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3132f345 CW |
1 | ;;; calc-bin.el --- binary functions for Calc |
2 | ||
58ba2f8f | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
5df4f04c | 4 | ;; 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. |
3132f345 CW |
5 | |
6 | ;; Author: David Gillespie <daveg@synaptics.com> | |
e8fff8ed | 7 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 EZ |
8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
662c9c64 | 11 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
7c671b23 | 12 | ;; it under the terms of the GNU General Public License as published by |
662c9c64 GM |
13 | ;; the Free Software Foundation, either version 3 of the License, or |
14 | ;; (at your option) any later version. | |
7c671b23 | 15 | |
136211a9 | 16 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
17 | ;; but WITHOUT ANY WARRANTY; without even the implied warranty of |
18 | ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
19 | ;; GNU General Public License for more details. | |
20 | ||
21 | ;; You should have received a copy of the GNU General Public License | |
662c9c64 | 22 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
136211a9 | 23 | |
3132f345 | 24 | ;;; Commentary: |
136211a9 | 25 | |
3132f345 | 26 | ;;; Code: |
136211a9 EZ |
27 | |
28 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 29 | |
fb9ec5ef | 30 | (require 'calc-ext) |
136211a9 EZ |
31 | (require 'calc-macs) |
32 | ||
3fa5c462 JB |
33 | ;;; Some useful numbers |
34 | (defconst math-bignum-logb-digit-size | |
b411074b | 35 | (logb math-bignum-digit-size) |
3fa5c462 JB |
36 | "The logb of the size of a bignum digit. |
37 | This is the largest value of B such that 2^B is less than | |
38 | the size of a Calc bignum digit.") | |
39 | ||
40 | (defconst math-bignum-digit-power-of-two | |
b411074b | 41 | (expt 2 (logb math-bignum-digit-size)) |
3fa5c462 JB |
42 | "The largest power of 2 less than the size of a Calc bignum digit.") |
43 | ||
136211a9 EZ |
44 | ;;; b-prefix binary commands. |
45 | ||
46 | (defun calc-and (n) | |
47 | (interactive "P") | |
48 | (calc-slow-wrapper | |
49 | (calc-enter-result 2 "and" | |
50 | (append '(calcFunc-and) | |
51 | (calc-top-list-n 2) | |
7d70a3ba | 52 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
53 | |
54 | (defun calc-or (n) | |
55 | (interactive "P") | |
56 | (calc-slow-wrapper | |
57 | (calc-enter-result 2 "or" | |
58 | (append '(calcFunc-or) | |
59 | (calc-top-list-n 2) | |
7d70a3ba | 60 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
61 | |
62 | (defun calc-xor (n) | |
63 | (interactive "P") | |
64 | (calc-slow-wrapper | |
65 | (calc-enter-result 2 "xor" | |
66 | (append '(calcFunc-xor) | |
67 | (calc-top-list-n 2) | |
7d70a3ba | 68 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
69 | |
70 | (defun calc-diff (n) | |
71 | (interactive "P") | |
72 | (calc-slow-wrapper | |
73 | (calc-enter-result 2 "diff" | |
74 | (append '(calcFunc-diff) | |
75 | (calc-top-list-n 2) | |
7d70a3ba | 76 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
77 | |
78 | (defun calc-not (n) | |
79 | (interactive "P") | |
80 | (calc-slow-wrapper | |
81 | (calc-enter-result 1 "not" | |
82 | (append '(calcFunc-not) | |
83 | (calc-top-list-n 1) | |
7d70a3ba | 84 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
85 | |
86 | (defun calc-lshift-binary (n) | |
87 | (interactive "P") | |
88 | (calc-slow-wrapper | |
89 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
90 | (calc-enter-result hyp "lsh" | |
91 | (append '(calcFunc-lsh) | |
92 | (calc-top-list-n hyp) | |
7d70a3ba | 93 | (and n (list (prefix-numeric-value n)))))))) |
136211a9 EZ |
94 | |
95 | (defun calc-rshift-binary (n) | |
96 | (interactive "P") | |
97 | (calc-slow-wrapper | |
98 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
99 | (calc-enter-result hyp "rsh" | |
100 | (append '(calcFunc-rsh) | |
101 | (calc-top-list-n hyp) | |
7d70a3ba | 102 | (and n (list (prefix-numeric-value n)))))))) |
136211a9 EZ |
103 | |
104 | (defun calc-lshift-arith (n) | |
105 | (interactive "P") | |
106 | (calc-slow-wrapper | |
107 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
108 | (calc-enter-result hyp "ash" | |
109 | (append '(calcFunc-ash) | |
110 | (calc-top-list-n hyp) | |
7d70a3ba | 111 | (and n (list (prefix-numeric-value n)))))))) |
136211a9 EZ |
112 | |
113 | (defun calc-rshift-arith (n) | |
114 | (interactive "P") | |
115 | (calc-slow-wrapper | |
116 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
117 | (calc-enter-result hyp "rash" | |
118 | (append '(calcFunc-rash) | |
119 | (calc-top-list-n hyp) | |
7d70a3ba | 120 | (and n (list (prefix-numeric-value n)))))))) |
136211a9 EZ |
121 | |
122 | (defun calc-rotate-binary (n) | |
123 | (interactive "P") | |
124 | (calc-slow-wrapper | |
125 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
126 | (calc-enter-result hyp "rot" | |
127 | (append '(calcFunc-rot) | |
128 | (calc-top-list-n hyp) | |
7d70a3ba | 129 | (and n (list (prefix-numeric-value n)))))))) |
136211a9 EZ |
130 | |
131 | (defun calc-clip (n) | |
132 | (interactive "P") | |
133 | (calc-slow-wrapper | |
134 | (calc-enter-result 1 "clip" | |
135 | (append '(calcFunc-clip) | |
136 | (calc-top-list-n 1) | |
7d70a3ba | 137 | (and n (list (prefix-numeric-value n))))))) |
136211a9 EZ |
138 | |
139 | (defun calc-word-size (n) | |
140 | (interactive "P") | |
141 | (calc-wrapper | |
142 | (or n (setq n (read-string (format "Binary word size: (default %d) " | |
143 | calc-word-size)))) | |
144 | (setq n (if (stringp n) | |
145 | (if (equal n "") | |
146 | calc-word-size | |
147 | (if (string-match "\\`[-+]?[0-9]+\\'" n) | |
14e39ad4 | 148 | (string-to-number n) |
136211a9 EZ |
149 | (error "Expected an integer"))) |
150 | (prefix-numeric-value n))) | |
151 | (or (= n calc-word-size) | |
152 | (if (> (math-abs n) 100) | |
153 | (calc-change-mode 'calc-word-size n calc-leading-zeros) | |
154 | (calc-change-mode '(calc-word-size calc-previous-modulo) | |
155 | (list n (math-power-of-2 (math-abs n))) | |
156 | calc-leading-zeros))) | |
b1d9611c JB |
157 | (setq math-2-word-size (math-power-of-2 (math-abs n))) |
158 | (setq math-half-2-word-size (math-power-of-2 (1- (math-abs n)))) | |
159 | (calc-do-refresh) | |
160 | (calc-refresh-evaltos) | |
136211a9 | 161 | (if (< n 0) |
50a982d6 | 162 | (message "Binary word size is %d bits (two's complement)" (- n)) |
3132f345 | 163 | (message "Binary word size is %d bits" n)))) |
136211a9 EZ |
164 | |
165 | ||
166 | ||
167 | ||
168 | ||
169 | ;;; d-prefix mode commands. | |
170 | ||
b1d9611c | 171 | (defun calc-radix (n &optional arg) |
136211a9 EZ |
172 | (interactive "NDisplay radix (2-36): ") |
173 | (calc-wrapper | |
174 | (if (and (>= n 2) (<= n 36)) | |
175 | (progn | |
b1d9611c | 176 | (calc-change-mode |
50a982d6 JB |
177 | (list 'calc-number-radix 'calc-twos-complement-mode) |
178 | (list n (and (or (= n 2) (= n 8) (= n 16)) arg)) t) | |
136211a9 EZ |
179 | ;; also change global value so minibuffer sees it |
180 | (setq-default calc-number-radix calc-number-radix)) | |
181 | (setq n calc-number-radix)) | |
50a982d6 JB |
182 | (if calc-twos-complement-mode |
183 | (message "Number radix is %d, two's complement mode is on." n) | |
b1d9611c | 184 | (message "Number radix is %d" n)))) |
136211a9 EZ |
185 | |
186 | (defun calc-decimal-radix () | |
187 | (interactive) | |
7d70a3ba | 188 | (calc-radix 10)) |
136211a9 | 189 | |
b1d9611c JB |
190 | (defun calc-binary-radix (&optional arg) |
191 | (interactive "P") | |
192 | (calc-radix 2 arg)) | |
136211a9 | 193 | |
50a982d6 JB |
194 | (defun calc-octal-radix (&optional arg) |
195 | (interactive "P") | |
196 | (calc-radix 8 arg)) | |
136211a9 | 197 | |
50a982d6 JB |
198 | (defun calc-hex-radix (&optional arg) |
199 | (interactive "P") | |
200 | (calc-radix 16 arg)) | |
136211a9 EZ |
201 | |
202 | (defun calc-leading-zeros (n) | |
203 | (interactive "P") | |
204 | (calc-wrapper | |
205 | (if (calc-change-mode 'calc-leading-zeros n t t) | |
3132f345 | 206 | (message "Zero-padding integers to %d digits (assuming radix %d)" |
136211a9 EZ |
207 | (let* ((calc-internal-prec 6)) |
208 | (math-compute-max-digits (math-abs calc-word-size) | |
209 | calc-number-radix)) | |
210 | calc-number-radix) | |
3132f345 | 211 | (message "Omitting leading zeros on integers")))) |
136211a9 EZ |
212 | |
213 | ||
214 | (defvar math-power-of-2-cache (list 1 2 4 8 16 32 64 128 256 512 1024)) | |
215 | (defvar math-big-power-of-2-cache nil) | |
216 | (defun math-power-of-2 (n) ; [I I] [Public] | |
217 | (if (and (natnump n) (<= n 100)) | |
218 | (or (nth n math-power-of-2-cache) | |
219 | (let* ((i (length math-power-of-2-cache)) | |
220 | (val (nth (1- i) math-power-of-2-cache))) | |
221 | (while (<= i n) | |
222 | (setq val (math-mul val 2) | |
223 | math-power-of-2-cache (nconc math-power-of-2-cache | |
224 | (list val)) | |
225 | i (1+ i))) | |
226 | val)) | |
227 | (let ((found (assq n math-big-power-of-2-cache))) | |
228 | (if found | |
229 | (cdr found) | |
230 | (let ((po2 (math-ipow 2 n))) | |
231 | (setq math-big-power-of-2-cache | |
232 | (cons (cons n po2) math-big-power-of-2-cache)) | |
7d70a3ba | 233 | po2))))) |
136211a9 EZ |
234 | |
235 | (defun math-integer-log2 (n) ; [I I] [Public] | |
236 | (let ((i 0) | |
237 | (p math-power-of-2-cache) | |
238 | val) | |
239 | (while (and p (Math-natnum-lessp (setq val (car p)) n)) | |
240 | (setq p (cdr p) | |
241 | i (1+ i))) | |
242 | (if p | |
243 | (and (equal val n) | |
244 | i) | |
245 | (while (Math-natnum-lessp | |
246 | (prog1 | |
247 | (setq val (math-mul val 2)) | |
248 | (setq math-power-of-2-cache (nconc math-power-of-2-cache | |
249 | (list val)))) | |
250 | n) | |
251 | (setq i (1+ i))) | |
252 | (and (equal val n) | |
7d70a3ba | 253 | i)))) |
136211a9 EZ |
254 | |
255 | ||
256 | ||
257 | ||
258 | ;;; Bitwise operations. | |
259 | ||
260 | (defun calcFunc-and (a b &optional w) ; [I I I] [Public] | |
261 | (cond ((Math-messy-integerp w) | |
262 | (calcFunc-and a b (math-trunc w))) | |
263 | ((and w (not (integerp w))) | |
264 | (math-reject-arg w 'fixnump)) | |
265 | ((and (integerp a) (integerp b)) | |
266 | (math-clip (logand a b) w)) | |
267 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
268 | (math-binary-modulo-args 'calcFunc-and a b w)) | |
269 | ((not (Math-num-integerp a)) | |
270 | (math-reject-arg a 'integerp)) | |
271 | ((not (Math-num-integerp b)) | |
272 | (math-reject-arg b 'integerp)) | |
273 | (t (math-clip (cons 'bigpos | |
274 | (math-and-bignum (math-binary-arg a w) | |
275 | (math-binary-arg b w))) | |
7d70a3ba | 276 | w)))) |
136211a9 EZ |
277 | |
278 | (defun math-binary-arg (a w) | |
279 | (if (not (Math-integerp a)) | |
280 | (setq a (math-trunc a))) | |
281 | (if (Math-integer-negp a) | |
282 | (math-not-bignum (cdr (math-bignum-test (math-sub -1 a))) | |
283 | (math-abs (if w (math-trunc w) calc-word-size))) | |
7d70a3ba | 284 | (cdr (Math-bignum-test a)))) |
136211a9 EZ |
285 | |
286 | (defun math-binary-modulo-args (f a b w) | |
287 | (let (mod) | |
288 | (if (eq (car-safe a) 'mod) | |
289 | (progn | |
290 | (setq mod (nth 2 a) | |
291 | a (nth 1 a)) | |
292 | (if (eq (car-safe b) 'mod) | |
293 | (if (equal mod (nth 2 b)) | |
294 | (setq b (nth 1 b)) | |
295 | (math-reject-arg b "*Inconsistent modulos")))) | |
296 | (setq mod (nth 2 b) | |
297 | b (nth 1 b))) | |
298 | (if (Math-messy-integerp mod) | |
299 | (setq mod (math-trunc mod)) | |
300 | (or (Math-integerp mod) | |
301 | (math-reject-arg mod 'integerp))) | |
302 | (let ((bits (math-integer-log2 mod))) | |
303 | (if bits | |
304 | (if w | |
305 | (if (/= w bits) | |
306 | (calc-record-why | |
307 | "*Warning: Modulo inconsistent with word size")) | |
308 | (setq w bits)) | |
309 | (calc-record-why "*Warning: Modulo is not a power of 2")) | |
310 | (math-make-mod (if b | |
311 | (funcall f a b w) | |
312 | (funcall f a w)) | |
7d70a3ba | 313 | mod)))) |
136211a9 EZ |
314 | |
315 | (defun math-and-bignum (a b) ; [l l l] | |
316 | (and a b | |
3fa5c462 JB |
317 | (let ((qa (math-div-bignum-digit a math-bignum-digit-power-of-two)) |
318 | (qb (math-div-bignum-digit b math-bignum-digit-power-of-two))) | |
136211a9 EZ |
319 | (math-mul-bignum-digit (math-and-bignum (math-norm-bignum (car qa)) |
320 | (math-norm-bignum (car qb))) | |
3fa5c462 | 321 | math-bignum-digit-power-of-two |
7d70a3ba | 322 | (logand (cdr qa) (cdr qb)))))) |
136211a9 EZ |
323 | |
324 | (defun calcFunc-or (a b &optional w) ; [I I I] [Public] | |
325 | (cond ((Math-messy-integerp w) | |
326 | (calcFunc-or a b (math-trunc w))) | |
327 | ((and w (not (integerp w))) | |
328 | (math-reject-arg w 'fixnump)) | |
329 | ((and (integerp a) (integerp b)) | |
330 | (math-clip (logior a b) w)) | |
331 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
332 | (math-binary-modulo-args 'calcFunc-or a b w)) | |
333 | ((not (Math-num-integerp a)) | |
334 | (math-reject-arg a 'integerp)) | |
335 | ((not (Math-num-integerp b)) | |
336 | (math-reject-arg b 'integerp)) | |
337 | (t (math-clip (cons 'bigpos | |
338 | (math-or-bignum (math-binary-arg a w) | |
339 | (math-binary-arg b w))) | |
7d70a3ba | 340 | w)))) |
136211a9 EZ |
341 | |
342 | (defun math-or-bignum (a b) ; [l l l] | |
343 | (and (or a b) | |
3fa5c462 JB |
344 | (let ((qa (math-div-bignum-digit a math-bignum-digit-power-of-two)) |
345 | (qb (math-div-bignum-digit b math-bignum-digit-power-of-two))) | |
136211a9 EZ |
346 | (math-mul-bignum-digit (math-or-bignum (math-norm-bignum (car qa)) |
347 | (math-norm-bignum (car qb))) | |
3fa5c462 | 348 | math-bignum-digit-power-of-two |
7d70a3ba | 349 | (logior (cdr qa) (cdr qb)))))) |
136211a9 EZ |
350 | |
351 | (defun calcFunc-xor (a b &optional w) ; [I I I] [Public] | |
352 | (cond ((Math-messy-integerp w) | |
353 | (calcFunc-xor a b (math-trunc w))) | |
354 | ((and w (not (integerp w))) | |
355 | (math-reject-arg w 'fixnump)) | |
356 | ((and (integerp a) (integerp b)) | |
357 | (math-clip (logxor a b) w)) | |
358 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
359 | (math-binary-modulo-args 'calcFunc-xor a b w)) | |
360 | ((not (Math-num-integerp a)) | |
361 | (math-reject-arg a 'integerp)) | |
362 | ((not (Math-num-integerp b)) | |
363 | (math-reject-arg b 'integerp)) | |
364 | (t (math-clip (cons 'bigpos | |
365 | (math-xor-bignum (math-binary-arg a w) | |
366 | (math-binary-arg b w))) | |
7d70a3ba | 367 | w)))) |
136211a9 EZ |
368 | |
369 | (defun math-xor-bignum (a b) ; [l l l] | |
370 | (and (or a b) | |
3fa5c462 JB |
371 | (let ((qa (math-div-bignum-digit a math-bignum-digit-power-of-two)) |
372 | (qb (math-div-bignum-digit b math-bignum-digit-power-of-two))) | |
136211a9 EZ |
373 | (math-mul-bignum-digit (math-xor-bignum (math-norm-bignum (car qa)) |
374 | (math-norm-bignum (car qb))) | |
3fa5c462 | 375 | math-bignum-digit-power-of-two |
7d70a3ba | 376 | (logxor (cdr qa) (cdr qb)))))) |
136211a9 EZ |
377 | |
378 | (defun calcFunc-diff (a b &optional w) ; [I I I] [Public] | |
379 | (cond ((Math-messy-integerp w) | |
380 | (calcFunc-diff a b (math-trunc w))) | |
381 | ((and w (not (integerp w))) | |
382 | (math-reject-arg w 'fixnump)) | |
383 | ((and (integerp a) (integerp b)) | |
384 | (math-clip (logand a (lognot b)) w)) | |
385 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
386 | (math-binary-modulo-args 'calcFunc-diff a b w)) | |
387 | ((not (Math-num-integerp a)) | |
388 | (math-reject-arg a 'integerp)) | |
389 | ((not (Math-num-integerp b)) | |
390 | (math-reject-arg b 'integerp)) | |
391 | (t (math-clip (cons 'bigpos | |
392 | (math-diff-bignum (math-binary-arg a w) | |
393 | (math-binary-arg b w))) | |
7d70a3ba | 394 | w)))) |
136211a9 EZ |
395 | |
396 | (defun math-diff-bignum (a b) ; [l l l] | |
397 | (and a | |
3fa5c462 JB |
398 | (let ((qa (math-div-bignum-digit a math-bignum-digit-power-of-two)) |
399 | (qb (math-div-bignum-digit b math-bignum-digit-power-of-two))) | |
136211a9 EZ |
400 | (math-mul-bignum-digit (math-diff-bignum (math-norm-bignum (car qa)) |
401 | (math-norm-bignum (car qb))) | |
3fa5c462 | 402 | math-bignum-digit-power-of-two |
7d70a3ba | 403 | (logand (cdr qa) (lognot (cdr qb))))))) |
136211a9 EZ |
404 | |
405 | (defun calcFunc-not (a &optional w) ; [I I] [Public] | |
406 | (cond ((Math-messy-integerp w) | |
407 | (calcFunc-not a (math-trunc w))) | |
408 | ((eq (car-safe a) 'mod) | |
409 | (math-binary-modulo-args 'calcFunc-not a nil w)) | |
410 | ((and w (not (integerp w))) | |
411 | (math-reject-arg w 'fixnump)) | |
412 | ((not (Math-num-integerp a)) | |
413 | (math-reject-arg a 'integerp)) | |
414 | ((< (or w (setq w calc-word-size)) 0) | |
415 | (math-clip (calcFunc-not a (- w)) w)) | |
416 | (t (math-normalize | |
417 | (cons 'bigpos | |
418 | (math-not-bignum (math-binary-arg a w) | |
7d70a3ba | 419 | w)))))) |
136211a9 EZ |
420 | |
421 | (defun math-not-bignum (a w) ; [l l] | |
3fa5c462 JB |
422 | (let ((q (math-div-bignum-digit a math-bignum-digit-power-of-two))) |
423 | (if (<= w math-bignum-logb-digit-size) | |
136211a9 EZ |
424 | (list (logand (lognot (cdr q)) |
425 | (1- (lsh 1 w)))) | |
426 | (math-mul-bignum-digit (math-not-bignum (math-norm-bignum (car q)) | |
3fa5c462 JB |
427 | (- w math-bignum-logb-digit-size)) |
428 | math-bignum-digit-power-of-two | |
429 | (logxor (cdr q) | |
430 | (1- math-bignum-digit-power-of-two)))))) | |
136211a9 EZ |
431 | |
432 | (defun calcFunc-lsh (a &optional n w) ; [I I] [Public] | |
433 | (setq a (math-trunc a) | |
434 | n (if n (math-trunc n) 1)) | |
435 | (if (eq (car-safe a) 'mod) | |
436 | (math-binary-modulo-args 'calcFunc-lsh a n w) | |
437 | (setq w (if w (math-trunc w) calc-word-size)) | |
438 | (or (integerp w) | |
439 | (math-reject-arg w 'fixnump)) | |
440 | (or (Math-integerp a) | |
441 | (math-reject-arg a 'integerp)) | |
442 | (or (Math-integerp n) | |
443 | (math-reject-arg n 'integerp)) | |
444 | (if (< w 0) | |
445 | (math-clip (calcFunc-lsh a n (- w)) w) | |
446 | (if (Math-integer-negp a) | |
447 | (setq a (math-clip a w))) | |
448 | (cond ((or (Math-lessp n (- w)) | |
449 | (Math-lessp w n)) | |
450 | 0) | |
451 | ((< n 0) | |
452 | (math-quotient (math-clip a w) (math-power-of-2 (- n)))) | |
453 | (t | |
7d70a3ba | 454 | (math-clip (math-mul a (math-power-of-2 n)) w)))))) |
136211a9 EZ |
455 | |
456 | (defun calcFunc-rsh (a &optional n w) ; [I I] [Public] | |
7d70a3ba | 457 | (calcFunc-lsh a (math-neg (or n 1)) w)) |
136211a9 EZ |
458 | |
459 | (defun calcFunc-ash (a &optional n w) ; [I I] [Public] | |
460 | (if (or (null n) | |
461 | (not (Math-negp n))) | |
462 | (calcFunc-lsh a n w) | |
463 | (setq a (math-trunc a) | |
464 | n (if n (math-trunc n) 1)) | |
465 | (if (eq (car-safe a) 'mod) | |
466 | (math-binary-modulo-args 'calcFunc-ash a n w) | |
467 | (setq w (if w (math-trunc w) calc-word-size)) | |
468 | (or (integerp w) | |
469 | (math-reject-arg w 'fixnump)) | |
470 | (or (Math-integerp a) | |
471 | (math-reject-arg a 'integerp)) | |
472 | (or (Math-integerp n) | |
473 | (math-reject-arg n 'integerp)) | |
474 | (if (< w 0) | |
475 | (math-clip (calcFunc-ash a n (- w)) w) | |
476 | (if (Math-integer-negp a) | |
477 | (setq a (math-clip a w))) | |
478 | (let ((two-to-sizem1 (math-power-of-2 (1- w))) | |
479 | (sh (calcFunc-lsh a n w))) | |
480 | (cond ((Math-natnum-lessp a two-to-sizem1) | |
481 | sh) | |
482 | ((Math-lessp n (- 1 w)) | |
483 | (math-add (math-mul two-to-sizem1 2) -1)) | |
484 | (t (let ((two-to-n (math-power-of-2 (- n)))) | |
485 | (math-add (calcFunc-lsh (math-add two-to-n -1) | |
486 | (+ w n) w) | |
7d70a3ba | 487 | sh))))))))) |
136211a9 EZ |
488 | |
489 | (defun calcFunc-rash (a &optional n w) ; [I I] [Public] | |
7d70a3ba | 490 | (calcFunc-ash a (math-neg (or n 1)) w)) |
136211a9 EZ |
491 | |
492 | (defun calcFunc-rot (a &optional n w) ; [I I] [Public] | |
493 | (setq a (math-trunc a) | |
494 | n (if n (math-trunc n) 1)) | |
495 | (if (eq (car-safe a) 'mod) | |
496 | (math-binary-modulo-args 'calcFunc-rot a n w) | |
497 | (setq w (if w (math-trunc w) calc-word-size)) | |
498 | (or (integerp w) | |
499 | (math-reject-arg w 'fixnump)) | |
500 | (or (Math-integerp a) | |
501 | (math-reject-arg a 'integerp)) | |
502 | (or (Math-integerp n) | |
503 | (math-reject-arg n 'integerp)) | |
504 | (if (< w 0) | |
505 | (math-clip (calcFunc-rot a n (- w)) w) | |
506 | (if (Math-integer-negp a) | |
507 | (setq a (math-clip a w))) | |
508 | (cond ((or (Math-integer-negp n) | |
509 | (not (Math-natnum-lessp n w))) | |
510 | (calcFunc-rot a (math-mod n w) w)) | |
511 | (t | |
512 | (math-add (calcFunc-lsh a (- n w) w) | |
7d70a3ba | 513 | (calcFunc-lsh a n w))))))) |
136211a9 EZ |
514 | |
515 | (defun math-clip (a &optional w) ; [I I] [Public] | |
516 | (cond ((Math-messy-integerp w) | |
517 | (math-clip a (math-trunc w))) | |
518 | ((eq (car-safe a) 'mod) | |
519 | (math-binary-modulo-args 'math-clip a nil w)) | |
520 | ((and w (not (integerp w))) | |
521 | (math-reject-arg w 'fixnump)) | |
522 | ((not (Math-num-integerp a)) | |
523 | (math-reject-arg a 'integerp)) | |
524 | ((< (or w (setq w calc-word-size)) 0) | |
525 | (setq a (math-clip a (- w))) | |
526 | (if (Math-natnum-lessp a (math-power-of-2 (- -1 w))) | |
527 | a | |
528 | (math-sub a (math-power-of-2 (- w))))) | |
529 | ((Math-negp a) | |
530 | (math-normalize (cons 'bigpos (math-binary-arg a w)))) | |
3fa5c462 JB |
531 | ((and (integerp a) (< a math-small-integer-size)) |
532 | (if (> w (logb math-small-integer-size)) | |
136211a9 EZ |
533 | a |
534 | (logand a (1- (lsh 1 w))))) | |
535 | (t | |
536 | (math-normalize | |
537 | (cons 'bigpos | |
538 | (math-clip-bignum (cdr (math-bignum-test (math-trunc a))) | |
7d70a3ba CW |
539 | w)))))) |
540 | ||
541 | (defalias 'calcFunc-clip 'math-clip) | |
136211a9 EZ |
542 | |
543 | (defun math-clip-bignum (a w) ; [l l] | |
3fa5c462 JB |
544 | (let ((q (math-div-bignum-digit a math-bignum-digit-power-of-two))) |
545 | (if (<= w math-bignum-logb-digit-size) | |
136211a9 EZ |
546 | (list (logand (cdr q) |
547 | (1- (lsh 1 w)))) | |
548 | (math-mul-bignum-digit (math-clip-bignum (math-norm-bignum (car q)) | |
3fa5c462 JB |
549 | (- w math-bignum-logb-digit-size)) |
550 | math-bignum-digit-power-of-two | |
7d70a3ba | 551 | (cdr q))))) |
136211a9 EZ |
552 | |
553 | (defvar math-max-digits-cache nil) | |
554 | (defun math-compute-max-digits (w r) | |
555 | (let* ((pair (+ (* r 100000) w)) | |
556 | (res (assq pair math-max-digits-cache))) | |
557 | (if res | |
558 | (cdr res) | |
559 | (let* ((calc-command-flags nil) | |
560 | (digs (math-ceiling (math-div w (math-real-log2 r))))) | |
561 | (setq math-max-digits-cache (cons (cons pair digs) | |
562 | math-max-digits-cache)) | |
7d70a3ba | 563 | digs)))) |
136211a9 EZ |
564 | |
565 | (defvar math-log2-cache (list '(2 . 1) | |
566 | '(4 . 2) | |
567 | '(8 . 3) | |
568 | '(10 . (float 332193 -5)) | |
569 | '(16 . 4) | |
570 | '(32 . 5))) | |
571 | (defun math-real-log2 (x) ;;; calc-internal-prec must be 6 | |
572 | (let ((res (assq x math-log2-cache))) | |
573 | (if res | |
574 | (cdr res) | |
575 | (let* ((calc-symbolic-mode nil) | |
576 | (calc-display-working-message nil) | |
577 | (log (calcFunc-log x 2))) | |
578 | (setq math-log2-cache (cons (cons x log) math-log2-cache)) | |
7d70a3ba | 579 | log)))) |
136211a9 EZ |
580 | |
581 | (defconst math-radix-digits ["0" "1" "2" "3" "4" "5" "6" "7" "8" "9" | |
582 | "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" | |
583 | "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T" | |
584 | "U" "V" "W" "X" "Y" "Z"]) | |
585 | ||
3132f345 CW |
586 | (defsubst math-format-radix-digit (a) ; [X D] |
587 | (aref math-radix-digits a)) | |
588 | ||
136211a9 EZ |
589 | (defun math-format-radix (a) ; [X S] |
590 | (if (< a calc-number-radix) | |
591 | (if (< a 0) | |
592 | (concat "-" (math-format-radix (- a))) | |
593 | (math-format-radix-digit a)) | |
594 | (let ((s "")) | |
595 | (while (> a 0) | |
596 | (setq s (concat (math-format-radix-digit (% a calc-number-radix)) s) | |
597 | a (/ a calc-number-radix))) | |
7d70a3ba | 598 | s))) |
136211a9 EZ |
599 | |
600 | (defconst math-binary-digits ["000" "001" "010" "011" | |
601 | "100" "101" "110" "111"]) | |
602 | (defun math-format-binary (a) ; [X S] | |
603 | (if (< a 8) | |
604 | (if (< a 0) | |
605 | (concat "-" (math-format-binary (- a))) | |
606 | (math-format-radix a)) | |
607 | (let ((s "")) | |
608 | (while (> a 7) | |
609 | (setq s (concat (aref math-binary-digits (% a 8)) s) | |
610 | a (/ a 8))) | |
7d70a3ba | 611 | (concat (math-format-radix a) s)))) |
136211a9 EZ |
612 | |
613 | (defun math-format-bignum-radix (a) ; [X L] | |
614 | (cond ((null a) "0") | |
615 | ((and (null (cdr a)) | |
616 | (< (car a) calc-number-radix)) | |
617 | (math-format-radix-digit (car a))) | |
618 | (t | |
619 | (let ((q (math-div-bignum-digit a calc-number-radix))) | |
620 | (concat (math-format-bignum-radix (math-norm-bignum (car q))) | |
7d70a3ba | 621 | (math-format-radix-digit (cdr q))))))) |
136211a9 EZ |
622 | |
623 | (defun math-format-bignum-binary (a) ; [X L] | |
624 | (cond ((null a) "0") | |
625 | ((null (cdr a)) | |
626 | (math-format-binary (car a))) | |
627 | (t | |
628 | (let ((q (math-div-bignum-digit a 512))) | |
629 | (concat (math-format-bignum-binary (math-norm-bignum (car q))) | |
630 | (aref math-binary-digits (/ (cdr q) 64)) | |
631 | (aref math-binary-digits (% (/ (cdr q) 8) 8)) | |
7d70a3ba | 632 | (aref math-binary-digits (% (cdr q) 8))))))) |
136211a9 EZ |
633 | |
634 | (defun math-format-bignum-octal (a) ; [X L] | |
635 | (cond ((null a) "0") | |
636 | ((null (cdr a)) | |
637 | (math-format-radix (car a))) | |
638 | (t | |
639 | (let ((q (math-div-bignum-digit a 512))) | |
640 | (concat (math-format-bignum-octal (math-norm-bignum (car q))) | |
641 | (math-format-radix-digit (/ (cdr q) 64)) | |
642 | (math-format-radix-digit (% (/ (cdr q) 8) 8)) | |
7d70a3ba | 643 | (math-format-radix-digit (% (cdr q) 8))))))) |
136211a9 EZ |
644 | |
645 | (defun math-format-bignum-hex (a) ; [X L] | |
646 | (cond ((null a) "0") | |
647 | ((null (cdr a)) | |
648 | (math-format-radix (car a))) | |
649 | (t | |
650 | (let ((q (math-div-bignum-digit a 256))) | |
651 | (concat (math-format-bignum-hex (math-norm-bignum (car q))) | |
652 | (math-format-radix-digit (/ (cdr q) 16)) | |
7d70a3ba | 653 | (math-format-radix-digit (% (cdr q) 16))))))) |
136211a9 EZ |
654 | |
655 | ;;; Decompose into integer and fractional parts, without depending | |
656 | ;;; on calc-internal-prec. | |
657 | (defun math-float-parts (a need-frac) ; returns ( int frac fracdigs ) | |
658 | (if (>= (nth 2 a) 0) | |
659 | (list (math-scale-rounding (nth 1 a) (nth 2 a)) '(float 0 0) 0) | |
660 | (let* ((d (math-numdigs (nth 1 a))) | |
661 | (n (- (nth 2 a)))) | |
662 | (if need-frac | |
663 | (if (>= n d) | |
664 | (list 0 a n) | |
665 | (let ((qr (math-idivmod (nth 1 a) (math-scale-int 1 n)))) | |
666 | (list (car qr) (math-make-float (cdr qr) (- n)) n))) | |
667 | (list (math-scale-rounding (nth 1 a) (nth 2 a)) | |
7d70a3ba | 668 | '(float 0 0) 0))))) |
136211a9 EZ |
669 | |
670 | (defun math-format-radix-float (a prec) | |
671 | (let ((fmt (car calc-float-format)) | |
672 | (figs (nth 1 calc-float-format)) | |
673 | (point calc-point-char) | |
1bf345d1 JB |
674 | (str nil) |
675 | pos) | |
136211a9 EZ |
676 | (if (eq fmt 'fix) |
677 | (let* ((afigs (math-abs figs)) | |
678 | (fp (math-float-parts a (> afigs 0))) | |
679 | (calc-internal-prec (+ 3 (max (nth 2 fp) | |
680 | (math-convert-radix-digits | |
681 | afigs t)))) | |
682 | (int (car fp)) | |
683 | (frac (math-round (math-mul (math-normalize (nth 1 fp)) | |
684 | (math-radix-float-power afigs))))) | |
685 | (if (not (and (math-zerop frac) (math-zerop int) (< figs 0))) | |
686 | (let ((math-radix-explicit-format nil)) | |
687 | (let ((calc-group-digits nil)) | |
688 | (setq str (if (> afigs 0) (math-format-number frac) "")) | |
689 | (if (< (length str) afigs) | |
690 | (setq str (concat (make-string (- afigs (length str)) ?0) | |
691 | str)) | |
692 | (if (> (length str) afigs) | |
693 | (setq str (substring str 1) | |
694 | int (math-add int 1)))) | |
695 | (setq str (concat (math-format-number int) point str))) | |
23cbf556 | 696 | (when calc-group-digits |
23cbf556 | 697 | (setq str (math-group-float str)))) |
136211a9 EZ |
698 | (setq figs 0)))) |
699 | (or str | |
700 | (let* ((prec calc-internal-prec) | |
701 | (afigs (if (> figs 0) | |
702 | figs | |
703 | (max 1 (+ figs | |
704 | (1- (math-convert-radix-digits | |
705 | (max prec | |
706 | (math-numdigs (nth 1 a))))))))) | |
707 | (calc-internal-prec (+ 3 (math-convert-radix-digits afigs t))) | |
708 | (explo -1) (vlo (math-radix-float-power explo)) | |
709 | (exphi 1) (vhi (math-radix-float-power exphi)) | |
710 | expmid vmid eadj) | |
711 | (setq a (math-normalize a)) | |
712 | (if (Math-zerop a) | |
713 | (setq explo 0) | |
714 | (if (math-lessp-float '(float 1 0) a) | |
715 | (while (not (math-lessp-float a vhi)) | |
716 | (setq explo exphi vlo vhi | |
717 | exphi (math-mul exphi 2) | |
718 | vhi (math-radix-float-power exphi))) | |
719 | (while (math-lessp-float a vlo) | |
720 | (setq exphi explo vhi vlo | |
721 | explo (math-mul explo 2) | |
722 | vlo (math-radix-float-power explo)))) | |
723 | (while (not (eq (math-sub exphi explo) 1)) | |
724 | (setq expmid (math-div2 (math-add explo exphi)) | |
725 | vmid (math-radix-float-power expmid)) | |
726 | (if (math-lessp-float a vmid) | |
727 | (setq exphi expmid vhi vmid) | |
728 | (setq explo expmid vlo vmid))) | |
729 | (setq a (math-div-float a vlo))) | |
730 | (let* ((sc (math-round (math-mul a (math-radix-float-power | |
731 | (1- afigs))))) | |
732 | (math-radix-explicit-format nil)) | |
733 | (let ((calc-group-digits nil)) | |
734 | (setq str (math-format-number sc)))) | |
735 | (if (> (length str) afigs) | |
736 | (setq str (substring str 0 -1) | |
737 | explo (1+ explo))) | |
738 | (if (and (eq fmt 'float) | |
739 | (math-lessp explo (+ (if (= figs 0) | |
740 | (1- (math-convert-radix-digits | |
741 | prec)) | |
742 | afigs) | |
743 | calc-display-sci-high 1)) | |
744 | (math-lessp calc-display-sci-low explo)) | |
745 | (let ((dpos (1+ explo))) | |
746 | (cond ((<= dpos 0) | |
747 | (setq str (concat "0" point (make-string (- dpos) ?0) | |
748 | str))) | |
749 | ((> dpos (length str)) | |
750 | (setq str (concat str (make-string (- dpos (length str)) | |
751 | ?0) point))) | |
752 | (t | |
753 | (setq str (concat (substring str 0 dpos) point | |
754 | (substring str dpos))))) | |
755 | (setq explo nil)) | |
756 | (setq eadj (if (eq fmt 'eng) | |
757 | (min (math-mod explo 3) (length str)) | |
758 | 0) | |
759 | str (concat (substring str 0 (1+ eadj)) point | |
760 | (substring str (1+ eadj))))) | |
761 | (setq pos (length str)) | |
762 | (while (eq (aref str (1- pos)) ?0) (setq pos (1- pos))) | |
763 | (and explo (eq (aref str (1- pos)) ?.) (setq pos (1- pos))) | |
764 | (setq str (substring str 0 pos)) | |
23cbf556 CW |
765 | (when calc-group-digits |
766 | (setq str (math-group-float str))) | |
136211a9 EZ |
767 | (if explo |
768 | (let ((estr (let ((calc-number-radix 10) | |
769 | (calc-group-digits nil)) | |
1bf345d1 JB |
770 | (math-format-number |
771 | (math-sub explo eadj))))) | |
136211a9 EZ |
772 | (setq str (if (or (memq calc-language '(math maple)) |
773 | (> calc-number-radix 14)) | |
774 | (format "%s*%d.^%s" str calc-number-radix estr) | |
775 | (format "%se%s" str estr))))))) | |
7d70a3ba | 776 | str)) |
136211a9 | 777 | |
3132f345 CW |
778 | (defvar math-radix-digits-cache nil) |
779 | ||
136211a9 EZ |
780 | (defun math-convert-radix-digits (n &optional to-dec) |
781 | (let ((key (cons n (cons to-dec calc-number-radix)))) | |
782 | (or (cdr (assoc key math-radix-digits-cache)) | |
783 | (let* ((calc-internal-prec 6) | |
784 | (log (math-div (math-real-log2 calc-number-radix) | |
785 | '(float 332193 -5)))) | |
786 | (cdr (car (setq math-radix-digits-cache | |
787 | (cons (cons key (math-ceiling (if to-dec | |
788 | (math-mul n log) | |
789 | (math-div n log)))) | |
7d70a3ba CW |
790 | math-radix-digits-cache)))))))) |
791 | ||
3132f345 | 792 | (defvar math-radix-float-cache-tag nil) |
1bf345d1 | 793 | (defvar math-radix-float-cache) |
136211a9 EZ |
794 | |
795 | (defun math-radix-float-power (n) | |
796 | (if (eq n 0) | |
797 | '(float 1 0) | |
798 | (or (and (eq calc-number-radix (car math-radix-float-cache-tag)) | |
799 | (<= calc-internal-prec (cdr math-radix-float-cache-tag))) | |
800 | (setq math-radix-float-cache-tag (cons calc-number-radix | |
801 | calc-internal-prec) | |
802 | math-radix-float-cache nil)) | |
803 | (math-normalize | |
804 | (or (cdr (assoc n math-radix-float-cache)) | |
805 | (cdr (car (setq math-radix-float-cache | |
806 | (cons (cons | |
807 | n | |
808 | (let ((calc-internal-prec | |
809 | (cdr math-radix-float-cache-tag))) | |
810 | (if (math-negp n) | |
811 | (math-div-float '(float 1 0) | |
812 | (math-radix-float-power | |
813 | (math-neg n))) | |
814 | (math-mul-float (math-sqr-float | |
815 | (math-radix-float-power | |
816 | (math-div2 n))) | |
817 | (if (math-evenp n) | |
818 | '(float 1 0) | |
819 | (math-float | |
820 | calc-number-radix)))))) | |
7d70a3ba CW |
821 | math-radix-float-cache)))))))) |
822 | ||
50a982d6 | 823 | ;;; Two's complement mode |
b1d9611c | 824 | |
50a982d6 | 825 | (defun math-format-twos-complement (a) |
d772f28b | 826 | "Format an integer in two's complement mode." |
b1d9611c JB |
827 | (let* (;(calc-leading-zeros t) |
828 | (overflow nil) | |
829 | (negative nil) | |
830 | (num | |
831 | (cond | |
832 | ((or (eq a 0) | |
833 | (and (Math-integer-posp a))) | |
834 | (if (integerp a) | |
835 | (math-format-radix a) | |
836 | (math-format-bignum-radix (cdr a)))) | |
837 | ((Math-integer-negp a) | |
838 | (let ((newa (math-add a math-2-word-size))) | |
839 | (if (integerp newa) | |
840 | (math-format-radix newa) | |
841 | (math-format-bignum-radix (cdr newa)))))))) | |
842 | (let* ((calc-internal-prec 6) | |
843 | (digs (math-compute-max-digits (math-abs calc-word-size) | |
844 | calc-number-radix)) | |
845 | (len (length num))) | |
846 | (if (< len digs) | |
847 | (setq num (concat (make-string (- digs len) ?0) num)))) | |
848 | (concat | |
849 | (number-to-string calc-number-radix) | |
850 | "##" | |
851 | num))) | |
852 | ||
fb9ec5ef | 853 | (provide 'calc-bin) |
136211a9 | 854 | |
cbee283d | 855 | ;; arch-tag: f6dba7bc-53b2-41ae-919c-c266ab0ca8b3 |
7d70a3ba | 856 | ;;; calc-bin.el ends here |