| 546 | ((eq s1 2) (if (eq s2 4) 2 15)) |
| 547 | ((eq s2 2) (if (memq s1 '(1 5)) 2 15)) |
| 548 | ((Math-integerp (nth 2 a)) |
| 549 | (if (math-evenp (nth 2 a)) |
| 550 | (if (memq s1 '(3 6 7)) 6 4) |
| 551 | s1)) |
| 552 | ((eq s1 6) (if (eq s2 4) 6 15)) |
| 553 | (t 7)))) |
| 554 | ((eq (car a) '%) |
| 555 | (let ((s2 (math-possible-signs (nth 2 a)))) |
| 556 | (cond ((>= s2 8) 7) |
| 557 | ((eq s2 2) 2) |
| 558 | ((memq s2 '(4 6)) 6) |
| 559 | ((memq s2 '(1 3)) 3) |
| 560 | (t 7)))) |
| 561 | ((and (memq (car a) '(calcFunc-abs calcFunc-abssqr)) |
| 562 | (= (length a) 2)) |
| 563 | (let ((s1 (math-possible-signs (nth 1 a)))) |
| 564 | (cond ((eq s1 2) 2) |
| 565 | ((memq s1 '(1 4 5)) 4) |
| 566 | (t 6)))) |
| 567 | ((and (eq (car a) 'calcFunc-exp) (= (length a) 2)) |
| 568 | (let ((s1 (math-possible-signs (nth 1 a)))) |
| 569 | (if (>= s1 8) |
| 570 | 15 |
| 571 | (if (or (not origin) (math-negp origin)) |
| 572 | 4 |
| 573 | (setq origin (math-sub (or origin 0) 1)) |
| 574 | (if (Math-zerop origin) (setq origin nil)) |
| 575 | s1)))) |
| 576 | ((or (and (memq (car a) '(calcFunc-ln calcFunc-log10)) |
| 577 | (= (length a) 2)) |
| 578 | (and (eq (car a) 'calcFunc-log) |
| 579 | (= (length a) 3) |
| 580 | (math-known-posp (nth 2 a)))) |
| 581 | (if (math-known-nonnegp (nth 1 a)) |
| 582 | (math-possible-signs (nth 1 a) 1) |
| 583 | 15)) |
| 584 | ((and (eq (car a) 'calcFunc-sqrt) (= (length a) 2)) |
| 585 | (let ((s1 (math-possible-signs (nth 1 a)))) |
| 586 | (if (memq s1 '(2 4 6)) s1 15))) |
| 587 | ((memq (car a) math-nonnegative-functions) 6) |
| 588 | ((memq (car a) math-positive-functions) 4) |
| 589 | ((memq (car a) math-real-functions) 7) |
| 590 | ((memq (car a) math-real-scalar-functions) 7) |
| 591 | ((and (memq (car a) math-real-if-arg-functions) |
| 592 | (= (length a) 2)) |
| 593 | (if (math-known-realp (nth 1 a)) 7 15))))) |
| 594 | (cond (sign |
| 595 | (if origin |
| 596 | (+ (logand sign 8) |
| 597 | (if (Math-posp origin) |
| 598 | (if (memq sign '(1 2 3 8 9 10 11)) 1 7) |
| 599 | (if (memq sign '(2 4 6 8 10 12 14)) 4 7))) |
| 600 | sign)) |
| 601 | ((math-const-var a) |
| 602 | (cond ((eq (nth 2 a) 'var-pi) |
| 603 | (if origin |
| 604 | (math-possible-signs (math-pi) origin) |
| 605 | 4)) |
| 606 | ((eq (nth 2 a) 'var-e) |
| 607 | (if origin |
| 608 | (math-possible-signs (math-e) origin) |
| 609 | 4)) |
| 610 | ((eq (nth 2 a) 'var-inf) 4) |
| 611 | ((eq (nth 2 a) 'var-uinf) 13) |
| 612 | ((eq (nth 2 a) 'var-i) 8) |
| 613 | (t 15))) |
| 614 | (t |
| 615 | (math-setup-declarations) |
| 616 | (let ((decl (if (eq (car a) 'var) |
| 617 | (or (assq (nth 2 a) math-decls-cache) |
| 618 | math-decls-all) |
| 619 | (assq (car a) math-decls-cache)))) |
| 620 | (if (and origin |
| 621 | (memq 'int (nth 1 decl)) |
| 622 | (not (Math-num-integerp origin))) |
| 623 | 5 |
| 624 | (if (nth 2 decl) |
| 625 | (math-possible-signs (nth 2 decl) origin) |
| 626 | (if (memq 'real (nth 1 decl)) |
| 627 | 7 |
| 628 | 15)))))))))) |
| 629 | |
| 630 | (defun math-neg-signs (s1) |
| 631 | (if (>= s1 8) |
| 632 | (+ 8 (math-neg-signs (- s1 8))) |
| 633 | (+ (if (memq s1 '(1 3 5 7)) 4 0) |
| 634 | (if (memq s1 '(2 3 6 7)) 2 0) |
| 635 | (if (memq s1 '(4 5 6 7)) 1 0)))) |
| 636 | |
| 637 | |
| 638 | ;;; Try to prove that A is an integer. |
| 639 | (defun math-known-integerp (a) |
| 640 | (eq (math-possible-types a) 1)) |
| 641 | |
| 642 | (defun math-known-num-integerp (a) |
| 643 | (<= (math-possible-types a t) 3)) |
| 644 | |
| 645 | (defun math-known-imagp (a) |
| 646 | (= (math-possible-types a) 16)) |
| 647 | |
| 648 | |
| 649 | ;;; Find the possible types of A. |
| 650 | ;;; Returns an integer with bits: 1 may be integer. |
| 651 | ;;; 2 may be integer-valued float. |
| 652 | ;;; 4 may be fraction. |
| 653 | ;;; 8 may be non-integer-valued float. |
| 654 | ;;; 16 may be imaginary. |
| 655 | ;;; 32 may be non-real, non-imaginary. |
| 656 | ;;; Real infinities count as integers for the purposes of this function. |
| 657 | (defun math-possible-types (a &optional num) |
| 658 | (cond ((Math-objectp a) |
| 659 | (cond ((Math-integerp a) (if num 3 1)) |
| 660 | ((Math-messy-integerp a) (if num 3 2)) |
| 661 | ((eq (car a) 'frac) (if num 12 4)) |
| 662 | ((eq (car a) 'float) (if num 12 8)) |
| 663 | ((eq (car a) 'intv) |
| 664 | (if (equal (nth 2 a) (nth 3 a)) |
| 665 | (math-possible-types (nth 2 a)) |
| 666 | 15)) |
| 667 | ((eq (car a) 'sdev) |
| 668 | (if (math-known-realp (nth 1 a)) 15 63)) |
| 669 | ((eq (car a) 'cplx) |
| 670 | (if (math-zerop (nth 1 a)) 16 32)) |
| 671 | ((eq (car a) 'polar) |
| 672 | (if (or (Math-equal (nth 2 a) (math-quarter-circle nil)) |
| 673 | (Math-equal (nth 2 a) |
| 674 | (math-neg (math-quarter-circle nil)))) |
| 675 | 16 48)) |
| 676 | (t 63))) |
| 677 | ((eq (car a) '/) |
| 678 | (let* ((t1 (math-possible-types (nth 1 a) num)) |
| 679 | (t2 (math-possible-types (nth 2 a) num)) |
| 680 | (t12 (logior t1 t2))) |
| 681 | (if (< t12 16) |
| 682 | (if (> (logand t12 10) 0) |
| 683 | 10 |
| 684 | (if (or (= t1 4) (= t2 4) calc-prefer-frac) |
| 685 | 5 |
| 686 | 15)) |
| 687 | (if (< t12 32) |
| 688 | (if (= t1 16) |
| 689 | (if (= t2 16) 15 |
| 690 | (if (< t2 16) 16 31)) |
| 691 | (if (= t2 16) |
| 692 | (if (< t1 16) 16 31) |
| 693 | 31)) |
| 694 | 63)))) |
| 695 | ((memq (car a) '(+ - * %)) |
| 696 | (let* ((t1 (math-possible-types (nth 1 a) num)) |
| 697 | (t2 (math-possible-types (nth 2 a) num)) |
| 698 | (t12 (logior t1 t2))) |
| 699 | (if (eq (car a) '%) |
| 700 | (setq t1 (logand t1 15) t2 (logand t2 15) t12 (logand t12 15))) |
| 701 | (if (< t12 16) |
| 702 | (let ((mask (if (<= t12 3) |
| 703 | 1 |
| 704 | (if (and (or (and (<= t1 3) (= (logand t2 3) 0)) |
| 705 | (and (<= t2 3) (= (logand t1 3) 0))) |
| 706 | (memq (car a) '(+ -))) |
| 707 | 4 |
| 708 | 5)))) |
| 709 | (if num |
| 710 | (* mask 3) |
| 711 | (logior (if (and (> (logand t1 5) 0) (> (logand t2 5) 0)) |
| 712 | mask 0) |
| 713 | (if (> (logand t12 10) 0) |
| 714 | (* mask 2) 0)))) |
| 715 | (if (< t12 32) |
| 716 | (if (eq (car a) '*) |
| 717 | (if (= t1 16) |
| 718 | (if (= t2 16) 15 |
| 719 | (if (< t2 16) 16 31)) |
| 720 | (if (= t2 16) |
| 721 | (if (< t1 16) 16 31) |
| 722 | 31)) |
| 723 | (if (= t12 16) 16 |
| 724 | (if (or (and (= t1 16) (< t2 16)) |
| 725 | (and (= t2 16) (< t1 16))) 32 63))) |
| 726 | 63)))) |
| 727 | ((eq (car a) 'neg) |
| 728 | (math-possible-types (nth 1 a))) |
| 729 | ((eq (car a) '^) |
| 730 | (let* ((t1 (math-possible-types (nth 1 a) num)) |
| 731 | (t2 (math-possible-types (nth 2 a) num)) |
| 732 | (t12 (logior t1 t2))) |
| 733 | (if (and (<= t2 3) (math-known-nonnegp (nth 2 a)) (< t1 16)) |
| 734 | (let ((mask (logior (if (> (logand t1 3) 0) 1 0) |
| 735 | (logand t1 4) |
| 736 | (if (> (logand t1 12) 0) 5 0)))) |
| 737 | (if num |
| 738 | (* mask 3) |
| 739 | (logior (if (and (> (logand t1 5) 0) (> (logand t2 5) 0)) |
| 740 | mask 0) |
| 741 | (if (> (logand t12 10) 0) |
| 742 | (* mask 2) 0)))) |
| 743 | (if (and (math-known-nonnegp (nth 1 a)) |
| 744 | (math-known-posp (nth 2 a))) |
| 745 | 15 |
| 746 | 63)))) |
| 747 | ((eq (car a) 'calcFunc-sqrt) |
| 748 | (let ((t1 (math-possible-signs (nth 1 a)))) |
| 749 | (logior (if (> (logand t1 2) 0) 3 0) |
| 750 | (if (> (logand t1 1) 0) 16 0) |
| 751 | (if (> (logand t1 4) 0) 15 0) |
| 752 | (if (> (logand t1 8) 0) 32 0)))) |
| 753 | ((eq (car a) 'vec) |
| 754 | (let ((types 0)) |
| 755 | (while (and (setq a (cdr a)) (< types 63)) |
| 756 | (setq types (logior types (math-possible-types (car a) t)))) |
| 757 | types)) |
| 758 | ((or (memq (car a) math-integer-functions) |
| 759 | (and (memq (car a) math-rounding-functions) |
| 760 | (math-known-nonnegp (or (nth 2 a) 0)))) |
| 761 | 1) |
| 762 | ((or (memq (car a) math-num-integer-functions) |
| 763 | (and (memq (car a) math-float-rounding-functions) |
| 764 | (math-known-nonnegp (or (nth 2 a) 0)))) |
| 765 | 2) |
| 766 | ((eq (car a) 'calcFunc-frac) |
| 767 | 5) |
| 768 | ((and (eq (car a) 'calcFunc-float) (= (length a) 2)) |
| 769 | (let ((t1 (math-possible-types (nth 1 a)))) |
| 770 | (logior (if (> (logand t1 3) 0) 2 0) |
| 771 | (if (> (logand t1 12) 0) 8 0) |
| 772 | (logand t1 48)))) |
| 773 | ((and (memq (car a) '(calcFunc-abs calcFunc-abssqr)) |
| 774 | (= (length a) 2)) |
| 775 | (let ((t1 (math-possible-types (nth 1 a)))) |
| 776 | (if (>= t1 16) |
| 777 | 15 |
| 778 | t1))) |
| 779 | ((math-const-var a) |
| 780 | (cond ((memq (nth 2 a) '(var-e var-pi var-phi var-gamma)) 8) |
| 781 | ((eq (nth 2 a) 'var-inf) 1) |
| 782 | ((eq (nth 2 a) 'var-i) 16) |
| 783 | (t 63))) |
| 784 | (t |
| 785 | (math-setup-declarations) |
| 786 | (let ((decl (if (eq (car a) 'var) |
| 787 | (or (assq (nth 2 a) math-decls-cache) |
| 788 | math-decls-all) |
| 789 | (assq (car a) math-decls-cache)))) |
| 790 | (cond ((memq 'int (nth 1 decl)) |
| 791 | 1) |
| 792 | ((memq 'numint (nth 1 decl)) |
| 793 | 3) |
| 794 | ((memq 'frac (nth 1 decl)) |
| 795 | 4) |
| 796 | ((memq 'rat (nth 1 decl)) |
| 797 | 5) |
| 798 | ((memq 'float (nth 1 decl)) |
| 799 | 10) |
| 800 | ((nth 2 decl) |
| 801 | (math-possible-types (nth 2 decl))) |
| 802 | ((memq 'real (nth 1 decl)) |
| 803 | 15) |
| 804 | (t 63)))))) |
| 805 | |
| 806 | (defun math-known-evenp (a) |
| 807 | (cond ((Math-integerp a) |
| 808 | (math-evenp a)) |
| 809 | ((Math-messy-integerp a) |
| 810 | (or (> (nth 2 a) 0) |
| 811 | (math-evenp (math-trunc a)))) |
| 812 | ((eq (car a) '*) |
| 813 | (if (math-known-evenp (nth 1 a)) |
| 814 | (math-known-num-integerp (nth 2 a)) |
| 815 | (if (math-known-num-integerp (nth 1 a)) |
| 816 | (math-known-evenp (nth 2 a))))) |
| 817 | ((memq (car a) '(+ -)) |
| 818 | (or (and (math-known-evenp (nth 1 a)) |
| 819 | (math-known-evenp (nth 2 a))) |
| 820 | (and (math-known-oddp (nth 1 a)) |
| 821 | (math-known-oddp (nth 2 a))))) |
| 822 | ((eq (car a) 'neg) |
| 823 | (math-known-evenp (nth 1 a))))) |
| 824 | |
| 825 | (defun math-known-oddp (a) |
| 826 | (cond ((Math-integerp a) |
| 827 | (math-oddp a)) |
| 828 | ((Math-messy-integerp a) |
| 829 | (and (<= (nth 2 a) 0) |
| 830 | (math-oddp (math-trunc a)))) |
| 831 | ((memq (car a) '(+ -)) |
| 832 | (or (and (math-known-evenp (nth 1 a)) |
| 833 | (math-known-oddp (nth 2 a))) |
| 834 | (and (math-known-oddp (nth 1 a)) |
| 835 | (math-known-evenp (nth 2 a))))) |
| 836 | ((eq (car a) 'neg) |
| 837 | (math-known-oddp (nth 1 a))))) |
| 838 | |
| 839 | |
| 840 | (defun calcFunc-dreal (expr) |
| 841 | (let ((types (math-possible-types expr))) |
| 842 | (if (< types 16) 1 |
| 843 | (if (= (logand types 15) 0) 0 |
| 844 | (math-reject-arg expr 'realp 'quiet))))) |
| 845 | |
| 846 | (defun calcFunc-dimag (expr) |
| 847 | (let ((types (math-possible-types expr))) |
| 848 | (if (= types 16) 1 |
| 849 | (if (= (logand types 16) 0) 0 |
| 850 | (math-reject-arg expr "Expected an imaginary number"))))) |
| 851 | |
| 852 | (defun calcFunc-dpos (expr) |
| 853 | (let ((signs (math-possible-signs expr))) |
| 854 | (if (eq signs 4) 1 |
| 855 | (if (memq signs '(1 2 3)) 0 |
| 856 | (math-reject-arg expr 'posp 'quiet))))) |
| 857 | |
| 858 | (defun calcFunc-dneg (expr) |
| 859 | (let ((signs (math-possible-signs expr))) |
| 860 | (if (eq signs 1) 1 |
| 861 | (if (memq signs '(2 4 6)) 0 |
| 862 | (math-reject-arg expr 'negp 'quiet))))) |
| 863 | |
| 864 | (defun calcFunc-dnonneg (expr) |
| 865 | (let ((signs (math-possible-signs expr))) |
| 866 | (if (memq signs '(2 4 6)) 1 |
| 867 | (if (eq signs 1) 0 |
| 868 | (math-reject-arg expr 'posp 'quiet))))) |
| 869 | |
| 870 | (defun calcFunc-dnonzero (expr) |
| 871 | (let ((signs (math-possible-signs expr))) |
| 872 | (if (memq signs '(1 4 5 8 9 12 13)) 1 |
| 873 | (if (eq signs 2) 0 |
| 874 | (math-reject-arg expr 'nonzerop 'quiet))))) |
| 875 | |
| 876 | (defun calcFunc-dint (expr) |
| 877 | (let ((types (math-possible-types expr))) |
| 878 | (if (= types 1) 1 |
| 879 | (if (= (logand types 1) 0) 0 |
| 880 | (math-reject-arg expr 'integerp 'quiet))))) |
| 881 | |
| 882 | (defun calcFunc-dnumint (expr) |
| 883 | (let ((types (math-possible-types expr t))) |
| 884 | (if (<= types 3) 1 |
| 885 | (if (= (logand types 3) 0) 0 |
| 886 | (math-reject-arg expr 'integerp 'quiet))))) |
| 887 | |
| 888 | (defun calcFunc-dnatnum (expr) |
| 889 | (let ((res (calcFunc-dint expr))) |
| 890 | (if (eq res 1) |
| 891 | (calcFunc-dnonneg expr) |
| 892 | res))) |
| 893 | |
| 894 | (defun calcFunc-deven (expr) |
| 895 | (if (math-known-evenp expr) |
| 896 | 1 |
| 897 | (if (or (math-known-oddp expr) |
| 898 | (= (logand (math-possible-types expr) 3) 0)) |
| 899 | 0 |
| 900 | (math-reject-arg expr "Can't tell if expression is odd or even")))) |
| 901 | |
| 902 | (defun calcFunc-dodd (expr) |
| 903 | (if (math-known-oddp expr) |
| 904 | 1 |
| 905 | (if (or (math-known-evenp expr) |
| 906 | (= (logand (math-possible-types expr) 3) 0)) |
| 907 | 0 |
| 908 | (math-reject-arg expr "Can't tell if expression is odd or even")))) |
| 909 | |
| 910 | (defun calcFunc-drat (expr) |
| 911 | (let ((types (math-possible-types expr))) |
| 912 | (if (memq types '(1 4 5)) 1 |
| 913 | (if (= (logand types 5) 0) 0 |
| 914 | (math-reject-arg expr "Rational number expected"))))) |
| 915 | |
| 916 | (defun calcFunc-drange (expr) |
| 917 | (math-setup-declarations) |
| 918 | (let (range) |
| 919 | (if (Math-realp expr) |
| 920 | (list 'vec expr) |
| 921 | (if (eq (car-safe expr) 'intv) |
| 922 | expr |
| 923 | (if (eq (car-safe expr) 'var) |
| 924 | (setq range (nth 2 (or (assq (nth 2 expr) math-decls-cache) |
| 925 | math-decls-all))) |
| 926 | (setq range (nth 2 (assq (car-safe expr) math-decls-cache)))) |
| 927 | (if range |
| 928 | (math-clean-set (copy-sequence range)) |
| 929 | (setq range (math-possible-signs expr)) |
| 930 | (if (< range 8) |
| 931 | (aref [(vec) |
| 932 | (intv 2 (neg (var inf var-inf)) 0) |
| 933 | (vec 0) |
| 934 | (intv 3 (neg (var inf var-inf)) 0) |
| 935 | (intv 1 0 (var inf var-inf)) |
| 936 | (vec (intv 2 (neg (var inf var-inf)) 0) |
| 937 | (intv 1 0 (var inf var-inf))) |
| 938 | (intv 3 0 (var inf var-inf)) |
| 939 | (intv 3 (neg (var inf var-inf)) (var inf var-inf))] range) |
| 940 | (math-reject-arg expr 'realp 'quiet))))))) |
| 941 | |
| 942 | (defun calcFunc-dscalar (a) |
| 943 | (if (math-known-scalarp a) 1 |
| 944 | (if (math-known-matrixp a) 0 |
| 945 | (math-reject-arg a 'objectp 'quiet)))) |
| 946 | |
| 947 | |
| 948 | ;;;; Arithmetic. |
| 949 | |
| 950 | (defsubst calcFunc-neg (a) |
| 951 | (math-normalize (list 'neg a))) |
| 952 | |
| 953 | (defun math-neg-fancy (a) |
| 954 | (cond ((eq (car a) 'polar) |
| 955 | (list 'polar |
| 956 | (nth 1 a) |
| 957 | (if (math-posp (nth 2 a)) |
| 958 | (math-sub (nth 2 a) (math-half-circle nil)) |
| 959 | (math-add (nth 2 a) (math-half-circle nil))))) |
| 960 | ((eq (car a) 'mod) |
| 961 | (if (math-zerop (nth 1 a)) |
| 962 | a |
| 963 | (list 'mod (math-sub (nth 2 a) (nth 1 a)) (nth 2 a)))) |
| 964 | ((eq (car a) 'sdev) |
| 965 | (list 'sdev (math-neg (nth 1 a)) (nth 2 a))) |
| 966 | ((eq (car a) 'intv) |
| 967 | (math-make-intv (aref [0 2 1 3] (nth 1 a)) |
| 968 | (math-neg (nth 3 a)) |
| 969 | (math-neg (nth 2 a)))) |
| 970 | ((and math-simplify-only |
| 971 | (not (equal a math-simplify-only))) |
| 972 | (list 'neg a)) |
| 973 | ((eq (car a) '+) |
| 974 | (math-sub (math-neg (nth 1 a)) (nth 2 a))) |
| 975 | ((eq (car a) '-) |
| 976 | (math-sub (nth 2 a) (nth 1 a))) |
| 977 | ((and (memq (car a) '(* /)) |
| 978 | (math-okay-neg (nth 1 a))) |
| 979 | (list (car a) (math-neg (nth 1 a)) (nth 2 a))) |
| 980 | ((and (memq (car a) '(* /)) |
| 981 | (math-okay-neg (nth 2 a))) |
| 982 | (list (car a) (nth 1 a) (math-neg (nth 2 a)))) |
| 983 | ((and (memq (car a) '(* /)) |
| 984 | (or (math-objectp (nth 1 a)) |
| 985 | (and (eq (car (nth 1 a)) '*) |
| 986 | (math-objectp (nth 1 (nth 1 a)))))) |
| 987 | (list (car a) (math-neg (nth 1 a)) (nth 2 a))) |
| 988 | ((and (eq (car a) '/) |
| 989 | (or (math-objectp (nth 2 a)) |
| 990 | (and (eq (car (nth 2 a)) '*) |
| 991 | (math-objectp (nth 1 (nth 2 a)))))) |
| 992 | (list (car a) (nth 1 a) (math-neg (nth 2 a)))) |
| 993 | ((and (eq (car a) 'var) (memq (nth 2 a) '(var-uinf var-nan))) |
| 994 | a) |
| 995 | ((eq (car a) 'neg) |
| 996 | (nth 1 a)) |
| 997 | (t (list 'neg a)))) |
| 998 | |
| 999 | (defun math-okay-neg (a) |
| 1000 | (or (math-looks-negp a) |
| 1001 | (eq (car-safe a) '-))) |
| 1002 | |
| 1003 | (defun math-neg-float (a) |
| 1004 | (list 'float (Math-integer-neg (nth 1 a)) (nth 2 a))) |
| 1005 | |
| 1006 | |
| 1007 | (defun calcFunc-add (&rest rest) |
| 1008 | (if rest |
| 1009 | (let ((a (car rest))) |
| 1010 | (while (setq rest (cdr rest)) |
| 1011 | (setq a (list '+ a (car rest)))) |
| 1012 | (math-normalize a)) |
| 1013 | 0)) |
| 1014 | |
| 1015 | (defun calcFunc-sub (&rest rest) |
| 1016 | (if rest |
| 1017 | (let ((a (car rest))) |
| 1018 | (while (setq rest (cdr rest)) |
| 1019 | (setq a (list '- a (car rest)))) |
| 1020 | (math-normalize a)) |
| 1021 | 0)) |
| 1022 | |
| 1023 | (defun math-add-objects-fancy (a b) |
| 1024 | (cond ((and (Math-numberp a) (Math-numberp b)) |
| 1025 | (let ((aa (math-complex a)) |
| 1026 | (bb (math-complex b))) |
| 1027 | (math-normalize |
| 1028 | (let ((res (list 'cplx |
| 1029 | (math-add (nth 1 aa) (nth 1 bb)) |
| 1030 | (math-add (nth 2 aa) (nth 2 bb))))) |
| 1031 | (if (math-want-polar a b) |
| 1032 | (math-polar res) |
| 1033 | res))))) |
| 1034 | ((or (Math-vectorp a) (Math-vectorp b)) |
| 1035 | (math-map-vec-2 'math-add a b)) |
| 1036 | ((eq (car-safe a) 'sdev) |
| 1037 | (if (eq (car-safe b) 'sdev) |
| 1038 | (math-make-sdev (math-add (nth 1 a) (nth 1 b)) |
| 1039 | (math-hypot (nth 2 a) (nth 2 b))) |
| 1040 | (and (or (Math-scalarp b) |
| 1041 | (not (Math-objvecp b))) |
| 1042 | (math-make-sdev (math-add (nth 1 a) b) (nth 2 a))))) |
| 1043 | ((and (eq (car-safe b) 'sdev) |
| 1044 | (or (Math-scalarp a) |
| 1045 | (not (Math-objvecp a)))) |
| 1046 | (math-make-sdev (math-add a (nth 1 b)) (nth 2 b))) |
| 1047 | ((eq (car-safe a) 'intv) |
| 1048 | (if (eq (car-safe b) 'intv) |
| 1049 | (math-make-intv (logior (logand (nth 1 a) (nth 1 b)) |
| 1050 | (if (equal (nth 2 a) |
| 1051 | '(neg (var inf var-inf))) |
| 1052 | (logand (nth 1 a) 2) 0) |
| 1053 | (if (equal (nth 2 b) |
| 1054 | '(neg (var inf var-inf))) |
| 1055 | (logand (nth 1 b) 2) 0) |
| 1056 | (if (equal (nth 3 a) '(var inf var-inf)) |
| 1057 | (logand (nth 1 a) 1) 0) |
| 1058 | (if (equal (nth 3 b) '(var inf var-inf)) |
| 1059 | (logand (nth 1 b) 1) 0)) |
| 1060 | (math-add (nth 2 a) (nth 2 b)) |
| 1061 | (math-add (nth 3 a) (nth 3 b))) |
| 1062 | (and (or (Math-anglep b) |
| 1063 | (eq (car b) 'date) |
| 1064 | (not (Math-objvecp b))) |
| 1065 | (math-make-intv (nth 1 a) |
| 1066 | (math-add (nth 2 a) b) |
| 1067 | (math-add (nth 3 a) b))))) |
| 1068 | ((and (eq (car-safe b) 'intv) |
| 1069 | (or (Math-anglep a) |
| 1070 | (eq (car a) 'date) |
| 1071 | (not (Math-objvecp a)))) |
| 1072 | (math-make-intv (nth 1 b) |
| 1073 | (math-add a (nth 2 b)) |
| 1074 | (math-add a (nth 3 b)))) |
| 1075 | ((eq (car-safe a) 'date) |
| 1076 | (cond ((eq (car-safe b) 'date) |
| 1077 | (math-add (nth 1 a) (nth 1 b))) |
| 1078 | ((eq (car-safe b) 'hms) |
| 1079 | (let ((parts (math-date-parts (nth 1 a)))) |
| 1080 | (list 'date |
| 1081 | (math-add (car parts) ; this minimizes roundoff |
| 1082 | (math-div (math-add |
| 1083 | (math-add (nth 1 parts) |
| 1084 | (nth 2 parts)) |
| 1085 | (math-add |
| 1086 | (math-mul (nth 1 b) 3600) |
| 1087 | (math-add (math-mul (nth 2 b) 60) |
| 1088 | (nth 3 b)))) |
| 1089 | 86400))))) |
| 1090 | ((Math-realp b) |
| 1091 | (list 'date (math-add (nth 1 a) b))) |
| 1092 | (t nil))) |
| 1093 | ((eq (car-safe b) 'date) |
| 1094 | (math-add-objects-fancy b a)) |
| 1095 | ((and (eq (car-safe a) 'mod) |
| 1096 | (eq (car-safe b) 'mod) |
| 1097 | (equal (nth 2 a) (nth 2 b))) |
| 1098 | (math-make-mod (math-add (nth 1 a) (nth 1 b)) (nth 2 a))) |
| 1099 | ((and (eq (car-safe a) 'mod) |
| 1100 | (Math-anglep b)) |
| 1101 | (math-make-mod (math-add (nth 1 a) b) (nth 2 a))) |
| 1102 | ((and (eq (car-safe b) 'mod) |
| 1103 | (Math-anglep a)) |
| 1104 | (math-make-mod (math-add a (nth 1 b)) (nth 2 b))) |
| 1105 | ((and (or (eq (car-safe a) 'hms) (eq (car-safe b) 'hms)) |
| 1106 | (and (Math-anglep a) (Math-anglep b))) |
| 1107 | (or (eq (car-safe a) 'hms) (setq a (math-to-hms a))) |
| 1108 | (or (eq (car-safe b) 'hms) (setq b (math-to-hms b))) |
| 1109 | (math-normalize |
| 1110 | (if (math-negp a) |
| 1111 | (math-neg (math-add (math-neg a) (math-neg b))) |
| 1112 | (if (math-negp b) |
| 1113 | (let* ((s (math-add (nth 3 a) (nth 3 b))) |
| 1114 | (m (math-add (nth 2 a) (nth 2 b))) |
| 1115 | (h (math-add (nth 1 a) (nth 1 b)))) |
| 1116 | (if (math-negp s) |
| 1117 | (setq s (math-add s 60) |
| 1118 | m (math-add m -1))) |
| 1119 | (if (math-negp m) |
| 1120 | (setq m (math-add m 60) |
| 1121 | h (math-add h -1))) |
| 1122 | (if (math-negp h) |
| 1123 | (math-add b a) |
| 1124 | (list 'hms h m s))) |
| 1125 | (let* ((s (math-add (nth 3 a) (nth 3 b))) |
| 1126 | (m (math-add (nth 2 a) (nth 2 b))) |
| 1127 | (h (math-add (nth 1 a) (nth 1 b)))) |
| 1128 | (list 'hms h m s)))))) |
| 1129 | (t (calc-record-why "*Incompatible arguments for +" a b)))) |
| 1130 | |
| 1131 | (defun math-add-symb-fancy (a b) |
| 1132 | (or (and math-simplify-only |
| 1133 | (not (equal a math-simplify-only)) |
| 1134 | (list '+ a b)) |
| 1135 | (and (eq (car-safe b) '+) |
| 1136 | (math-add (math-add a (nth 1 b)) |
| 1137 | (nth 2 b))) |
| 1138 | (and (eq (car-safe b) '-) |
| 1139 | (math-sub (math-add a (nth 1 b)) |
| 1140 | (nth 2 b))) |
| 1141 | (and (eq (car-safe b) 'neg) |
| 1142 | (eq (car-safe (nth 1 b)) '+) |
| 1143 | (math-sub (math-sub a (nth 1 (nth 1 b))) |
| 1144 | (nth 2 (nth 1 b)))) |
| 1145 | (and (or (and (Math-vectorp a) (math-known-scalarp b)) |
| 1146 | (and (Math-vectorp b) (math-known-scalarp a))) |
| 1147 | (math-map-vec-2 'math-add a b)) |
| 1148 | (let ((inf (math-infinitep a))) |
| 1149 | (cond |
| 1150 | (inf |
| 1151 | (let ((inf2 (math-infinitep b))) |
| 1152 | (if inf2 |
| 1153 | (if (or (memq (nth 2 inf) '(var-uinf var-nan)) |
| 1154 | (memq (nth 2 inf2) '(var-uinf var-nan))) |
| 1155 | '(var nan var-nan) |
| 1156 | (let ((dir (math-infinite-dir a inf)) |
| 1157 | (dir2 (math-infinite-dir b inf2))) |
| 1158 | (if (and (Math-objectp dir) (Math-objectp dir2)) |
| 1159 | (if (Math-equal dir dir2) |
| 1160 | a |
| 1161 | '(var nan var-nan))))) |
| 1162 | (if (and (equal a '(var inf var-inf)) |
| 1163 | (eq (car-safe b) 'intv) |
| 1164 | (memq (nth 1 b) '(2 3)) |
| 1165 | (equal (nth 2 b) '(neg (var inf var-inf)))) |
| 1166 | (list 'intv 3 (nth 2 b) a) |
| 1167 | (if (and (equal a '(neg (var inf var-inf))) |
| 1168 | (eq (car-safe b) 'intv) |
| 1169 | (memq (nth 1 b) '(1 3)) |
| 1170 | (equal (nth 3 b) '(var inf var-inf))) |
| 1171 | (list 'intv 3 a (nth 3 b)) |
| 1172 | a))))) |
| 1173 | ((math-infinitep b) |
| 1174 | (if (eq (car-safe a) 'intv) |
| 1175 | (math-add b a) |
| 1176 | b)) |
| 1177 | ((eq (car-safe a) '+) |
| 1178 | (let ((temp (math-combine-sum (nth 2 a) b nil nil t))) |
| 1179 | (and temp |
| 1180 | (math-add (nth 1 a) temp)))) |
| 1181 | ((eq (car-safe a) '-) |
| 1182 | (let ((temp (math-combine-sum (nth 2 a) b t nil t))) |
| 1183 | (and temp |
| 1184 | (math-add (nth 1 a) temp)))) |
| 1185 | ((and (Math-objectp a) (Math-objectp b)) |
| 1186 | nil) |
| 1187 | (t |
| 1188 | (math-combine-sum a b nil nil nil)))) |
| 1189 | (and (Math-looks-negp b) |
| 1190 | (list '- a (math-neg b))) |
| 1191 | (and (Math-looks-negp a) |
| 1192 | (list '- b (math-neg a))) |
| 1193 | (and (eq (car-safe a) 'calcFunc-idn) |
| 1194 | (= (length a) 2) |
| 1195 | (or (and (eq (car-safe b) 'calcFunc-idn) |
| 1196 | (= (length b) 2) |
| 1197 | (list 'calcFunc-idn (math-add (nth 1 a) (nth 1 b)))) |
| 1198 | (and (math-square-matrixp b) |
| 1199 | (math-add (math-mimic-ident (nth 1 a) b) b)) |
| 1200 | (and (math-known-scalarp b) |
| 1201 | (math-add (nth 1 a) b)))) |
| 1202 | (and (eq (car-safe b) 'calcFunc-idn) |
| 1203 | (= (length b) 2) |
| 1204 | (or (and (math-square-matrixp a) |
| 1205 | (math-add a (math-mimic-ident (nth 1 b) a))) |
| 1206 | (and (math-known-scalarp a) |
| 1207 | (math-add a (nth 1 b))))) |
| 1208 | (list '+ a b))) |
| 1209 | |
| 1210 | |
| 1211 | (defun calcFunc-mul (&rest rest) |
| 1212 | (if rest |
| 1213 | (let ((a (car rest))) |
| 1214 | (while (setq rest (cdr rest)) |
| 1215 | (setq a (list '* a (car rest)))) |
| 1216 | (math-normalize a)) |
| 1217 | 1)) |
| 1218 | |
| 1219 | (defun math-mul-objects-fancy (a b) |
| 1220 | (cond ((and (Math-numberp a) (Math-numberp b)) |
| 1221 | (math-normalize |
| 1222 | (if (math-want-polar a b) |
| 1223 | (let ((a (math-polar a)) |
| 1224 | (b (math-polar b))) |
| 1225 | (list 'polar |
| 1226 | (math-mul (nth 1 a) (nth 1 b)) |
| 1227 | (math-fix-circular (math-add (nth 2 a) (nth 2 b))))) |
| 1228 | (setq a (math-complex a) |
| 1229 | b (math-complex b)) |
| 1230 | (list 'cplx |
| 1231 | (math-sub (math-mul (nth 1 a) (nth 1 b)) |
| 1232 | (math-mul (nth 2 a) (nth 2 b))) |
| 1233 | (math-add (math-mul (nth 1 a) (nth 2 b)) |
| 1234 | (math-mul (nth 2 a) (nth 1 b))))))) |
| 1235 | ((Math-vectorp a) |
| 1236 | (if (Math-vectorp b) |
| 1237 | (if (math-matrixp a) |
| 1238 | (if (math-matrixp b) |
| 1239 | (if (= (length (nth 1 a)) (length b)) |
| 1240 | (math-mul-mats a b) |
| 1241 | (math-dimension-error)) |
| 1242 | (if (= (length (nth 1 a)) 2) |
| 1243 | (if (= (length a) (length b)) |
| 1244 | (math-mul-mats a (list 'vec b)) |
| 1245 | (math-dimension-error)) |
| 1246 | (if (= (length (nth 1 a)) (length b)) |
| 1247 | (math-mul-mat-vec a b) |
| 1248 | (math-dimension-error)))) |
| 1249 | (if (math-matrixp b) |
| 1250 | (if (= (length a) (length b)) |
| 1251 | (nth 1 (math-mul-mats (list 'vec a) b)) |
| 1252 | (math-dimension-error)) |
| 1253 | (if (= (length a) (length b)) |
| 1254 | (math-dot-product a b) |
| 1255 | (math-dimension-error)))) |
| 1256 | (math-map-vec-2 'math-mul a b))) |
| 1257 | ((Math-vectorp b) |
| 1258 | (math-map-vec-2 'math-mul a b)) |
| 1259 | ((eq (car-safe a) 'sdev) |
| 1260 | (if (eq (car-safe b) 'sdev) |
| 1261 | (math-make-sdev (math-mul (nth 1 a) (nth 1 b)) |
| 1262 | (math-hypot (math-mul (nth 2 a) (nth 1 b)) |
| 1263 | (math-mul (nth 2 b) (nth 1 a)))) |
| 1264 | (and (or (Math-scalarp b) |
| 1265 | (not (Math-objvecp b))) |
| 1266 | (math-make-sdev (math-mul (nth 1 a) b) |
| 1267 | (math-mul (nth 2 a) b))))) |
| 1268 | ((and (eq (car-safe b) 'sdev) |
| 1269 | (or (Math-scalarp a) |
| 1270 | (not (Math-objvecp a)))) |
| 1271 | (math-make-sdev (math-mul a (nth 1 b)) (math-mul a (nth 2 b)))) |
| 1272 | ((and (eq (car-safe a) 'intv) (Math-anglep b)) |
| 1273 | (if (Math-negp b) |
| 1274 | (math-neg (math-mul a (math-neg b))) |
| 1275 | (math-make-intv (nth 1 a) |
| 1276 | (math-mul (nth 2 a) b) |
| 1277 | (math-mul (nth 3 a) b)))) |
| 1278 | ((and (eq (car-safe b) 'intv) (Math-anglep a)) |
| 1279 | (math-mul b a)) |
| 1280 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) |
| 1281 | (eq (car-safe b) 'intv) (math-intv-constp b)) |
| 1282 | (let ((lo (math-mul a (nth 2 b))) |
| 1283 | (hi (math-mul a (nth 3 b)))) |
| 1284 | (or (eq (car-safe lo) 'intv) |
| 1285 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) lo lo))) |
| 1286 | (or (eq (car-safe hi) 'intv) |
| 1287 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) hi hi))) |
| 1288 | (math-combine-intervals |
| 1289 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 1290 | (math-infinitep (nth 2 lo))) |
| 1291 | (memq (nth 1 lo) '(2 3))) |
| 1292 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 1293 | (math-infinitep (nth 3 lo))) |
| 1294 | (memq (nth 1 lo) '(1 3))) |
| 1295 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 1296 | (math-infinitep (nth 2 hi))) |
| 1297 | (memq (nth 1 hi) '(2 3))) |
| 1298 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 1299 | (math-infinitep (nth 3 hi))) |
| 1300 | (memq (nth 1 hi) '(1 3)))))) |
| 1301 | ((and (eq (car-safe a) 'mod) |
| 1302 | (eq (car-safe b) 'mod) |
| 1303 | (equal (nth 2 a) (nth 2 b))) |
| 1304 | (math-make-mod (math-mul (nth 1 a) (nth 1 b)) (nth 2 a))) |
| 1305 | ((and (eq (car-safe a) 'mod) |
| 1306 | (Math-anglep b)) |
| 1307 | (math-make-mod (math-mul (nth 1 a) b) (nth 2 a))) |
| 1308 | ((and (eq (car-safe b) 'mod) |
| 1309 | (Math-anglep a)) |
| 1310 | (math-make-mod (math-mul a (nth 1 b)) (nth 2 b))) |
| 1311 | ((and (eq (car-safe a) 'hms) (Math-realp b)) |
| 1312 | (math-with-extra-prec 2 |
| 1313 | (math-to-hms (math-mul (math-from-hms a 'deg) b) 'deg))) |
| 1314 | ((and (eq (car-safe b) 'hms) (Math-realp a)) |
| 1315 | (math-mul b a)) |
| 1316 | (t (calc-record-why "*Incompatible arguments for *" a b)))) |
| 1317 | |
| 1318 | ;;; Fast function to multiply floating-point numbers. |
| 1319 | (defun math-mul-float (a b) ; [F F F] |
| 1320 | (math-make-float (math-mul (nth 1 a) (nth 1 b)) |
| 1321 | (+ (nth 2 a) (nth 2 b)))) |
| 1322 | |
| 1323 | (defun math-sqr-float (a) ; [F F] |
| 1324 | (math-make-float (math-mul (nth 1 a) (nth 1 a)) |
| 1325 | (+ (nth 2 a) (nth 2 a)))) |
| 1326 | |
| 1327 | (defun math-intv-constp (a &optional finite) |
| 1328 | (and (or (Math-anglep (nth 2 a)) |
| 1329 | (and (equal (nth 2 a) '(neg (var inf var-inf))) |
| 1330 | (or (not finite) |
| 1331 | (memq (nth 1 a) '(0 1))))) |
| 1332 | (or (Math-anglep (nth 3 a)) |
| 1333 | (and (equal (nth 3 a) '(var inf var-inf)) |
| 1334 | (or (not finite) |
| 1335 | (memq (nth 1 a) '(0 2))))))) |
| 1336 | |
| 1337 | (defun math-mul-zero (a b) |
| 1338 | (if (math-known-matrixp b) |
| 1339 | (if (math-vectorp b) |
| 1340 | (math-map-vec-2 'math-mul a b) |
| 1341 | (math-mimic-ident 0 b)) |
| 1342 | (if (math-infinitep b) |
| 1343 | '(var nan var-nan) |
| 1344 | (let ((aa nil) (bb nil)) |
| 1345 | (if (and (eq (car-safe b) 'intv) |
| 1346 | (progn |
| 1347 | (and (equal (nth 2 b) '(neg (var inf var-inf))) |
| 1348 | (memq (nth 1 b) '(2 3)) |
| 1349 | (setq aa (nth 2 b))) |
| 1350 | (and (equal (nth 3 b) '(var inf var-inf)) |
| 1351 | (memq (nth 1 b) '(1 3)) |
| 1352 | (setq bb (nth 3 b))) |
| 1353 | (or aa bb))) |
| 1354 | (if (or (math-posp a) |
| 1355 | (and (math-zerop a) |
| 1356 | (or (memq calc-infinite-mode '(-1 1)) |
| 1357 | (setq aa '(neg (var inf var-inf)) |
| 1358 | bb '(var inf var-inf))))) |
| 1359 | (list 'intv 3 (or aa 0) (or bb 0)) |
| 1360 | (if (math-negp a) |
| 1361 | (math-neg (list 'intv 3 (or aa 0) (or bb 0))) |
| 1362 | '(var nan var-nan))) |
| 1363 | (if (or (math-floatp a) (math-floatp b)) '(float 0 0) 0)))))) |
| 1364 | |
| 1365 | |
| 1366 | (defun math-mul-symb-fancy (a b) |
| 1367 | (or (and math-simplify-only |
| 1368 | (not (equal a math-simplify-only)) |
| 1369 | (list '* a b)) |
| 1370 | (and (Math-equal-int a 1) |
| 1371 | b) |
| 1372 | (and (Math-equal-int a -1) |
| 1373 | (math-neg b)) |
| 1374 | (and (or (and (Math-vectorp a) (math-known-scalarp b)) |
| 1375 | (and (Math-vectorp b) (math-known-scalarp a))) |
| 1376 | (math-map-vec-2 'math-mul a b)) |
| 1377 | (and (Math-objectp b) (not (Math-objectp a)) |
| 1378 | (math-mul b a)) |
| 1379 | (and (eq (car-safe a) 'neg) |
| 1380 | (math-neg (math-mul (nth 1 a) b))) |
| 1381 | (and (eq (car-safe b) 'neg) |
| 1382 | (math-neg (math-mul a (nth 1 b)))) |
| 1383 | (and (eq (car-safe a) '*) |
| 1384 | (math-mul (nth 1 a) |
| 1385 | (math-mul (nth 2 a) b))) |
| 1386 | (and (eq (car-safe a) '^) |
| 1387 | (Math-looks-negp (nth 2 a)) |
| 1388 | (not (and (eq (car-safe b) '^) (Math-looks-negp (nth 2 b)))) |
| 1389 | (math-known-scalarp b t) |
| 1390 | (math-div b (math-normalize |
| 1391 | (list '^ (nth 1 a) (math-neg (nth 2 a)))))) |
| 1392 | (and (eq (car-safe b) '^) |
| 1393 | (Math-looks-negp (nth 2 b)) |
| 1394 | (not (and (eq (car-safe a) '^) (Math-looks-negp (nth 2 a)))) |
| 1395 | (not (math-known-matrixp (nth 1 b))) |
| 1396 | (math-div a (math-normalize |
| 1397 | (list '^ (nth 1 b) (math-neg (nth 2 b)))))) |
| 1398 | (and (eq (car-safe a) '/) |
| 1399 | (or (math-known-scalarp a t) (math-known-scalarp b t)) |
| 1400 | (let ((temp (math-combine-prod (nth 2 a) b t nil t))) |
| 1401 | (if temp |
| 1402 | (math-mul (nth 1 a) temp) |
| 1403 | (math-div (math-mul (nth 1 a) b) (nth 2 a))))) |
| 1404 | (and (eq (car-safe b) '/) |
| 1405 | (math-div (math-mul a (nth 1 b)) (nth 2 b))) |
| 1406 | (and (eq (car-safe b) '+) |
| 1407 | (Math-numberp a) |
| 1408 | (or (Math-numberp (nth 1 b)) |
| 1409 | (Math-numberp (nth 2 b))) |
| 1410 | (math-add (math-mul a (nth 1 b)) |
| 1411 | (math-mul a (nth 2 b)))) |
| 1412 | (and (eq (car-safe b) '-) |
| 1413 | (Math-numberp a) |
| 1414 | (or (Math-numberp (nth 1 b)) |
| 1415 | (Math-numberp (nth 2 b))) |
| 1416 | (math-sub (math-mul a (nth 1 b)) |
| 1417 | (math-mul a (nth 2 b)))) |
| 1418 | (and (eq (car-safe b) '*) |
| 1419 | (Math-numberp (nth 1 b)) |
| 1420 | (not (Math-numberp a)) |
| 1421 | (math-mul (nth 1 b) (math-mul a (nth 2 b)))) |
| 1422 | (and (eq (car-safe a) 'calcFunc-idn) |
| 1423 | (= (length a) 2) |
| 1424 | (or (and (eq (car-safe b) 'calcFunc-idn) |
| 1425 | (= (length b) 2) |
| 1426 | (list 'calcFunc-idn (math-mul (nth 1 a) (nth 1 b)))) |
| 1427 | (and (math-known-scalarp b) |
| 1428 | (list 'calcFunc-idn (math-mul (nth 1 a) b))) |
| 1429 | (and (math-known-matrixp b) |
| 1430 | (math-mul (nth 1 a) b)))) |
| 1431 | (and (eq (car-safe b) 'calcFunc-idn) |
| 1432 | (= (length b) 2) |
| 1433 | (or (and (math-known-scalarp a) |
| 1434 | (list 'calcFunc-idn (math-mul a (nth 1 b)))) |
| 1435 | (and (math-known-matrixp a) |
| 1436 | (math-mul a (nth 1 b))))) |
| 1437 | (and (math-identity-matrix-p a t) |
| 1438 | (or (and (eq (car-safe b) 'calcFunc-idn) |
| 1439 | (= (length b) 2) |
| 1440 | (list 'calcFunc-idn (math-mul |
| 1441 | (nth 1 (nth 1 a)) |
| 1442 | (nth 1 b)) |
| 1443 | (1- (length a)))) |
| 1444 | (and (math-known-scalarp b) |
| 1445 | (list 'calcFunc-idn (math-mul |
| 1446 | (nth 1 (nth 1 a)) b) |
| 1447 | (1- (length a)))) |
| 1448 | (and (math-known-matrixp b) |
| 1449 | (math-mul (nth 1 (nth 1 a)) b)))) |
| 1450 | (and (math-identity-matrix-p b t) |
| 1451 | (or (and (eq (car-safe a) 'calcFunc-idn) |
| 1452 | (= (length a) 2) |
| 1453 | (list 'calcFunc-idn (math-mul (nth 1 a) |
| 1454 | (nth 1 (nth 1 b))) |
| 1455 | (1- (length b)))) |
| 1456 | (and (math-known-scalarp a) |
| 1457 | (list 'calcFunc-idn (math-mul a (nth 1 (nth 1 b))) |
| 1458 | (1- (length b)))) |
| 1459 | (and (math-known-matrixp a) |
| 1460 | (math-mul a (nth 1 (nth 1 b)))))) |
| 1461 | (and (math-looks-negp b) |
| 1462 | (math-mul (math-neg a) (math-neg b))) |
| 1463 | (and (eq (car-safe b) '-) |
| 1464 | (math-looks-negp a) |
| 1465 | (math-mul (math-neg a) (math-neg b))) |
| 1466 | (cond |
| 1467 | ((eq (car-safe b) '*) |
| 1468 | (let ((temp (math-combine-prod a (nth 1 b) nil nil t))) |
| 1469 | (and temp |
| 1470 | (math-mul temp (nth 2 b))))) |
| 1471 | (t |
| 1472 | (math-combine-prod a b nil nil nil))) |
| 1473 | (and (equal a '(var nan var-nan)) |
| 1474 | a) |
| 1475 | (and (equal b '(var nan var-nan)) |
| 1476 | b) |
| 1477 | (and (equal a '(var uinf var-uinf)) |
| 1478 | a) |
| 1479 | (and (equal b '(var uinf var-uinf)) |
| 1480 | b) |
| 1481 | (and (equal b '(var inf var-inf)) |
| 1482 | (let ((s1 (math-possible-signs a))) |
| 1483 | (cond ((eq s1 4) |
| 1484 | b) |
| 1485 | ((eq s1 6) |
| 1486 | '(intv 3 0 (var inf var-inf))) |
| 1487 | ((eq s1 1) |
| 1488 | (math-neg b)) |
| 1489 | ((eq s1 3) |
| 1490 | '(intv 3 (neg (var inf var-inf)) 0)) |
| 1491 | ((and (eq (car a) 'intv) (math-intv-constp a)) |
| 1492 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf))) |
| 1493 | ((and (eq (car a) 'cplx) |
| 1494 | (math-zerop (nth 1 a))) |
| 1495 | (list '* (list 'cplx 0 (calcFunc-sign (nth 2 a))) b)) |
| 1496 | ((eq (car a) 'polar) |
| 1497 | (list '* (list 'polar 1 (nth 2 a)) b))))) |
| 1498 | (and (equal a '(var inf var-inf)) |
| 1499 | (math-mul b a)) |
| 1500 | (list '* a b))) |
| 1501 | |
| 1502 | |
| 1503 | (defun calcFunc-div (a &rest rest) |
| 1504 | (while rest |
| 1505 | (setq a (list '/ a (car rest)) |
| 1506 | rest (cdr rest))) |
| 1507 | (math-normalize a)) |
| 1508 | |
| 1509 | (defun math-div-objects-fancy (a b) |
| 1510 | (cond ((and (Math-numberp a) (Math-numberp b)) |
| 1511 | (math-normalize |
| 1512 | (cond ((math-want-polar a b) |
| 1513 | (let ((a (math-polar a)) |
| 1514 | (b (math-polar b))) |
| 1515 | (list 'polar |
| 1516 | (math-div (nth 1 a) (nth 1 b)) |
| 1517 | (math-fix-circular (math-sub (nth 2 a) |
| 1518 | (nth 2 b)))))) |
| 1519 | ((Math-realp b) |
| 1520 | (setq a (math-complex a)) |
| 1521 | (list 'cplx (math-div (nth 1 a) b) |
| 1522 | (math-div (nth 2 a) b))) |
| 1523 | (t |
| 1524 | (setq a (math-complex a) |
| 1525 | b (math-complex b)) |
| 1526 | (math-div |
| 1527 | (list 'cplx |
| 1528 | (math-add (math-mul (nth 1 a) (nth 1 b)) |
| 1529 | (math-mul (nth 2 a) (nth 2 b))) |
| 1530 | (math-sub (math-mul (nth 2 a) (nth 1 b)) |
| 1531 | (math-mul (nth 1 a) (nth 2 b)))) |
| 1532 | (math-add (math-sqr (nth 1 b)) |
| 1533 | (math-sqr (nth 2 b)))))))) |
| 1534 | ((math-matrixp b) |
| 1535 | (if (math-square-matrixp b) |
| 1536 | (let ((n1 (length b))) |
| 1537 | (if (Math-vectorp a) |
| 1538 | (if (math-matrixp a) |
| 1539 | (if (= (length a) n1) |
| 1540 | (math-lud-solve (math-matrix-lud b) a b) |
| 1541 | (if (= (length (nth 1 a)) n1) |
| 1542 | (math-transpose |
| 1543 | (math-lud-solve (math-matrix-lud |
| 1544 | (math-transpose b)) |
| 1545 | (math-transpose a) b)) |
| 1546 | (math-dimension-error))) |
| 1547 | (if (= (length a) n1) |
| 1548 | (math-mat-col (math-lud-solve (math-matrix-lud b) |
| 1549 | (math-col-matrix a) b) |
| 1550 | 1) |
| 1551 | (math-dimension-error))) |
| 1552 | (if (Math-equal-int a 1) |
| 1553 | (calcFunc-inv b) |
| 1554 | (math-mul a (calcFunc-inv b))))) |
| 1555 | (math-reject-arg b 'square-matrixp))) |
| 1556 | ((and (Math-vectorp a) (Math-objectp b)) |
| 1557 | (math-map-vec-2 'math-div a b)) |
| 1558 | ((eq (car-safe a) 'sdev) |
| 1559 | (if (eq (car-safe b) 'sdev) |
| 1560 | (let ((x (math-div (nth 1 a) (nth 1 b)))) |
| 1561 | (math-make-sdev x |
| 1562 | (math-div (math-hypot (nth 2 a) |
| 1563 | (math-mul (nth 2 b) x)) |
| 1564 | (nth 1 b)))) |
| 1565 | (if (or (Math-scalarp b) |
| 1566 | (not (Math-objvecp b))) |
| 1567 | (math-make-sdev (math-div (nth 1 a) b) (math-div (nth 2 a) b)) |
| 1568 | (math-reject-arg 'realp b)))) |
| 1569 | ((and (eq (car-safe b) 'sdev) |
| 1570 | (or (Math-scalarp a) |
| 1571 | (not (Math-objvecp a)))) |
| 1572 | (let ((x (math-div a (nth 1 b)))) |
| 1573 | (math-make-sdev x |
| 1574 | (math-div (math-mul (nth 2 b) x) (nth 1 b))))) |
| 1575 | ((and (eq (car-safe a) 'intv) (Math-anglep b)) |
| 1576 | (if (Math-negp b) |
| 1577 | (math-neg (math-div a (math-neg b))) |
| 1578 | (math-make-intv (nth 1 a) |
| 1579 | (math-div (nth 2 a) b) |
| 1580 | (math-div (nth 3 a) b)))) |
| 1581 | ((and (eq (car-safe b) 'intv) (Math-anglep a)) |
| 1582 | (if (or (Math-posp (nth 2 b)) |
| 1583 | (and (Math-zerop (nth 2 b)) (or (memq (nth 1 b) '(0 1)) |
| 1584 | calc-infinite-mode))) |
| 1585 | (if (Math-negp a) |
| 1586 | (math-neg (math-div (math-neg a) b)) |
| 1587 | (let ((calc-infinite-mode 1)) |
| 1588 | (math-make-intv (aref [0 2 1 3] (nth 1 b)) |
| 1589 | (math-div a (nth 3 b)) |
| 1590 | (math-div a (nth 2 b))))) |
| 1591 | (if (or (Math-negp (nth 3 b)) |
| 1592 | (and (Math-zerop (nth 3 b)) (or (memq (nth 1 b) '(0 2)) |
| 1593 | calc-infinite-mode))) |
| 1594 | (math-neg (math-div a (math-neg b))) |
| 1595 | (if calc-infinite-mode |
| 1596 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) |
| 1597 | (math-reject-arg b "*Division by zero"))))) |
| 1598 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) |
| 1599 | (eq (car-safe b) 'intv) (math-intv-constp b)) |
| 1600 | (if (or (Math-posp (nth 2 b)) |
| 1601 | (and (Math-zerop (nth 2 b)) (or (memq (nth 1 b) '(0 1)) |
| 1602 | calc-infinite-mode))) |
| 1603 | (let* ((calc-infinite-mode 1) |
| 1604 | (lo (math-div a (nth 2 b))) |
| 1605 | (hi (math-div a (nth 3 b)))) |
| 1606 | (or (eq (car-safe lo) 'intv) |
| 1607 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) |
| 1608 | lo lo))) |
| 1609 | (or (eq (car-safe hi) 'intv) |
| 1610 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) |
| 1611 | hi hi))) |
| 1612 | (math-combine-intervals |
| 1613 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 1614 | (and (math-infinitep (nth 2 lo)) |
| 1615 | (not (math-zerop (nth 2 b))))) |
| 1616 | (memq (nth 1 lo) '(2 3))) |
| 1617 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 1618 | (and (math-infinitep (nth 3 lo)) |
| 1619 | (not (math-zerop (nth 2 b))))) |
| 1620 | (memq (nth 1 lo) '(1 3))) |
| 1621 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 1622 | (and (math-infinitep (nth 2 hi)) |
| 1623 | (not (math-zerop (nth 3 b))))) |
| 1624 | (memq (nth 1 hi) '(2 3))) |
| 1625 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 1626 | (and (math-infinitep (nth 3 hi)) |
| 1627 | (not (math-zerop (nth 3 b))))) |
| 1628 | (memq (nth 1 hi) '(1 3))))) |
| 1629 | (if (or (Math-negp (nth 3 b)) |
| 1630 | (and (Math-zerop (nth 3 b)) (or (memq (nth 1 b) '(0 2)) |
| 1631 | calc-infinite-mode))) |
| 1632 | (math-neg (math-div a (math-neg b))) |
| 1633 | (if calc-infinite-mode |
| 1634 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) |
| 1635 | (math-reject-arg b "*Division by zero"))))) |
| 1636 | ((and (eq (car-safe a) 'mod) |
| 1637 | (eq (car-safe b) 'mod) |
| 1638 | (equal (nth 2 a) (nth 2 b))) |
| 1639 | (math-make-mod (math-div-mod (nth 1 a) (nth 1 b) (nth 2 a)) |
| 1640 | (nth 2 a))) |
| 1641 | ((and (eq (car-safe a) 'mod) |
| 1642 | (Math-anglep b)) |
| 1643 | (math-make-mod (math-div-mod (nth 1 a) b (nth 2 a)) (nth 2 a))) |
| 1644 | ((and (eq (car-safe b) 'mod) |
| 1645 | (Math-anglep a)) |
| 1646 | (math-make-mod (math-div-mod a (nth 1 b) (nth 2 b)) (nth 2 b))) |
| 1647 | ((eq (car-safe a) 'hms) |
| 1648 | (if (eq (car-safe b) 'hms) |
| 1649 | (math-with-extra-prec 1 |
| 1650 | (math-div (math-from-hms a 'deg) |
| 1651 | (math-from-hms b 'deg))) |
| 1652 | (math-with-extra-prec 2 |
| 1653 | (math-to-hms (math-div (math-from-hms a 'deg) b) 'deg)))) |
| 1654 | (t (calc-record-why "*Incompatible arguments for /" a b)))) |
| 1655 | |
| 1656 | (defun math-div-by-zero (a b) |
| 1657 | (if (math-infinitep a) |
| 1658 | (if (or (equal a '(var nan var-nan)) |
| 1659 | (equal b '(var uinf var-uinf)) |
| 1660 | (memq calc-infinite-mode '(-1 1))) |
| 1661 | a |
| 1662 | '(var uinf var-uinf)) |
| 1663 | (if calc-infinite-mode |
| 1664 | (if (math-zerop a) |
| 1665 | '(var nan var-nan) |
| 1666 | (if (eq calc-infinite-mode 1) |
| 1667 | (math-mul a '(var inf var-inf)) |
| 1668 | (if (eq calc-infinite-mode -1) |
| 1669 | (math-mul a '(neg (var inf var-inf))) |
| 1670 | (if (eq (car-safe a) 'intv) |
| 1671 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) |
| 1672 | '(var uinf var-uinf))))) |
| 1673 | (math-reject-arg a "*Division by zero")))) |
| 1674 | |
| 1675 | (defun math-div-zero (a b) |
| 1676 | (if (math-known-matrixp b) |
| 1677 | (if (math-vectorp b) |
| 1678 | (math-map-vec-2 'math-div a b) |
| 1679 | (math-mimic-ident 0 b)) |
| 1680 | (if (equal b '(var nan var-nan)) |
| 1681 | b |
| 1682 | (if (and (eq (car-safe b) 'intv) (math-intv-constp b) |
| 1683 | (not (math-posp b)) (not (math-negp b))) |
| 1684 | (if calc-infinite-mode |
| 1685 | (list 'intv 3 |
| 1686 | (if (and (math-zerop (nth 2 b)) |
| 1687 | (memq calc-infinite-mode '(1 -1))) |
| 1688 | (nth 2 b) '(neg (var inf var-inf))) |
| 1689 | (if (and (math-zerop (nth 3 b)) |
| 1690 | (memq calc-infinite-mode '(1 -1))) |
| 1691 | (nth 3 b) '(var inf var-inf))) |
| 1692 | (math-reject-arg b "*Division by zero")) |
| 1693 | a)))) |
| 1694 | |
| 1695 | ;; For math-div-symb-fancy |
| 1696 | (defvar math-trig-inverses |
| 1697 | '((calcFunc-sin . calcFunc-csc) |
| 1698 | (calcFunc-cos . calcFunc-sec) |
| 1699 | (calcFunc-tan . calcFunc-cot) |
| 1700 | (calcFunc-sec . calcFunc-cos) |
| 1701 | (calcFunc-csc . calcFunc-sin) |
| 1702 | (calcFunc-cot . calcFunc-tan) |
| 1703 | (calcFunc-sinh . calcFunc-csch) |
| 1704 | (calcFunc-cosh . calcFunc-sech) |
| 1705 | (calcFunc-tanh . calcFunc-coth) |
| 1706 | (calcFunc-sech . calcFunc-cosh) |
| 1707 | (calcFunc-csch . calcFunc-sinh) |
| 1708 | (calcFunc-coth . calcFunc-tanh))) |
| 1709 | |
| 1710 | (defvar math-div-trig) |
| 1711 | (defvar math-div-non-trig) |
| 1712 | |
| 1713 | (defun math-div-new-trig (tr) |
| 1714 | (if math-div-trig |
| 1715 | (setq math-div-trig |
| 1716 | (list '* tr math-div-trig)) |
| 1717 | (setq math-div-trig tr))) |
| 1718 | |
| 1719 | (defun math-div-new-non-trig (ntr) |
| 1720 | (if math-div-non-trig |
| 1721 | (setq math-div-non-trig |
| 1722 | (list '* ntr math-div-non-trig)) |
| 1723 | (setq math-div-non-trig ntr))) |
| 1724 | |
| 1725 | (defun math-div-isolate-trig (expr) |
| 1726 | (if (eq (car-safe expr) '*) |
| 1727 | (progn |
| 1728 | (math-div-isolate-trig-term (nth 1 expr)) |
| 1729 | (math-div-isolate-trig (nth 2 expr))) |
| 1730 | (math-div-isolate-trig-term expr))) |
| 1731 | |
| 1732 | (defun math-div-isolate-trig-term (term) |
| 1733 | (let ((fn (assoc (car-safe term) math-trig-inverses))) |
| 1734 | (if fn |
| 1735 | (math-div-new-trig |
| 1736 | (cons (cdr fn) (cdr term))) |
| 1737 | (math-div-new-non-trig term)))) |
| 1738 | |
| 1739 | (defun math-div-symb-fancy (a b) |
| 1740 | (or (and (math-known-matrixp b) |
| 1741 | (math-mul a (math-pow b -1))) |
| 1742 | (and math-simplify-only |
| 1743 | (not (equal a math-simplify-only)) |
| 1744 | (list '/ a b)) |
| 1745 | (and (Math-equal-int b 1) a) |
| 1746 | (and (Math-equal-int b -1) (math-neg a)) |
| 1747 | (and (Math-vectorp a) (math-known-scalarp b) |
| 1748 | (math-map-vec-2 'math-div a b)) |
| 1749 | (and (eq (car-safe b) '^) |
| 1750 | (or (Math-looks-negp (nth 2 b)) (Math-equal-int a 1)) |
| 1751 | (math-mul a (math-normalize |
| 1752 | (list '^ (nth 1 b) (math-neg (nth 2 b)))))) |
| 1753 | (and (eq (car-safe a) 'neg) |
| 1754 | (math-neg (math-div (nth 1 a) b))) |
| 1755 | (and (eq (car-safe b) 'neg) |
| 1756 | (math-neg (math-div a (nth 1 b)))) |
| 1757 | (and (eq (car-safe a) '/) |
| 1758 | (math-div (nth 1 a) (math-mul (nth 2 a) b))) |
| 1759 | (and (eq (car-safe b) '/) |
| 1760 | (or (math-known-scalarp (nth 1 b) t) |
| 1761 | (math-known-scalarp (nth 2 b) t)) |
| 1762 | (math-div (math-mul a (nth 2 b)) (nth 1 b))) |
| 1763 | (and (eq (car-safe b) 'frac) |
| 1764 | (math-mul (math-make-frac (nth 2 b) (nth 1 b)) a)) |
| 1765 | (and (eq (car-safe a) '+) |
| 1766 | (or (Math-numberp (nth 1 a)) |
| 1767 | (Math-numberp (nth 2 a))) |
| 1768 | (Math-numberp b) |
| 1769 | (math-add (math-div (nth 1 a) b) |
| 1770 | (math-div (nth 2 a) b))) |
| 1771 | (and (eq (car-safe a) '-) |
| 1772 | (or (Math-numberp (nth 1 a)) |
| 1773 | (Math-numberp (nth 2 a))) |
| 1774 | (Math-numberp b) |
| 1775 | (math-sub (math-div (nth 1 a) b) |
| 1776 | (math-div (nth 2 a) b))) |
| 1777 | (and (or (eq (car-safe a) '-) |
| 1778 | (math-looks-negp a)) |
| 1779 | (math-looks-negp b) |
| 1780 | (math-div (math-neg a) (math-neg b))) |
| 1781 | (and (eq (car-safe b) '-) |
| 1782 | (math-looks-negp a) |
| 1783 | (math-div (math-neg a) (math-neg b))) |
| 1784 | (and (eq (car-safe a) 'calcFunc-idn) |
| 1785 | (= (length a) 2) |
| 1786 | (or (and (eq (car-safe b) 'calcFunc-idn) |
| 1787 | (= (length b) 2) |
| 1788 | (list 'calcFunc-idn (math-div (nth 1 a) (nth 1 b)))) |
| 1789 | (and (math-known-scalarp b) |
| 1790 | (list 'calcFunc-idn (math-div (nth 1 a) b))) |
| 1791 | (and (math-known-matrixp b) |
| 1792 | (math-div (nth 1 a) b)))) |
| 1793 | (and (eq (car-safe b) 'calcFunc-idn) |
| 1794 | (= (length b) 2) |
| 1795 | (or (and (math-known-scalarp a) |
| 1796 | (list 'calcFunc-idn (math-div a (nth 1 b)))) |
| 1797 | (and (math-known-matrixp a) |
| 1798 | (math-div a (nth 1 b))))) |
| 1799 | (and math-simplifying |
| 1800 | (let ((math-div-trig nil) |
| 1801 | (math-div-non-trig nil)) |
| 1802 | (math-div-isolate-trig b) |
| 1803 | (if math-div-trig |
| 1804 | (if math-div-non-trig |
| 1805 | (math-div (math-mul a math-div-trig) math-div-non-trig) |
| 1806 | (math-mul a math-div-trig)) |
| 1807 | nil))) |
| 1808 | (if (and calc-matrix-mode |
| 1809 | (or (math-known-matrixp a) (math-known-matrixp b))) |
| 1810 | (math-combine-prod a b nil t nil) |
| 1811 | (if (eq (car-safe a) '*) |
| 1812 | (if (eq (car-safe b) '*) |
| 1813 | (let ((c (math-combine-prod (nth 1 a) (nth 1 b) nil t t))) |
| 1814 | (and c |
| 1815 | (math-div (math-mul c (nth 2 a)) (nth 2 b)))) |
| 1816 | (let ((c (math-combine-prod (nth 1 a) b nil t t))) |
| 1817 | (and c |
| 1818 | (math-mul c (nth 2 a))))) |
| 1819 | (if (eq (car-safe b) '*) |
| 1820 | (let ((c (math-combine-prod a (nth 1 b) nil t t))) |
| 1821 | (and c |
| 1822 | (math-div c (nth 2 b)))) |
| 1823 | (math-combine-prod a b nil t nil)))) |
| 1824 | (and (math-infinitep a) |
| 1825 | (if (math-infinitep b) |
| 1826 | '(var nan var-nan) |
| 1827 | (if (or (equal a '(var nan var-nan)) |
| 1828 | (equal a '(var uinf var-uinf))) |
| 1829 | a |
| 1830 | (if (equal a '(var inf var-inf)) |
| 1831 | (if (or (math-posp b) |
| 1832 | (and (eq (car-safe b) 'intv) |
| 1833 | (math-zerop (nth 2 b)))) |
| 1834 | (if (and (eq (car-safe b) 'intv) |
| 1835 | (not (math-intv-constp b t))) |
| 1836 | '(intv 3 0 (var inf var-inf)) |
| 1837 | a) |
| 1838 | (if (or (math-negp b) |
| 1839 | (and (eq (car-safe b) 'intv) |
| 1840 | (math-zerop (nth 3 b)))) |
| 1841 | (if (and (eq (car-safe b) 'intv) |
| 1842 | (not (math-intv-constp b t))) |
| 1843 | '(intv 3 (neg (var inf var-inf)) 0) |
| 1844 | (math-neg a)) |
| 1845 | (if (and (eq (car-safe b) 'intv) |
| 1846 | (math-negp (nth 2 b)) (math-posp (nth 3 b))) |
| 1847 | '(intv 3 (neg (var inf var-inf)) |
| 1848 | (var inf var-inf))))))))) |
| 1849 | (and (math-infinitep b) |
| 1850 | (if (equal b '(var nan var-nan)) |
| 1851 | b |
| 1852 | (let ((calc-infinite-mode 1)) |
| 1853 | (math-mul-zero b a)))) |
| 1854 | (list '/ a b))) |
| 1855 | |
| 1856 | ;;; Division from the left. |
| 1857 | (defun calcFunc-ldiv (a b) |
| 1858 | (if (math-known-scalarp a) |
| 1859 | (math-div b a) |
| 1860 | (math-mul (math-pow a -1) b))) |
| 1861 | |
| 1862 | (defun calcFunc-mod (a b) |
| 1863 | (math-normalize (list '% a b))) |
| 1864 | |
| 1865 | (defun math-mod-fancy (a b) |
| 1866 | (cond ((equal b '(var inf var-inf)) |
| 1867 | (if (or (math-posp a) (math-zerop a)) |
| 1868 | a |
| 1869 | (if (math-negp a) |
| 1870 | b |
| 1871 | (if (eq (car-safe a) 'intv) |
| 1872 | (if (math-negp (nth 2 a)) |
| 1873 | '(intv 3 0 (var inf var-inf)) |
| 1874 | a) |
| 1875 | (list '% a b))))) |
| 1876 | ((and (eq (car-safe a) 'mod) (Math-realp b) (math-posp b)) |
| 1877 | (math-make-mod (nth 1 a) b)) |
| 1878 | ((and (eq (car-safe a) 'intv) (math-intv-constp a t) (math-posp b)) |
| 1879 | (math-mod-intv a b)) |
| 1880 | (t |
| 1881 | (if (Math-anglep a) |
| 1882 | (calc-record-why 'anglep b) |
| 1883 | (calc-record-why 'anglep a)) |
| 1884 | (list '% a b)))) |
| 1885 | |
| 1886 | |
| 1887 | (defun calcFunc-pow (a b) |
| 1888 | (math-normalize (list '^ a b))) |
| 1889 | |
| 1890 | (defun math-pow-of-zero (a b) |
| 1891 | "Raise A to the power of B, where A is a form of zero." |
| 1892 | (if (math-floatp b) (setq a (math-float a))) |
| 1893 | (cond |
| 1894 | ;; 0^0 = 1 |
| 1895 | ((eq b 0) |
| 1896 | 1) |
| 1897 | ;; 0^0.0, etc., are undetermined |
| 1898 | ((Math-zerop b) |
| 1899 | (if calc-infinite-mode |
| 1900 | '(var nan var-nan) |
| 1901 | (math-reject-arg (list '^ a b) "*Indeterminate form"))) |
| 1902 | ;; 0^positive = 0 |
| 1903 | ((math-known-posp b) |
| 1904 | a) |
| 1905 | ;; 0^negative is undefined (let math-div handle it) |
| 1906 | ((math-known-negp b) |
| 1907 | (math-div 1 a)) |
| 1908 | ;; 0^infinity is undefined |
| 1909 | ((math-infinitep b) |
| 1910 | '(var nan var-nan)) |
| 1911 | ;; Some intervals |
| 1912 | ((and (eq (car b) 'intv) |
| 1913 | calc-infinite-mode |
| 1914 | (math-negp (nth 2 b)) |
| 1915 | (math-posp (nth 3 b))) |
| 1916 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf))) |
| 1917 | ;; If none of the above, leave it alone. |
| 1918 | (t |
| 1919 | (list '^ a b)))) |
| 1920 | |
| 1921 | (defun math-pow-zero (a b) |
| 1922 | (if (eq (car-safe a) 'mod) |
| 1923 | (math-make-mod 1 (nth 2 a)) |
| 1924 | (if (math-known-matrixp a) |
| 1925 | (math-mimic-ident 1 a) |
| 1926 | (if (math-infinitep a) |
| 1927 | '(var nan var-nan) |
| 1928 | (if (and (eq (car a) 'intv) (math-intv-constp a) |
| 1929 | (or (and (not (math-posp a)) (not (math-negp a))) |
| 1930 | (not (math-intv-constp a t)))) |
| 1931 | '(intv 3 (neg (var inf var-inf)) (var inf var-inf)) |
| 1932 | (if (or (math-floatp a) (math-floatp b)) |
| 1933 | '(float 1 0) 1)))))) |
| 1934 | |
| 1935 | (defun math-pow-fancy (a b) |
| 1936 | (cond ((and (Math-numberp a) (Math-numberp b)) |
| 1937 | (or (if (memq (math-quarter-integer b) '(1 2 3)) |
| 1938 | (let ((sqrt (math-sqrt (if (math-floatp b) |
| 1939 | (math-float a) a)))) |
| 1940 | (and (Math-numberp sqrt) |
| 1941 | (math-pow sqrt (math-mul 2 b)))) |
| 1942 | (and (eq (car b) 'frac) |
| 1943 | (integerp (nth 2 b)) |
| 1944 | (<= (nth 2 b) 10) |
| 1945 | (let ((root (math-nth-root a (nth 2 b)))) |
| 1946 | (and root (math-ipow root (nth 1 b)))))) |
| 1947 | (and (or (eq a 10) (equal a '(float 1 1))) |
| 1948 | (math-num-integerp b) |
| 1949 | (calcFunc-scf '(float 1 0) b)) |
| 1950 | (and calc-symbolic-mode |
| 1951 | (list '^ a b)) |
| 1952 | (math-with-extra-prec 2 |
| 1953 | (math-exp-raw |
| 1954 | (math-float (math-mul b (math-ln-raw (math-float a)))))))) |
| 1955 | ((or (not (Math-objvecp a)) |
| 1956 | (not (Math-objectp b))) |
| 1957 | (let (temp) |
| 1958 | (cond ((and math-simplify-only |
| 1959 | (not (equal a math-simplify-only))) |
| 1960 | (list '^ a b)) |
| 1961 | ((and (eq (car-safe a) '*) |
| 1962 | (or |
| 1963 | (and |
| 1964 | (math-known-matrixp (nth 1 a)) |
| 1965 | (math-known-matrixp (nth 2 a))) |
| 1966 | (and |
| 1967 | calc-matrix-mode |
| 1968 | (not (eq calc-matrix-mode 'scalar)) |
| 1969 | (and (not (math-known-scalarp (nth 1 a))) |
| 1970 | (not (math-known-scalarp (nth 2 a))))))) |
| 1971 | (if (and (= b -1) |
| 1972 | (math-known-square-matrixp (nth 1 a)) |
| 1973 | (math-known-square-matrixp (nth 2 a))) |
| 1974 | (math-mul (math-pow-fancy (nth 2 a) -1) |
| 1975 | (math-pow-fancy (nth 1 a) -1)) |
| 1976 | (list '^ a b))) |
| 1977 | ((and (eq (car-safe a) '*) |
| 1978 | (or (math-known-num-integerp b) |
| 1979 | (math-known-nonnegp (nth 1 a)) |
| 1980 | (math-known-nonnegp (nth 2 a)))) |
| 1981 | (math-mul (math-pow (nth 1 a) b) |
| 1982 | (math-pow (nth 2 a) b))) |
| 1983 | ((and (eq (car-safe a) '/) |
| 1984 | (or (math-known-num-integerp b) |
| 1985 | (math-known-nonnegp (nth 2 a)))) |
| 1986 | (math-div (math-pow (nth 1 a) b) |
| 1987 | (math-pow (nth 2 a) b))) |
| 1988 | ((and (eq (car-safe a) '/) |
| 1989 | (math-known-nonnegp (nth 1 a)) |
| 1990 | (not (math-equal-int (nth 1 a) 1))) |
| 1991 | (math-mul (math-pow (nth 1 a) b) |
| 1992 | (math-pow (math-div 1 (nth 2 a)) b))) |
| 1993 | ((and (eq (car-safe a) '^) |
| 1994 | (or (math-known-num-integerp b) |
| 1995 | (math-known-nonnegp (nth 1 a)))) |
| 1996 | (math-pow (nth 1 a) (math-mul (nth 2 a) b))) |
| 1997 | ((and (eq (car-safe a) 'calcFunc-sqrt) |
| 1998 | (or (math-known-num-integerp b) |
| 1999 | (math-known-nonnegp (nth 1 a)))) |
| 2000 | (math-pow (nth 1 a) (math-div b 2))) |
| 2001 | ((and (eq (car-safe a) '^) |
| 2002 | (math-known-evenp (nth 2 a)) |
| 2003 | (memq (math-quarter-integer b) '(1 2 3)) |
| 2004 | (math-known-realp (nth 1 a))) |
| 2005 | (math-abs (math-pow (nth 1 a) (math-mul (nth 2 a) b)))) |
| 2006 | ((and (math-looks-negp a) |
| 2007 | (math-known-integerp b) |
| 2008 | (setq temp (or (and (math-known-evenp b) |
| 2009 | (math-pow (math-neg a) b)) |
| 2010 | (and (math-known-oddp b) |
| 2011 | (math-neg (math-pow (math-neg a) |
| 2012 | b)))))) |
| 2013 | temp) |
| 2014 | ((and (eq (car-safe a) 'calcFunc-abs) |
| 2015 | (math-known-realp (nth 1 a)) |
| 2016 | (math-known-evenp b)) |
| 2017 | (math-pow (nth 1 a) b)) |
| 2018 | ((math-infinitep a) |
| 2019 | (cond ((equal a '(var nan var-nan)) |
| 2020 | a) |
| 2021 | ((eq (car a) 'neg) |
| 2022 | (math-mul (math-pow -1 b) (math-pow (nth 1 a) b))) |
| 2023 | ((math-posp b) |
| 2024 | a) |
| 2025 | ((math-negp b) |
| 2026 | (if (math-floatp b) '(float 0 0) 0)) |
| 2027 | ((and (eq (car-safe b) 'intv) |
| 2028 | (math-intv-constp b)) |
| 2029 | '(intv 3 0 (var inf var-inf))) |
| 2030 | (t |
| 2031 | '(var nan var-nan)))) |
| 2032 | ((math-infinitep b) |
| 2033 | (let (scale) |
| 2034 | (cond ((math-negp b) |
| 2035 | (math-pow (math-div 1 a) (math-neg b))) |
| 2036 | ((not (math-posp b)) |
| 2037 | '(var nan var-nan)) |
| 2038 | ((math-equal-int (setq scale (calcFunc-abssqr a)) 1) |
| 2039 | '(var nan var-nan)) |
| 2040 | ((Math-lessp scale 1) |
| 2041 | (if (math-floatp a) '(float 0 0) 0)) |
| 2042 | ((Math-lessp 1 a) |
| 2043 | b) |
| 2044 | ((Math-lessp a -1) |
| 2045 | '(var uinf var-uinf)) |
| 2046 | ((and (eq (car a) 'intv) |
| 2047 | (math-intv-constp a)) |
| 2048 | (if (Math-lessp -1 a) |
| 2049 | (if (math-equal-int (nth 3 a) 1) |
| 2050 | '(intv 3 0 1) |
| 2051 | '(intv 3 0 (var inf var-inf))) |
| 2052 | '(intv 3 (neg (var inf var-inf)) |
| 2053 | (var inf var-inf)))) |
| 2054 | (t (list '^ a b))))) |
| 2055 | ((and (eq (car-safe a) 'calcFunc-idn) |
| 2056 | (= (length a) 2) |
| 2057 | (math-known-num-integerp b)) |
| 2058 | (list 'calcFunc-idn (math-pow (nth 1 a) b))) |
| 2059 | (t (if (Math-objectp a) |
| 2060 | (calc-record-why 'objectp b) |
| 2061 | (calc-record-why 'objectp a)) |
| 2062 | (list '^ a b))))) |
| 2063 | ((and (eq (car-safe a) 'sdev) (eq (car-safe b) 'sdev)) |
| 2064 | (if (and (math-constp a) (math-constp b)) |
| 2065 | (math-with-extra-prec 2 |
| 2066 | (let* ((ln (math-ln-raw (math-float (nth 1 a)))) |
| 2067 | (pow (math-exp-raw |
| 2068 | (math-float (math-mul (nth 1 b) ln))))) |
| 2069 | (math-make-sdev |
| 2070 | pow |
| 2071 | (math-mul |
| 2072 | pow |
| 2073 | (math-hypot (math-mul (nth 2 a) |
| 2074 | (math-div (nth 1 b) (nth 1 a))) |
| 2075 | (math-mul (nth 2 b) ln)))))) |
| 2076 | (let ((pow (math-pow (nth 1 a) (nth 1 b)))) |
| 2077 | (math-make-sdev |
| 2078 | pow |
| 2079 | (math-mul pow |
| 2080 | (math-hypot (math-mul (nth 2 a) |
| 2081 | (math-div (nth 1 b) (nth 1 a))) |
| 2082 | (math-mul (nth 2 b) (calcFunc-ln |
| 2083 | (nth 1 a))))))))) |
| 2084 | ((and (eq (car-safe a) 'sdev) (Math-numberp b)) |
| 2085 | (if (math-constp a) |
| 2086 | (math-with-extra-prec 2 |
| 2087 | (let ((pow (math-pow (nth 1 a) (math-sub b 1)))) |
| 2088 | (math-make-sdev (math-mul pow (nth 1 a)) |
| 2089 | (math-mul pow (math-mul (nth 2 a) b))))) |
| 2090 | (math-make-sdev (math-pow (nth 1 a) b) |
| 2091 | (math-mul (math-pow (nth 1 a) (math-add b -1)) |
| 2092 | (math-mul (nth 2 a) b))))) |
| 2093 | ((and (eq (car-safe b) 'sdev) (Math-numberp a)) |
| 2094 | (math-with-extra-prec 2 |
| 2095 | (let* ((ln (math-ln-raw (math-float a))) |
| 2096 | (pow (calcFunc-exp (math-mul (nth 1 b) ln)))) |
| 2097 | (math-make-sdev pow (math-mul pow (math-mul (nth 2 b) ln)))))) |
| 2098 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) |
| 2099 | (Math-realp b) |
| 2100 | (or (Math-natnump b) |
| 2101 | (Math-posp (nth 2 a)) |
| 2102 | (and (math-zerop (nth 2 a)) |
| 2103 | (or (Math-posp b) |
| 2104 | (and (Math-integerp b) calc-infinite-mode))) |
| 2105 | (Math-negp (nth 3 a)) |
| 2106 | (and (math-zerop (nth 3 a)) |
| 2107 | (or (Math-posp b) |
| 2108 | (and (Math-integerp b) calc-infinite-mode))))) |
| 2109 | (if (math-evenp b) |
| 2110 | (setq a (math-abs a))) |
| 2111 | (let ((calc-infinite-mode (if (math-zerop (nth 3 a)) -1 1))) |
| 2112 | (math-sort-intv (nth 1 a) |
| 2113 | (math-pow (nth 2 a) b) |
| 2114 | (math-pow (nth 3 a) b)))) |
| 2115 | ((and (eq (car-safe b) 'intv) (math-intv-constp b) |
| 2116 | (Math-realp a) (Math-posp a)) |
| 2117 | (math-sort-intv (nth 1 b) |
| 2118 | (math-pow a (nth 2 b)) |
| 2119 | (math-pow a (nth 3 b)))) |
| 2120 | ((and (eq (car-safe a) 'intv) (math-intv-constp a) |
| 2121 | (eq (car-safe b) 'intv) (math-intv-constp b) |
| 2122 | (or (and (not (Math-negp (nth 2 a))) |
| 2123 | (not (Math-negp (nth 2 b)))) |
| 2124 | (and (Math-posp (nth 2 a)) |
| 2125 | (not (Math-posp (nth 3 b)))))) |
| 2126 | (let ((lo (math-pow a (nth 2 b))) |
| 2127 | (hi (math-pow a (nth 3 b)))) |
| 2128 | (or (eq (car-safe lo) 'intv) |
| 2129 | (setq lo (list 'intv (if (memq (nth 1 b) '(2 3)) 3 0) lo lo))) |
| 2130 | (or (eq (car-safe hi) 'intv) |
| 2131 | (setq hi (list 'intv (if (memq (nth 1 b) '(1 3)) 3 0) hi hi))) |
| 2132 | (math-combine-intervals |
| 2133 | (nth 2 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 2134 | (math-infinitep (nth 2 lo))) |
| 2135 | (memq (nth 1 lo) '(2 3))) |
| 2136 | (nth 3 lo) (and (or (memq (nth 1 b) '(2 3)) |
| 2137 | (math-infinitep (nth 3 lo))) |
| 2138 | (memq (nth 1 lo) '(1 3))) |
| 2139 | (nth 2 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 2140 | (math-infinitep (nth 2 hi))) |
| 2141 | (memq (nth 1 hi) '(2 3))) |
| 2142 | (nth 3 hi) (and (or (memq (nth 1 b) '(1 3)) |
| 2143 | (math-infinitep (nth 3 hi))) |
| 2144 | (memq (nth 1 hi) '(1 3)))))) |
| 2145 | ((and (eq (car-safe a) 'mod) (eq (car-safe b) 'mod) |
| 2146 | (equal (nth 2 a) (nth 2 b))) |
| 2147 | (math-make-mod (math-pow-mod (nth 1 a) (nth 1 b) (nth 2 a)) |
| 2148 | (nth 2 a))) |
| 2149 | ((and (eq (car-safe a) 'mod) (Math-anglep b)) |
| 2150 | (math-make-mod (math-pow-mod (nth 1 a) b (nth 2 a)) (nth 2 a))) |
| 2151 | ((and (eq (car-safe b) 'mod) (Math-anglep a)) |
| 2152 | (math-make-mod (math-pow-mod a (nth 1 b) (nth 2 b)) (nth 2 b))) |
| 2153 | ((not (Math-numberp a)) |
| 2154 | (math-reject-arg a 'numberp)) |
| 2155 | (t |
| 2156 | (math-reject-arg b 'numberp)))) |
| 2157 | |
| 2158 | (defun math-quarter-integer (x) |
| 2159 | (if (Math-integerp x) |
| 2160 | 0 |
| 2161 | (if (math-negp x) |
| 2162 | (progn |
| 2163 | (setq x (math-quarter-integer (math-neg x))) |
| 2164 | (and x (- 4 x))) |
| 2165 | (if (eq (car x) 'frac) |
| 2166 | (if (eq (nth 2 x) 2) |
| 2167 | 2 |
| 2168 | (and (eq (nth 2 x) 4) |
| 2169 | (progn |
| 2170 | (setq x (nth 1 x)) |
| 2171 | (% (if (consp x) (nth 1 x) x) 4)))) |
| 2172 | (if (eq (car x) 'float) |
| 2173 | (if (>= (nth 2 x) 0) |
| 2174 | 0 |
| 2175 | (if (= (nth 2 x) -1) |
| 2176 | (progn |
| 2177 | (setq x (nth 1 x)) |
| 2178 | (and (= (% (if (consp x) (nth 1 x) x) 10) 5) 2)) |
| 2179 | (if (= (nth 2 x) -2) |
| 2180 | (progn |
| 2181 | (setq x (nth 1 x) |
| 2182 | x (% (if (consp x) (nth 1 x) x) 100)) |
| 2183 | (if (= x 25) 1 |
| 2184 | (if (= x 75) 3))))))))))) |
| 2185 | |
| 2186 | ;;; This assumes A < M and M > 0. |
| 2187 | (defun math-pow-mod (a b m) ; [R R R R] |
| 2188 | (if (and (Math-integerp a) (Math-integerp b) (Math-integerp m)) |
| 2189 | (if (Math-negp b) |
| 2190 | (math-div-mod 1 (math-pow-mod a (Math-integer-neg b) m) m) |
| 2191 | (if (eq m 1) |
| 2192 | 0 |
| 2193 | (math-pow-mod-step a b m))) |
| 2194 | (math-mod (math-pow a b) m))) |
| 2195 | |
| 2196 | (defun math-pow-mod-step (a n m) ; [I I I I] |
| 2197 | (math-working "pow" a) |
| 2198 | (let ((val (cond |
| 2199 | ((eq n 0) 1) |
| 2200 | ((eq n 1) a) |
| 2201 | (t |
| 2202 | (let ((rest (math-pow-mod-step |
| 2203 | (math-imod (math-mul a a) m) |
| 2204 | (math-div2 n) |
| 2205 | m))) |
| 2206 | (if (math-evenp n) |
| 2207 | rest |
| 2208 | (math-mod (math-mul a rest) m))))))) |
| 2209 | (math-working "pow" val) |
| 2210 | val)) |
| 2211 | |
| 2212 | |
| 2213 | ;;; Compute the minimum of two real numbers. [R R R] [Public] |
| 2214 | (defun math-min (a b) |
| 2215 | (if (and (consp a) (eq (car a) 'intv)) |
| 2216 | (if (and (consp b) (eq (car b) 'intv)) |
| 2217 | (let ((lo (nth 2 a)) |
| 2218 | (lom (memq (nth 1 a) '(2 3))) |
| 2219 | (hi (nth 3 a)) |
| 2220 | (him (memq (nth 1 a) '(1 3))) |
| 2221 | res) |
| 2222 | (if (= (setq res (math-compare (nth 2 b) lo)) -1) |
| 2223 | (setq lo (nth 2 b) lom (memq (nth 1 b) '(2 3))) |
| 2224 | (if (= res 0) |
| 2225 | (setq lom (or lom (memq (nth 1 b) '(2 3)))))) |
| 2226 | (if (= (setq res (math-compare (nth 3 b) hi)) -1) |
| 2227 | (setq hi (nth 3 b) him (memq (nth 1 b) '(1 3))) |
| 2228 | (if (= res 0) |
| 2229 | (setq him (or him (memq (nth 1 b) '(1 3)))))) |
| 2230 | (math-make-intv (+ (if lom 2 0) (if him 1 0)) lo hi)) |
| 2231 | (math-min a (list 'intv 3 b b))) |
| 2232 | (if (and (consp b) (eq (car b) 'intv)) |
| 2233 | (math-min (list 'intv 3 a a) b) |
| 2234 | (let ((res (math-compare a b))) |
| 2235 | (if (= res 1) |
| 2236 | b |
| 2237 | (if (= res 2) |
| 2238 | '(var nan var-nan) |
| 2239 | a)))))) |
| 2240 | |
| 2241 | (defun calcFunc-min (&optional a &rest b) |
| 2242 | (if (not a) |
| 2243 | '(var inf var-inf) |
| 2244 | (if (not (or (Math-anglep a) (eq (car a) 'date) |
| 2245 | (and (eq (car a) 'intv) (math-intv-constp a)) |
| 2246 | (math-infinitep a))) |
| 2247 | (math-reject-arg a 'anglep)) |
| 2248 | (math-min-list a b))) |
| 2249 | |
| 2250 | (defun math-min-list (a b) |
| 2251 | (if b |
| 2252 | (if (or (Math-anglep (car b)) (eq (car b) 'date) |
| 2253 | (and (eq (car (car b)) 'intv) (math-intv-constp (car b))) |
| 2254 | (math-infinitep (car b))) |
| 2255 | (math-min-list (math-min a (car b)) (cdr b)) |
| 2256 | (math-reject-arg (car b) 'anglep)) |
| 2257 | a)) |
| 2258 | |
| 2259 | ;;; Compute the maximum of two real numbers. [R R R] [Public] |
| 2260 | (defun math-max (a b) |
| 2261 | (if (or (and (consp a) (eq (car a) 'intv)) |
| 2262 | (and (consp b) (eq (car b) 'intv))) |
| 2263 | (math-neg (math-min (math-neg a) (math-neg b))) |
| 2264 | (let ((res (math-compare a b))) |
| 2265 | (if (= res -1) |
| 2266 | b |
| 2267 | (if (= res 2) |
| 2268 | '(var nan var-nan) |
| 2269 | a))))) |
| 2270 | |
| 2271 | (defun calcFunc-max (&optional a &rest b) |
| 2272 | (if (not a) |
| 2273 | '(neg (var inf var-inf)) |
| 2274 | (if (not (or (Math-anglep a) (eq (car a) 'date) |
| 2275 | (and (eq (car a) 'intv) (math-intv-constp a)) |
| 2276 | (math-infinitep a))) |
| 2277 | (math-reject-arg a 'anglep)) |
| 2278 | (math-max-list a b))) |
| 2279 | |
| 2280 | (defun math-max-list (a b) |
| 2281 | (if b |
| 2282 | (if (or (Math-anglep (car b)) (eq (car b) 'date) |
| 2283 | (and (eq (car (car b)) 'intv) (math-intv-constp (car b))) |
| 2284 | (math-infinitep (car b))) |
| 2285 | (math-max-list (math-max a (car b)) (cdr b)) |
| 2286 | (math-reject-arg (car b) 'anglep)) |
| 2287 | a)) |
| 2288 | |
| 2289 | |
| 2290 | ;;; Compute the absolute value of A. [O O; r r] [Public] |
| 2291 | (defun math-abs (a) |
| 2292 | (cond ((Math-negp a) |
| 2293 | (math-neg a)) |
| 2294 | ((Math-anglep a) |
| 2295 | a) |
| 2296 | ((eq (car a) 'cplx) |
| 2297 | (math-hypot (nth 1 a) (nth 2 a))) |
| 2298 | ((eq (car a) 'polar) |
| 2299 | (nth 1 a)) |
| 2300 | ((eq (car a) 'vec) |
| 2301 | (if (cdr (cdr (cdr a))) |
| 2302 | (math-sqrt (calcFunc-abssqr a)) |
| 2303 | (if (cdr (cdr a)) |
| 2304 | (math-hypot (nth 1 a) (nth 2 a)) |
| 2305 | (if (cdr a) |
| 2306 | (math-abs (nth 1 a)) |
| 2307 | a)))) |
| 2308 | ((eq (car a) 'sdev) |
| 2309 | (list 'sdev (math-abs (nth 1 a)) (nth 2 a))) |
| 2310 | ((and (eq (car a) 'intv) (math-intv-constp a)) |
| 2311 | (if (Math-posp a) |
| 2312 | a |
| 2313 | (let* ((nlo (math-neg (nth 2 a))) |
| 2314 | (res (math-compare nlo (nth 3 a)))) |
| 2315 | (cond ((= res 1) |
| 2316 | (math-make-intv (if (memq (nth 1 a) '(0 1)) 2 3) 0 nlo)) |
| 2317 | ((= res 0) |
| 2318 | (math-make-intv (if (eq (nth 1 a) 0) 2 3) 0 nlo)) |
| 2319 | (t |
| 2320 | (math-make-intv (if (memq (nth 1 a) '(0 2)) 2 3) |
| 2321 | 0 (nth 3 a))))))) |
| 2322 | ((math-looks-negp a) |
| 2323 | (list 'calcFunc-abs (math-neg a))) |
| 2324 | ((let ((signs (math-possible-signs a))) |
| 2325 | (or (and (memq signs '(2 4 6)) a) |
| 2326 | (and (memq signs '(1 3)) (math-neg a))))) |
| 2327 | ((let ((inf (math-infinitep a))) |
| 2328 | (and inf |
| 2329 | (if (equal inf '(var nan var-nan)) |
| 2330 | inf |
| 2331 | '(var inf var-inf))))) |
| 2332 | (t (calc-record-why 'numvecp a) |
| 2333 | (list 'calcFunc-abs a)))) |
| 2334 | |
| 2335 | (defalias 'calcFunc-abs 'math-abs) |
| 2336 | |
| 2337 | (defun math-float-fancy (a) |
| 2338 | (cond ((eq (car a) 'intv) |
| 2339 | (cons (car a) (cons (nth 1 a) (mapcar 'math-float (nthcdr 2 a))))) |
| 2340 | ((and (memq (car a) '(* /)) |
| 2341 | (math-numberp (nth 1 a))) |
| 2342 | (list (car a) (math-float (nth 1 a)) |
| 2343 | (list 'calcFunc-float (nth 2 a)))) |
| 2344 | ((and (eq (car a) '/) |
| 2345 | (eq (car (nth 1 a)) '*) |
| 2346 | (math-numberp (nth 1 (nth 1 a)))) |
| 2347 | (list '* (math-float (nth 1 (nth 1 a))) |
| 2348 | (list 'calcFunc-float (list '/ (nth 2 (nth 1 a)) (nth 2 a))))) |
| 2349 | ((math-infinitep a) a) |
| 2350 | ((eq (car a) 'calcFunc-float) a) |
| 2351 | ((let ((func (assq (car a) '((calcFunc-floor . calcFunc-ffloor) |
| 2352 | (calcFunc-ceil . calcFunc-fceil) |
| 2353 | (calcFunc-trunc . calcFunc-ftrunc) |
| 2354 | (calcFunc-round . calcFunc-fround) |
| 2355 | (calcFunc-rounde . calcFunc-frounde) |
| 2356 | (calcFunc-roundu . calcFunc-froundu))))) |
| 2357 | (and func (cons (cdr func) (cdr a))))) |
| 2358 | (t (math-reject-arg a 'objectp)))) |
| 2359 | |
| 2360 | (defalias 'calcFunc-float 'math-float) |
| 2361 | |
| 2362 | ;; The variable math-trunc-prec is local to math-trunc in calc-misc.el, |
| 2363 | ;; but used by math-trunc-fancy which is called by math-trunc. |
| 2364 | (defvar math-trunc-prec) |
| 2365 | |
| 2366 | (defun math-trunc-fancy (a) |
| 2367 | (cond ((eq (car a) 'frac) (math-quotient (nth 1 a) (nth 2 a))) |
| 2368 | ((eq (car a) 'cplx) (math-trunc (nth 1 a))) |
| 2369 | ((eq (car a) 'polar) (math-trunc (math-complex a))) |
| 2370 | ((eq (car a) 'hms) (list 'hms (nth 1 a) 0 0)) |
| 2371 | ((eq (car a) 'date) (list 'date (math-trunc (nth 1 a)))) |
| 2372 | ((eq (car a) 'mod) |
| 2373 | (if (math-messy-integerp (nth 2 a)) |
| 2374 | (math-trunc (math-make-mod (nth 1 a) (math-trunc (nth 2 a)))) |
| 2375 | (math-make-mod (math-trunc (nth 1 a)) (nth 2 a)))) |
| 2376 | ((eq (car a) 'intv) |
| 2377 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) |
| 2378 | (memq (nth 1 a) '(0 1))) |
| 2379 | 0 2) |
| 2380 | (if (and (equal (nth 3 a) '(var inf var-inf)) |
| 2381 | (memq (nth 1 a) '(0 2))) |
| 2382 | 0 1)) |
| 2383 | (if (and (Math-negp (nth 2 a)) |
| 2384 | (Math-num-integerp (nth 2 a)) |
| 2385 | (memq (nth 1 a) '(0 1))) |
| 2386 | (math-add (math-trunc (nth 2 a)) 1) |
| 2387 | (math-trunc (nth 2 a))) |
| 2388 | (if (and (Math-posp (nth 3 a)) |
| 2389 | (Math-num-integerp (nth 3 a)) |
| 2390 | (memq (nth 1 a) '(0 2))) |
| 2391 | (math-add (math-trunc (nth 3 a)) -1) |
| 2392 | (math-trunc (nth 3 a))))) |
| 2393 | ((math-provably-integerp a) a) |
| 2394 | ((Math-vectorp a) |
| 2395 | (math-map-vec (function (lambda (x) (math-trunc x math-trunc-prec))) a)) |
| 2396 | ((math-infinitep a) |
| 2397 | (if (or (math-posp a) (math-negp a)) |
| 2398 | a |
| 2399 | '(var nan var-nan))) |
| 2400 | ((math-to-integer a)) |
| 2401 | (t (math-reject-arg a 'numberp)))) |
| 2402 | |
| 2403 | (defun math-trunc-special (a prec) |
| 2404 | (if (Math-messy-integerp prec) |
| 2405 | (setq prec (math-trunc prec))) |
| 2406 | (or (integerp prec) |
| 2407 | (math-reject-arg prec 'fixnump)) |
| 2408 | (if (and (<= prec 0) |
| 2409 | (math-provably-integerp a)) |
| 2410 | a |
| 2411 | (calcFunc-scf (math-trunc (let ((calc-prefer-frac t)) |
| 2412 | (calcFunc-scf a prec))) |
| 2413 | (- prec)))) |
| 2414 | |
| 2415 | (defun math-to-integer (a) |
| 2416 | (let ((func (assq (car-safe a) '((calcFunc-ffloor . calcFunc-floor) |
| 2417 | (calcFunc-fceil . calcFunc-ceil) |
| 2418 | (calcFunc-ftrunc . calcFunc-trunc) |
| 2419 | (calcFunc-fround . calcFunc-round) |
| 2420 | (calcFunc-frounde . calcFunc-rounde) |
| 2421 | (calcFunc-froundu . calcFunc-roundu))))) |
| 2422 | (and func (= (length a) 2) |
| 2423 | (cons (cdr func) (cdr a))))) |
| 2424 | |
| 2425 | (defun calcFunc-ftrunc (a &optional prec) |
| 2426 | (if (and (Math-messy-integerp a) |
| 2427 | (or (not prec) (and (integerp prec) |
| 2428 | (<= prec 0)))) |
| 2429 | a |
| 2430 | (math-float (math-trunc a prec)))) |
| 2431 | |
| 2432 | ;; The variable math-floor-prec is local to math-floor in calc-misc.el, |
| 2433 | ;; but used by math-floor-fancy which is called by math-floor. |
| 2434 | (defvar math-floor-prec) |
| 2435 | |
| 2436 | (defun math-floor-fancy (a) |
| 2437 | (cond ((math-provably-integerp a) a) |
| 2438 | ((eq (car a) 'hms) |
| 2439 | (if (or (math-posp a) |
| 2440 | (and (math-zerop (nth 2 a)) |
| 2441 | (math-zerop (nth 3 a)))) |
| 2442 | (math-trunc a) |
| 2443 | (math-add (math-trunc a) -1))) |
| 2444 | ((eq (car a) 'date) (list 'date (math-floor (nth 1 a)))) |
| 2445 | ((eq (car a) 'intv) |
| 2446 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) |
| 2447 | (memq (nth 1 a) '(0 1))) |
| 2448 | 0 2) |
| 2449 | (if (and (equal (nth 3 a) '(var inf var-inf)) |
| 2450 | (memq (nth 1 a) '(0 2))) |
| 2451 | 0 1)) |
| 2452 | (math-floor (nth 2 a)) |
| 2453 | (if (and (Math-num-integerp (nth 3 a)) |
| 2454 | (memq (nth 1 a) '(0 2))) |
| 2455 | (math-add (math-floor (nth 3 a)) -1) |
| 2456 | (math-floor (nth 3 a))))) |
| 2457 | ((Math-vectorp a) |
| 2458 | (math-map-vec (function (lambda (x) (math-floor x math-floor-prec))) a)) |
| 2459 | ((math-infinitep a) |
| 2460 | (if (or (math-posp a) (math-negp a)) |
| 2461 | a |
| 2462 | '(var nan var-nan))) |
| 2463 | ((math-to-integer a)) |
| 2464 | (t (math-reject-arg a 'anglep)))) |
| 2465 | |
| 2466 | (defun math-floor-special (a prec) |
| 2467 | (if (Math-messy-integerp prec) |
| 2468 | (setq prec (math-trunc prec))) |
| 2469 | (or (integerp prec) |
| 2470 | (math-reject-arg prec 'fixnump)) |
| 2471 | (if (and (<= prec 0) |
| 2472 | (math-provably-integerp a)) |
| 2473 | a |
| 2474 | (calcFunc-scf (math-floor (let ((calc-prefer-frac t)) |
| 2475 | (calcFunc-scf a prec))) |
| 2476 | (- prec)))) |
| 2477 | |
| 2478 | (defun calcFunc-ffloor (a &optional prec) |
| 2479 | (if (and (Math-messy-integerp a) |
| 2480 | (or (not prec) (and (integerp prec) |
| 2481 | (<= prec 0)))) |
| 2482 | a |
| 2483 | (math-float (math-floor a prec)))) |
| 2484 | |
| 2485 | ;;; Coerce A to be an integer (by truncation toward plus infinity). [I N] |
| 2486 | (defun math-ceiling (a &optional prec) ; [Public] |
| 2487 | (cond (prec |
| 2488 | (if (Math-messy-integerp prec) |
| 2489 | (setq prec (math-trunc prec))) |
| 2490 | (or (integerp prec) |
| 2491 | (math-reject-arg prec 'fixnump)) |
| 2492 | (if (and (<= prec 0) |
| 2493 | (math-provably-integerp a)) |
| 2494 | a |
| 2495 | (calcFunc-scf (math-ceiling (let ((calc-prefer-frac t)) |
| 2496 | (calcFunc-scf a prec))) |
| 2497 | (- prec)))) |
| 2498 | ((Math-integerp a) a) |
| 2499 | ((Math-messy-integerp a) (math-trunc a)) |
| 2500 | ((Math-realp a) |
| 2501 | (if (Math-posp a) |
| 2502 | (math-add (math-trunc a) 1) |
| 2503 | (math-trunc a))) |
| 2504 | ((math-provably-integerp a) a) |
| 2505 | ((eq (car a) 'hms) |
| 2506 | (if (or (math-negp a) |
| 2507 | (and (math-zerop (nth 2 a)) |
| 2508 | (math-zerop (nth 3 a)))) |
| 2509 | (math-trunc a) |
| 2510 | (math-add (math-trunc a) 1))) |
| 2511 | ((eq (car a) 'date) (list 'date (math-ceiling (nth 1 a)))) |
| 2512 | ((eq (car a) 'intv) |
| 2513 | (math-make-intv (+ (if (and (equal (nth 2 a) '(neg (var inf var-inf))) |
| 2514 | (memq (nth 1 a) '(0 1))) |
| 2515 | 0 2) |
| 2516 | (if (and (equal (nth 3 a) '(var inf var-inf)) |
| 2517 | (memq (nth 1 a) '(0 2))) |
| 2518 | 0 1)) |
| 2519 | (if (and (Math-num-integerp (nth 2 a)) |
| 2520 | (memq (nth 1 a) '(0 1))) |
| 2521 | (math-add (math-floor (nth 2 a)) 1) |
| 2522 | (math-ceiling (nth 2 a))) |
| 2523 | (math-ceiling (nth 3 a)))) |
| 2524 | ((Math-vectorp a) |
| 2525 | (math-map-vec (function (lambda (x) (math-ceiling x prec))) a)) |
| 2526 | ((math-infinitep a) |
| 2527 | (if (or (math-posp a) (math-negp a)) |
| 2528 | a |
| 2529 | '(var nan var-nan))) |
| 2530 | ((math-to-integer a)) |
| 2531 | (t (math-reject-arg a 'anglep)))) |
| 2532 | |
| 2533 | (defalias 'calcFunc-ceil 'math-ceiling) |
| 2534 | |
| 2535 | (defun calcFunc-fceil (a &optional prec) |
| 2536 | (if (and (Math-messy-integerp a) |
| 2537 | (or (not prec) (and (integerp prec) |
| 2538 | (<= prec 0)))) |
| 2539 | a |
| 2540 | (math-float (math-ceiling a prec)))) |
| 2541 | |
| 2542 | (defvar math-rounding-mode nil) |
| 2543 | |
| 2544 | ;;; Coerce A to be an integer (by rounding to nearest integer). [I N] [Public] |
| 2545 | (defun math-round (a &optional prec) |
| 2546 | (cond (prec |
| 2547 | (if (Math-messy-integerp prec) |
| 2548 | (setq prec (math-trunc prec))) |
| 2549 | (or (integerp prec) |
| 2550 | (math-reject-arg prec 'fixnump)) |
| 2551 | (if (and (<= prec 0) |
| 2552 | (math-provably-integerp a)) |
| 2553 | a |
| 2554 | (calcFunc-scf (math-round (let ((calc-prefer-frac t)) |
| 2555 | (calcFunc-scf a prec))) |
| 2556 | (- prec)))) |
| 2557 | ((Math-anglep a) |
| 2558 | (if (Math-num-integerp a) |
| 2559 | (math-trunc a) |
| 2560 | (if (and (Math-negp a) (not (eq math-rounding-mode 'up))) |
| 2561 | (math-neg (math-round (math-neg a))) |
| 2562 | (setq a (let ((calc-angle-mode 'deg)) ; in case of HMS forms |
| 2563 | (math-add a (if (Math-ratp a) |
| 2564 | '(frac 1 2) |
| 2565 | '(float 5 -1))))) |
| 2566 | (if (and (Math-num-integerp a) (eq math-rounding-mode 'even)) |
| 2567 | (progn |
| 2568 | (setq a (math-floor a)) |
| 2569 | (or (math-evenp a) |
| 2570 | (setq a (math-sub a 1))) |
| 2571 | a) |
| 2572 | (math-floor a))))) |
| 2573 | ((math-provably-integerp a) a) |
| 2574 | ((eq (car a) 'date) (list 'date (math-round (nth 1 a)))) |
| 2575 | ((eq (car a) 'intv) |
| 2576 | (math-floor (math-add a '(frac 1 2)))) |
| 2577 | ((Math-vectorp a) |
| 2578 | (math-map-vec (function (lambda (x) (math-round x prec))) a)) |
| 2579 | ((math-infinitep a) |
| 2580 | (if (or (math-posp a) (math-negp a)) |
| 2581 | a |
| 2582 | '(var nan var-nan))) |
| 2583 | ((math-to-integer a)) |
| 2584 | (t (math-reject-arg a 'anglep)))) |
| 2585 | |
| 2586 | (defalias 'calcFunc-round 'math-round) |
| 2587 | |
| 2588 | (defsubst calcFunc-rounde (a &optional prec) |
| 2589 | (let ((math-rounding-mode 'even)) |
| 2590 | (math-round a prec))) |
| 2591 | |
| 2592 | (defsubst calcFunc-roundu (a &optional prec) |
| 2593 | (let ((math-rounding-mode 'up)) |
| 2594 | (math-round a prec))) |
| 2595 | |
| 2596 | (defun calcFunc-fround (a &optional prec) |
| 2597 | (if (and (Math-messy-integerp a) |
| 2598 | (or (not prec) (and (integerp prec) |
| 2599 | (<= prec 0)))) |
| 2600 | a |
| 2601 | (math-float (math-round a prec)))) |
| 2602 | |
| 2603 | (defsubst calcFunc-frounde (a &optional prec) |
| 2604 | (let ((math-rounding-mode 'even)) |
| 2605 | (calcFunc-fround a prec))) |
| 2606 | |
| 2607 | (defsubst calcFunc-froundu (a &optional prec) |
| 2608 | (let ((math-rounding-mode 'up)) |
| 2609 | (calcFunc-fround a prec))) |
| 2610 | |
| 2611 | ;;; Pull floating-point values apart into mantissa and exponent. |
| 2612 | (defun calcFunc-mant (x) |
| 2613 | (if (Math-realp x) |
| 2614 | (if (or (Math-ratp x) |
| 2615 | (eq (nth 1 x) 0)) |
| 2616 | x |
| 2617 | (list 'float (nth 1 x) (- 1 (math-numdigs (nth 1 x))))) |
| 2618 | (calc-record-why 'realp x) |
| 2619 | (list 'calcFunc-mant x))) |
| 2620 | |
| 2621 | (defun calcFunc-xpon (x) |
| 2622 | (if (Math-realp x) |
| 2623 | (if (or (Math-ratp x) |
| 2624 | (eq (nth 1 x) 0)) |
| 2625 | 0 |
| 2626 | (math-normalize (+ (nth 2 x) (1- (math-numdigs (nth 1 x)))))) |
| 2627 | (calc-record-why 'realp x) |
| 2628 | (list 'calcFunc-xpon x))) |
| 2629 | |
| 2630 | (defun calcFunc-scf (x n) |
| 2631 | (if (integerp n) |
| 2632 | (cond ((eq n 0) |
| 2633 | x) |
| 2634 | ((Math-integerp x) |
| 2635 | (if (> n 0) |
| 2636 | (math-scale-int x n) |
| 2637 | (math-div x (math-scale-int 1 (- n))))) |
| 2638 | ((eq (car x) 'frac) |
| 2639 | (if (> n 0) |
| 2640 | (math-make-frac (math-scale-int (nth 1 x) n) (nth 2 x)) |
| 2641 | (math-make-frac (nth 1 x) (math-scale-int (nth 2 x) (- n))))) |
| 2642 | ((eq (car x) 'float) |
| 2643 | (math-make-float (nth 1 x) (+ (nth 2 x) n))) |
| 2644 | ((memq (car x) '(cplx sdev)) |
| 2645 | (math-normalize |
| 2646 | (list (car x) |
| 2647 | (calcFunc-scf (nth 1 x) n) |
| 2648 | (calcFunc-scf (nth 2 x) n)))) |
| 2649 | ((memq (car x) '(polar mod)) |
| 2650 | (math-normalize |
| 2651 | (list (car x) |
| 2652 | (calcFunc-scf (nth 1 x) n) |
| 2653 | (nth 2 x)))) |
| 2654 | ((eq (car x) 'intv) |
| 2655 | (math-normalize |
| 2656 | (list (car x) |
| 2657 | (nth 1 x) |
| 2658 | (calcFunc-scf (nth 2 x) n) |
| 2659 | (calcFunc-scf (nth 3 x) n)))) |
| 2660 | ((eq (car x) 'vec) |
| 2661 | (math-map-vec (function (lambda (x) (calcFunc-scf x n))) x)) |
| 2662 | ((math-infinitep x) |
| 2663 | x) |
| 2664 | (t |
| 2665 | (calc-record-why 'realp x) |
| 2666 | (list 'calcFunc-scf x n))) |
| 2667 | (if (math-messy-integerp n) |
| 2668 | (if (< (nth 2 n) 10) |
| 2669 | (calcFunc-scf x (math-trunc n)) |
| 2670 | (math-overflow n)) |
| 2671 | (if (math-integerp n) |
| 2672 | (math-overflow n) |
| 2673 | (calc-record-why 'integerp n) |
| 2674 | (list 'calcFunc-scf x n))))) |
| 2675 | |
| 2676 | |
| 2677 | (defun calcFunc-incr (x &optional step relative-to) |
| 2678 | (or step (setq step 1)) |
| 2679 | (cond ((not (Math-integerp step)) |
| 2680 | (math-reject-arg step 'integerp)) |
| 2681 | ((Math-integerp x) |
| 2682 | (math-add x step)) |
| 2683 | ((eq (car x) 'float) |
| 2684 | (if (and (math-zerop x) |
| 2685 | (eq (car-safe relative-to) 'float)) |
| 2686 | (math-mul step |
| 2687 | (calcFunc-scf relative-to (- 1 calc-internal-prec))) |
| 2688 | (math-add-float x (math-make-float |
| 2689 | step |
| 2690 | (+ (nth 2 x) |
| 2691 | (- (math-numdigs (nth 1 x)) |
| 2692 | calc-internal-prec)))))) |
| 2693 | ((eq (car x) 'date) |
| 2694 | (if (Math-integerp (nth 1 x)) |
| 2695 | (math-add x step) |
| 2696 | (math-add x (list 'hms 0 0 step)))) |
| 2697 | (t |
| 2698 | (math-reject-arg x 'realp)))) |
| 2699 | |
| 2700 | (defsubst calcFunc-decr (x &optional step relative-to) |
| 2701 | (calcFunc-incr x (math-neg (or step 1)) relative-to)) |
| 2702 | |
| 2703 | (defun calcFunc-percent (x) |
| 2704 | (if (math-objectp x) |
| 2705 | (let ((calc-prefer-frac nil)) |
| 2706 | (math-div x 100)) |
| 2707 | (list 'calcFunc-percent x))) |
| 2708 | |
| 2709 | (defun calcFunc-relch (x y) |
| 2710 | (if (and (math-objectp x) (math-objectp y)) |
| 2711 | (math-div (math-sub y x) x) |
| 2712 | (list 'calcFunc-relch x y))) |
| 2713 | |
| 2714 | ;;; Compute the absolute value squared of A. [F N] [Public] |
| 2715 | (defun calcFunc-abssqr (a) |
| 2716 | (cond ((Math-realp a) |
| 2717 | (math-mul a a)) |
| 2718 | ((eq (car a) 'cplx) |
| 2719 | (math-add (math-sqr (nth 1 a)) |
| 2720 | (math-sqr (nth 2 a)))) |
| 2721 | ((eq (car a) 'polar) |
| 2722 | (math-sqr (nth 1 a))) |
| 2723 | ((and (memq (car a) '(sdev intv)) (math-constp a)) |
| 2724 | (math-sqr (math-abs a))) |
| 2725 | ((eq (car a) 'vec) |
| 2726 | (math-reduce-vec 'math-add (math-map-vec 'calcFunc-abssqr a))) |
| 2727 | ((math-known-realp a) |
| 2728 | (math-pow a 2)) |
| 2729 | ((let ((inf (math-infinitep a))) |
| 2730 | (and inf |
| 2731 | (math-mul (calcFunc-abssqr (math-infinite-dir a inf)) inf)))) |
| 2732 | (t (calc-record-why 'numvecp a) |
| 2733 | (list 'calcFunc-abssqr a)))) |
| 2734 | |
| 2735 | (defsubst math-sqr (a) |
| 2736 | (math-mul a a)) |
| 2737 | |
| 2738 | ;;;; Number theory. |
| 2739 | |
| 2740 | (defun calcFunc-idiv (a b) ; [I I I] [Public] |
| 2741 | (cond ((and (Math-natnump a) (Math-natnump b) (not (eq b 0))) |
| 2742 | (math-quotient a b)) |
| 2743 | ((Math-realp a) |
| 2744 | (if (Math-realp b) |
| 2745 | (let ((calc-prefer-frac t)) |
| 2746 | (math-floor (math-div a b))) |
| 2747 | (math-reject-arg b 'realp))) |
| 2748 | ((eq (car-safe a) 'hms) |
| 2749 | (if (eq (car-safe b) 'hms) |
| 2750 | (let ((calc-prefer-frac t)) |
| 2751 | (math-floor (math-div a b))) |
| 2752 | (math-reject-arg b 'hmsp))) |
| 2753 | ((and (or (eq (car-safe a) 'intv) (Math-realp a)) |
| 2754 | (or (eq (car-safe b) 'intv) (Math-realp b))) |
| 2755 | (math-floor (math-div a b))) |
| 2756 | ((or (math-infinitep a) |
| 2757 | (math-infinitep b)) |
| 2758 | (math-div a b)) |
| 2759 | (t (math-reject-arg a 'anglep)))) |
| 2760 | |
| 2761 | |
| 2762 | ;;; Combine two terms being added, if possible. |
| 2763 | (defun math-combine-sum (a b nega negb scalar-okay) |
| 2764 | (if (and scalar-okay (Math-objvecp a) (Math-objvecp b)) |
| 2765 | (math-add-or-sub a b nega negb) |
| 2766 | (let ((amult 1) (bmult 1)) |
| 2767 | (and (consp a) |
| 2768 | (cond ((and (eq (car a) '*) |
| 2769 | (Math-objectp (nth 1 a))) |
| 2770 | (setq amult (nth 1 a) |
| 2771 | a (nth 2 a))) |
| 2772 | ((and (eq (car a) '/) |
| 2773 | (Math-objectp (nth 2 a))) |
| 2774 | (setq amult (if (Math-integerp (nth 2 a)) |
| 2775 | (list 'frac 1 (nth 2 a)) |
| 2776 | (math-div 1 (nth 2 a))) |
| 2777 | a (nth 1 a))) |
| 2778 | ((eq (car a) 'neg) |
| 2779 | (setq amult -1 |
| 2780 | a (nth 1 a))))) |
| 2781 | (and (consp b) |
| 2782 | (cond ((and (eq (car b) '*) |
| 2783 | (Math-objectp (nth 1 b))) |
| 2784 | (setq bmult (nth 1 b) |
| 2785 | b (nth 2 b))) |
| 2786 | ((and (eq (car b) '/) |
| 2787 | (Math-objectp (nth 2 b))) |
| 2788 | (setq bmult (if (Math-integerp (nth 2 b)) |
| 2789 | (list 'frac 1 (nth 2 b)) |
| 2790 | (math-div 1 (nth 2 b))) |
| 2791 | b (nth 1 b))) |
| 2792 | ((eq (car b) 'neg) |
| 2793 | (setq bmult -1 |
| 2794 | b (nth 1 b))))) |
| 2795 | (and (if math-simplifying |
| 2796 | (Math-equal a b) |
| 2797 | (equal a b)) |
| 2798 | (progn |
| 2799 | (if nega (setq amult (math-neg amult))) |
| 2800 | (if negb (setq bmult (math-neg bmult))) |
| 2801 | (setq amult (math-add amult bmult)) |
| 2802 | (math-mul amult a)))))) |
| 2803 | |
| 2804 | (defun math-add-or-sub (a b aneg bneg) |
| 2805 | (if aneg (setq a (math-neg a))) |
| 2806 | (if bneg (setq b (math-neg b))) |
| 2807 | (if (or (Math-vectorp a) (Math-vectorp b)) |
| 2808 | (math-normalize (list '+ a b)) |
| 2809 | (math-add a b))) |
| 2810 | |
| 2811 | (defvar math-combine-prod-e '(var e var-e)) |
| 2812 | |
| 2813 | ;;; The following is expanded out four ways for speed. |
| 2814 | |
| 2815 | ;; math-unit-prefixes is defined in calc-units.el, |
| 2816 | ;; but used here. |
| 2817 | (defvar math-unit-prefixes) |
| 2818 | |
| 2819 | (defun math-combine-prod (a b inva invb scalar-okay) |
| 2820 | (cond |
| 2821 | ((or (and inva (Math-zerop a)) |
| 2822 | (and invb (Math-zerop b))) |
| 2823 | nil) |
| 2824 | ((and scalar-okay (Math-objvecp a) (Math-objvecp b)) |
| 2825 | (setq a (math-mul-or-div a b inva invb)) |
| 2826 | (and (Math-objvecp a) |
| 2827 | a)) |
| 2828 | ((and (eq (car-safe a) '^) |
| 2829 | inva |
| 2830 | (math-looks-negp (nth 2 a))) |
| 2831 | (math-mul (math-pow (nth 1 a) (math-neg (nth 2 a))) b)) |
| 2832 | ((and (eq (car-safe b) '^) |
| 2833 | invb |
| 2834 | (math-looks-negp (nth 2 b))) |
| 2835 | (math-mul a (math-pow (nth 1 b) (math-neg (nth 2 b))))) |
| 2836 | ((and math-simplifying |
| 2837 | (math-combine-prod-trig a b))) |
| 2838 | (t (let ((apow 1) (bpow 1)) |
| 2839 | (and (consp a) |
| 2840 | (cond ((and (eq (car a) '^) |
| 2841 | (or math-simplifying |
| 2842 | (Math-numberp (nth 2 a)))) |
| 2843 | (setq apow (nth 2 a) |
| 2844 | a (nth 1 a))) |
| 2845 | ((eq (car a) 'calcFunc-sqrt) |
| 2846 | (setq apow '(frac 1 2) |
| 2847 | a (nth 1 a))) |
| 2848 | ((and (eq (car a) 'calcFunc-exp) |
| 2849 | (or math-simplifying |
| 2850 | (Math-numberp (nth 1 a)))) |
| 2851 | (setq apow (nth 1 a) |
| 2852 | a math-combine-prod-e)))) |
| 2853 | (and (consp a) (eq (car a) 'frac) |
| 2854 | (Math-lessp (nth 1 a) (nth 2 a)) |
| 2855 | (setq a (math-div 1 a) apow (math-neg apow))) |
| 2856 | (and (consp b) |
| 2857 | (cond ((and (eq (car b) '^) |
| 2858 | (or math-simplifying |
| 2859 | (Math-numberp (nth 2 b)))) |
| 2860 | (setq bpow (nth 2 b) |
| 2861 | b (nth 1 b))) |
| 2862 | ((eq (car b) 'calcFunc-sqrt) |
| 2863 | (setq bpow '(frac 1 2) |
| 2864 | b (nth 1 b))) |
| 2865 | ((and (eq (car b) 'calcFunc-exp) |
| 2866 | (or math-simplifying |
| 2867 | (Math-numberp (nth 1 b)))) |
| 2868 | (setq bpow (nth 1 b) |
| 2869 | b math-combine-prod-e)))) |
| 2870 | (and (consp b) (eq (car b) 'frac) |
| 2871 | (Math-lessp (nth 1 b) (nth 2 b)) |
| 2872 | (setq b (math-div 1 b) bpow (math-neg bpow))) |
| 2873 | (if inva (setq apow (math-neg apow))) |
| 2874 | (if invb (setq bpow (math-neg bpow))) |
| 2875 | (or (and (if math-simplifying |
| 2876 | (math-commutative-equal a b) |
| 2877 | (equal a b)) |
| 2878 | (let ((sumpow (math-add apow bpow))) |
| 2879 | (and (or (not (Math-integerp a)) |
| 2880 | (Math-zerop sumpow) |
| 2881 | (eq (eq (car-safe apow) 'frac) |
| 2882 | (eq (car-safe bpow) 'frac))) |
| 2883 | (progn |
| 2884 | (and (math-looks-negp sumpow) |
| 2885 | (Math-ratp a) (Math-posp a) |
| 2886 | (setq a (math-div 1 a) |
| 2887 | sumpow (math-neg sumpow))) |
| 2888 | (cond ((equal sumpow '(frac 1 2)) |
| 2889 | (list 'calcFunc-sqrt a)) |
| 2890 | ((equal sumpow '(frac -1 2)) |
| 2891 | (math-div 1 (list 'calcFunc-sqrt a))) |
| 2892 | ((and (eq a math-combine-prod-e) |
| 2893 | (eq a b)) |
| 2894 | (list 'calcFunc-exp sumpow)) |
| 2895 | (t |
| 2896 | (condition-case err |
| 2897 | (math-pow a sumpow) |
| 2898 | (inexact-result (list '^ a sumpow))))))))) |
| 2899 | (and math-simplifying-units |
| 2900 | math-combining-units |
| 2901 | (let* ((ua (math-check-unit-name a)) |
| 2902 | ub) |
| 2903 | (and ua |
| 2904 | (eq ua (setq ub (math-check-unit-name b))) |
| 2905 | (progn |
| 2906 | (setq ua (if (eq (nth 1 a) (car ua)) |
| 2907 | 1 |
| 2908 | (nth 1 (assq (aref (symbol-name (nth 1 a)) |
| 2909 | 0) |
| 2910 | math-unit-prefixes))) |
| 2911 | ub (if (eq (nth 1 b) (car ub)) |
| 2912 | 1 |
| 2913 | (nth 1 (assq (aref (symbol-name (nth 1 b)) |
| 2914 | 0) |
| 2915 | math-unit-prefixes)))) |
| 2916 | (if (Math-lessp ua ub) |
| 2917 | (let (temp) |
| 2918 | (setq temp a a b b temp |
| 2919 | temp ua ua ub ub temp |
| 2920 | temp apow apow bpow bpow temp))) |
| 2921 | (math-mul (math-pow (math-div ua ub) apow) |
| 2922 | (math-pow b (math-add apow bpow))))))) |
| 2923 | (and (equal apow bpow) |
| 2924 | (Math-natnump a) (Math-natnump b) |
| 2925 | (cond ((equal apow '(frac 1 2)) |
| 2926 | (list 'calcFunc-sqrt (math-mul a b))) |
| 2927 | ((equal apow '(frac -1 2)) |
| 2928 | (math-div 1 (list 'calcFunc-sqrt (math-mul a b)))) |
| 2929 | (t |
| 2930 | (setq a (math-mul a b)) |
| 2931 | (condition-case err |
| 2932 | (math-pow a apow) |
| 2933 | (inexact-result (list '^ a apow))))))))))) |
| 2934 | |
| 2935 | (defun math-combine-prod-trig (a b) |
| 2936 | (cond |
| 2937 | ((and (eq (car-safe a) 'calcFunc-sin) |
| 2938 | (eq (car-safe b) 'calcFunc-csc) |
| 2939 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2940 | 1) |
| 2941 | ((and (eq (car-safe a) 'calcFunc-sin) |
| 2942 | (eq (car-safe b) 'calcFunc-sec) |
| 2943 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2944 | (cons 'calcFunc-tan (cdr a))) |
| 2945 | ((and (eq (car-safe a) 'calcFunc-sin) |
| 2946 | (eq (car-safe b) 'calcFunc-cot) |
| 2947 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2948 | (cons 'calcFunc-cos (cdr a))) |
| 2949 | ((and (eq (car-safe a) 'calcFunc-cos) |
| 2950 | (eq (car-safe b) 'calcFunc-sec) |
| 2951 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2952 | 1) |
| 2953 | ((and (eq (car-safe a) 'calcFunc-cos) |
| 2954 | (eq (car-safe b) 'calcFunc-csc) |
| 2955 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2956 | (cons 'calcFunc-cot (cdr a))) |
| 2957 | ((and (eq (car-safe a) 'calcFunc-cos) |
| 2958 | (eq (car-safe b) 'calcFunc-tan) |
| 2959 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2960 | (cons 'calcFunc-sin (cdr a))) |
| 2961 | ((and (eq (car-safe a) 'calcFunc-tan) |
| 2962 | (eq (car-safe b) 'calcFunc-cot) |
| 2963 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2964 | 1) |
| 2965 | ((and (eq (car-safe a) 'calcFunc-tan) |
| 2966 | (eq (car-safe b) 'calcFunc-csc) |
| 2967 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2968 | (cons 'calcFunc-sec (cdr a))) |
| 2969 | ((and (eq (car-safe a) 'calcFunc-sec) |
| 2970 | (eq (car-safe b) 'calcFunc-cot) |
| 2971 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2972 | (cons 'calcFunc-csc (cdr a))) |
| 2973 | ((and (eq (car-safe a) 'calcFunc-sinh) |
| 2974 | (eq (car-safe b) 'calcFunc-csch) |
| 2975 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2976 | 1) |
| 2977 | ((and (eq (car-safe a) 'calcFunc-sinh) |
| 2978 | (eq (car-safe b) 'calcFunc-sech) |
| 2979 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2980 | (cons 'calcFunc-tanh (cdr a))) |
| 2981 | ((and (eq (car-safe a) 'calcFunc-sinh) |
| 2982 | (eq (car-safe b) 'calcFunc-coth) |
| 2983 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2984 | (cons 'calcFunc-cosh (cdr a))) |
| 2985 | ((and (eq (car-safe a) 'calcFunc-cosh) |
| 2986 | (eq (car-safe b) 'calcFunc-sech) |
| 2987 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2988 | 1) |
| 2989 | ((and (eq (car-safe a) 'calcFunc-cosh) |
| 2990 | (eq (car-safe b) 'calcFunc-csch) |
| 2991 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2992 | (cons 'calcFunc-coth (cdr a))) |
| 2993 | ((and (eq (car-safe a) 'calcFunc-cosh) |
| 2994 | (eq (car-safe b) 'calcFunc-tanh) |
| 2995 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 2996 | (cons 'calcFunc-sinh (cdr a))) |
| 2997 | ((and (eq (car-safe a) 'calcFunc-tanh) |
| 2998 | (eq (car-safe b) 'calcFunc-coth) |
| 2999 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 3000 | 1) |
| 3001 | ((and (eq (car-safe a) 'calcFunc-tanh) |
| 3002 | (eq (car-safe b) 'calcFunc-csch) |
| 3003 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 3004 | (cons 'calcFunc-sech (cdr a))) |
| 3005 | ((and (eq (car-safe a) 'calcFunc-sech) |
| 3006 | (eq (car-safe b) 'calcFunc-coth) |
| 3007 | (= 0 (math-simplify (math-sub (cdr a) (cdr b))))) |
| 3008 | (cons 'calcFunc-csch (cdr a))) |
| 3009 | (t |
| 3010 | nil))) |
| 3011 | |
| 3012 | (defun math-mul-or-div (a b ainv binv) |
| 3013 | (if (or (Math-vectorp a) (Math-vectorp b)) |
| 3014 | (math-normalize |
| 3015 | (if ainv |
| 3016 | (if binv |
| 3017 | (list '/ (math-div 1 a) b) |
| 3018 | (list '/ b a)) |
| 3019 | (if binv |
| 3020 | (list '/ a b) |
| 3021 | (list '* a b)))) |
| 3022 | (if ainv |
| 3023 | (if binv |
| 3024 | (math-div (math-div 1 a) b) |
| 3025 | (math-div b a)) |
| 3026 | (if binv |
| 3027 | (math-div a b) |
| 3028 | (math-mul a b))))) |
| 3029 | |
| 3030 | ;; The variable math-com-bterms is local to math-commutative-equal, |
| 3031 | ;; but is used by math-commutative collect, which is called by |
| 3032 | ;; math-commutative-equal. |
| 3033 | (defvar math-com-bterms) |
| 3034 | |
| 3035 | (defun math-commutative-equal (a b) |
| 3036 | (if (memq (car-safe a) '(+ -)) |
| 3037 | (and (memq (car-safe b) '(+ -)) |
| 3038 | (let ((math-com-bterms nil) aterms p) |
| 3039 | (math-commutative-collect b nil) |
| 3040 | (setq aterms math-com-bterms math-com-bterms nil) |
| 3041 | (math-commutative-collect a nil) |
| 3042 | (and (= (length aterms) (length math-com-bterms)) |
| 3043 | (progn |
| 3044 | (while (and aterms |
| 3045 | (progn |
| 3046 | (setq p math-com-bterms) |
| 3047 | (while (and p (not (equal (car aterms) |
| 3048 | (car p)))) |
| 3049 | (setq p (cdr p))) |
| 3050 | p)) |
| 3051 | (setq math-com-bterms (delq (car p) math-com-bterms) |
| 3052 | aterms (cdr aterms))) |
| 3053 | (not aterms))))) |
| 3054 | (equal a b))) |
| 3055 | |
| 3056 | (defun math-commutative-collect (b neg) |
| 3057 | (if (eq (car-safe b) '+) |
| 3058 | (progn |
| 3059 | (math-commutative-collect (nth 1 b) neg) |
| 3060 | (math-commutative-collect (nth 2 b) neg)) |
| 3061 | (if (eq (car-safe b) '-) |
| 3062 | (progn |
| 3063 | (math-commutative-collect (nth 1 b) neg) |
| 3064 | (math-commutative-collect (nth 2 b) (not neg))) |
| 3065 | (setq math-com-bterms (cons (if neg (math-neg b) b) math-com-bterms))))) |
| 3066 | |
| 3067 | (provide 'calc-arith) |
| 3068 | |
| 3069 | ;;; calc-arith.el ends here |