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3132f345 CW |
1 | ;;; calc-bin.el --- binary functions for Calc |
2 | ||
7d70a3ba | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
a1506d29 | 6 | ;; Maintainers: D. Goel <deego@gnufans.org> |
6e1c888a | 7 | ;; Colin Walters <walters@debian.org> |
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8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
11 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
12 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
13 | ;; accepts responsibility to anyone for the consequences of using it | |
14 | ;; or for whether it serves any particular purpose or works at all, | |
15 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
16 | ;; License for full details. | |
17 | ||
18 | ;; Everyone is granted permission to copy, modify and redistribute | |
19 | ;; GNU Emacs, but only under the conditions described in the | |
20 | ;; GNU Emacs General Public License. A copy of this license is | |
21 | ;; supposed to have been given to you along with GNU Emacs so you | |
22 | ;; can know your rights and responsibilities. It should be in a | |
23 | ;; file named COPYING. Among other things, the copyright notice | |
24 | ;; and this notice must be preserved on all copies. | |
25 | ||
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
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29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
31 | (require 'calc-ext) | |
32 | ||
33 | (require 'calc-macs) | |
34 | ||
35 | (defun calc-Need-calc-bin () nil) | |
36 | ||
37 | ||
38 | ;;; b-prefix binary commands. | |
39 | ||
40 | (defun calc-and (n) | |
41 | (interactive "P") | |
42 | (calc-slow-wrapper | |
43 | (calc-enter-result 2 "and" | |
44 | (append '(calcFunc-and) | |
45 | (calc-top-list-n 2) | |
7d70a3ba | 46 | (and n (list (prefix-numeric-value n))))))) |
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47 | |
48 | (defun calc-or (n) | |
49 | (interactive "P") | |
50 | (calc-slow-wrapper | |
51 | (calc-enter-result 2 "or" | |
52 | (append '(calcFunc-or) | |
53 | (calc-top-list-n 2) | |
7d70a3ba | 54 | (and n (list (prefix-numeric-value n))))))) |
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55 | |
56 | (defun calc-xor (n) | |
57 | (interactive "P") | |
58 | (calc-slow-wrapper | |
59 | (calc-enter-result 2 "xor" | |
60 | (append '(calcFunc-xor) | |
61 | (calc-top-list-n 2) | |
7d70a3ba | 62 | (and n (list (prefix-numeric-value n))))))) |
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63 | |
64 | (defun calc-diff (n) | |
65 | (interactive "P") | |
66 | (calc-slow-wrapper | |
67 | (calc-enter-result 2 "diff" | |
68 | (append '(calcFunc-diff) | |
69 | (calc-top-list-n 2) | |
7d70a3ba | 70 | (and n (list (prefix-numeric-value n))))))) |
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71 | |
72 | (defun calc-not (n) | |
73 | (interactive "P") | |
74 | (calc-slow-wrapper | |
75 | (calc-enter-result 1 "not" | |
76 | (append '(calcFunc-not) | |
77 | (calc-top-list-n 1) | |
7d70a3ba | 78 | (and n (list (prefix-numeric-value n))))))) |
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79 | |
80 | (defun calc-lshift-binary (n) | |
81 | (interactive "P") | |
82 | (calc-slow-wrapper | |
83 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
84 | (calc-enter-result hyp "lsh" | |
85 | (append '(calcFunc-lsh) | |
86 | (calc-top-list-n hyp) | |
7d70a3ba | 87 | (and n (list (prefix-numeric-value n)))))))) |
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88 | |
89 | (defun calc-rshift-binary (n) | |
90 | (interactive "P") | |
91 | (calc-slow-wrapper | |
92 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
93 | (calc-enter-result hyp "rsh" | |
94 | (append '(calcFunc-rsh) | |
95 | (calc-top-list-n hyp) | |
7d70a3ba | 96 | (and n (list (prefix-numeric-value n)))))))) |
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97 | |
98 | (defun calc-lshift-arith (n) | |
99 | (interactive "P") | |
100 | (calc-slow-wrapper | |
101 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
102 | (calc-enter-result hyp "ash" | |
103 | (append '(calcFunc-ash) | |
104 | (calc-top-list-n hyp) | |
7d70a3ba | 105 | (and n (list (prefix-numeric-value n)))))))) |
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106 | |
107 | (defun calc-rshift-arith (n) | |
108 | (interactive "P") | |
109 | (calc-slow-wrapper | |
110 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
111 | (calc-enter-result hyp "rash" | |
112 | (append '(calcFunc-rash) | |
113 | (calc-top-list-n hyp) | |
7d70a3ba | 114 | (and n (list (prefix-numeric-value n)))))))) |
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115 | |
116 | (defun calc-rotate-binary (n) | |
117 | (interactive "P") | |
118 | (calc-slow-wrapper | |
119 | (let ((hyp (if (calc-is-hyperbolic) 2 1))) | |
120 | (calc-enter-result hyp "rot" | |
121 | (append '(calcFunc-rot) | |
122 | (calc-top-list-n hyp) | |
7d70a3ba | 123 | (and n (list (prefix-numeric-value n)))))))) |
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124 | |
125 | (defun calc-clip (n) | |
126 | (interactive "P") | |
127 | (calc-slow-wrapper | |
128 | (calc-enter-result 1 "clip" | |
129 | (append '(calcFunc-clip) | |
130 | (calc-top-list-n 1) | |
7d70a3ba | 131 | (and n (list (prefix-numeric-value n))))))) |
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132 | |
133 | (defun calc-word-size (n) | |
134 | (interactive "P") | |
135 | (calc-wrapper | |
136 | (or n (setq n (read-string (format "Binary word size: (default %d) " | |
137 | calc-word-size)))) | |
138 | (setq n (if (stringp n) | |
139 | (if (equal n "") | |
140 | calc-word-size | |
141 | (if (string-match "\\`[-+]?[0-9]+\\'" n) | |
142 | (string-to-int n) | |
143 | (error "Expected an integer"))) | |
144 | (prefix-numeric-value n))) | |
145 | (or (= n calc-word-size) | |
146 | (if (> (math-abs n) 100) | |
147 | (calc-change-mode 'calc-word-size n calc-leading-zeros) | |
148 | (calc-change-mode '(calc-word-size calc-previous-modulo) | |
149 | (list n (math-power-of-2 (math-abs n))) | |
150 | calc-leading-zeros))) | |
151 | (if (< n 0) | |
3132f345 CW |
152 | (message "Binary word size is %d bits (2's complement)" (- n)) |
153 | (message "Binary word size is %d bits" n)))) | |
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154 | |
155 | ||
156 | ||
157 | ||
158 | ||
159 | ;;; d-prefix mode commands. | |
160 | ||
161 | (defun calc-radix (n) | |
162 | (interactive "NDisplay radix (2-36): ") | |
163 | (calc-wrapper | |
164 | (if (and (>= n 2) (<= n 36)) | |
165 | (progn | |
166 | (calc-change-mode 'calc-number-radix n t) | |
167 | ;; also change global value so minibuffer sees it | |
168 | (setq-default calc-number-radix calc-number-radix)) | |
169 | (setq n calc-number-radix)) | |
3132f345 | 170 | (message "Number radix is %d" n))) |
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171 | |
172 | (defun calc-decimal-radix () | |
173 | (interactive) | |
7d70a3ba | 174 | (calc-radix 10)) |
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175 | |
176 | (defun calc-binary-radix () | |
177 | (interactive) | |
7d70a3ba | 178 | (calc-radix 2)) |
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179 | |
180 | (defun calc-octal-radix () | |
181 | (interactive) | |
7d70a3ba | 182 | (calc-radix 8)) |
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183 | |
184 | (defun calc-hex-radix () | |
185 | (interactive) | |
7d70a3ba | 186 | (calc-radix 16)) |
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187 | |
188 | (defun calc-leading-zeros (n) | |
189 | (interactive "P") | |
190 | (calc-wrapper | |
191 | (if (calc-change-mode 'calc-leading-zeros n t t) | |
3132f345 | 192 | (message "Zero-padding integers to %d digits (assuming radix %d)" |
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193 | (let* ((calc-internal-prec 6)) |
194 | (math-compute-max-digits (math-abs calc-word-size) | |
195 | calc-number-radix)) | |
196 | calc-number-radix) | |
3132f345 | 197 | (message "Omitting leading zeros on integers")))) |
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198 | |
199 | ||
200 | (defvar math-power-of-2-cache (list 1 2 4 8 16 32 64 128 256 512 1024)) | |
201 | (defvar math-big-power-of-2-cache nil) | |
202 | (defun math-power-of-2 (n) ; [I I] [Public] | |
203 | (if (and (natnump n) (<= n 100)) | |
204 | (or (nth n math-power-of-2-cache) | |
205 | (let* ((i (length math-power-of-2-cache)) | |
206 | (val (nth (1- i) math-power-of-2-cache))) | |
207 | (while (<= i n) | |
208 | (setq val (math-mul val 2) | |
209 | math-power-of-2-cache (nconc math-power-of-2-cache | |
210 | (list val)) | |
211 | i (1+ i))) | |
212 | val)) | |
213 | (let ((found (assq n math-big-power-of-2-cache))) | |
214 | (if found | |
215 | (cdr found) | |
216 | (let ((po2 (math-ipow 2 n))) | |
217 | (setq math-big-power-of-2-cache | |
218 | (cons (cons n po2) math-big-power-of-2-cache)) | |
7d70a3ba | 219 | po2))))) |
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220 | |
221 | (defun math-integer-log2 (n) ; [I I] [Public] | |
222 | (let ((i 0) | |
223 | (p math-power-of-2-cache) | |
224 | val) | |
225 | (while (and p (Math-natnum-lessp (setq val (car p)) n)) | |
226 | (setq p (cdr p) | |
227 | i (1+ i))) | |
228 | (if p | |
229 | (and (equal val n) | |
230 | i) | |
231 | (while (Math-natnum-lessp | |
232 | (prog1 | |
233 | (setq val (math-mul val 2)) | |
234 | (setq math-power-of-2-cache (nconc math-power-of-2-cache | |
235 | (list val)))) | |
236 | n) | |
237 | (setq i (1+ i))) | |
238 | (and (equal val n) | |
7d70a3ba | 239 | i)))) |
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240 | |
241 | ||
242 | ||
243 | ||
244 | ;;; Bitwise operations. | |
245 | ||
246 | (defun calcFunc-and (a b &optional w) ; [I I I] [Public] | |
247 | (cond ((Math-messy-integerp w) | |
248 | (calcFunc-and a b (math-trunc w))) | |
249 | ((and w (not (integerp w))) | |
250 | (math-reject-arg w 'fixnump)) | |
251 | ((and (integerp a) (integerp b)) | |
252 | (math-clip (logand a b) w)) | |
253 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
254 | (math-binary-modulo-args 'calcFunc-and a b w)) | |
255 | ((not (Math-num-integerp a)) | |
256 | (math-reject-arg a 'integerp)) | |
257 | ((not (Math-num-integerp b)) | |
258 | (math-reject-arg b 'integerp)) | |
259 | (t (math-clip (cons 'bigpos | |
260 | (math-and-bignum (math-binary-arg a w) | |
261 | (math-binary-arg b w))) | |
7d70a3ba | 262 | w)))) |
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263 | |
264 | (defun math-binary-arg (a w) | |
265 | (if (not (Math-integerp a)) | |
266 | (setq a (math-trunc a))) | |
267 | (if (Math-integer-negp a) | |
268 | (math-not-bignum (cdr (math-bignum-test (math-sub -1 a))) | |
269 | (math-abs (if w (math-trunc w) calc-word-size))) | |
7d70a3ba | 270 | (cdr (Math-bignum-test a)))) |
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271 | |
272 | (defun math-binary-modulo-args (f a b w) | |
273 | (let (mod) | |
274 | (if (eq (car-safe a) 'mod) | |
275 | (progn | |
276 | (setq mod (nth 2 a) | |
277 | a (nth 1 a)) | |
278 | (if (eq (car-safe b) 'mod) | |
279 | (if (equal mod (nth 2 b)) | |
280 | (setq b (nth 1 b)) | |
281 | (math-reject-arg b "*Inconsistent modulos")))) | |
282 | (setq mod (nth 2 b) | |
283 | b (nth 1 b))) | |
284 | (if (Math-messy-integerp mod) | |
285 | (setq mod (math-trunc mod)) | |
286 | (or (Math-integerp mod) | |
287 | (math-reject-arg mod 'integerp))) | |
288 | (let ((bits (math-integer-log2 mod))) | |
289 | (if bits | |
290 | (if w | |
291 | (if (/= w bits) | |
292 | (calc-record-why | |
293 | "*Warning: Modulo inconsistent with word size")) | |
294 | (setq w bits)) | |
295 | (calc-record-why "*Warning: Modulo is not a power of 2")) | |
296 | (math-make-mod (if b | |
297 | (funcall f a b w) | |
298 | (funcall f a w)) | |
7d70a3ba | 299 | mod)))) |
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300 | |
301 | (defun math-and-bignum (a b) ; [l l l] | |
302 | (and a b | |
303 | (let ((qa (math-div-bignum-digit a 512)) | |
304 | (qb (math-div-bignum-digit b 512))) | |
305 | (math-mul-bignum-digit (math-and-bignum (math-norm-bignum (car qa)) | |
306 | (math-norm-bignum (car qb))) | |
307 | 512 | |
7d70a3ba | 308 | (logand (cdr qa) (cdr qb)))))) |
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309 | |
310 | (defun calcFunc-or (a b &optional w) ; [I I I] [Public] | |
311 | (cond ((Math-messy-integerp w) | |
312 | (calcFunc-or a b (math-trunc w))) | |
313 | ((and w (not (integerp w))) | |
314 | (math-reject-arg w 'fixnump)) | |
315 | ((and (integerp a) (integerp b)) | |
316 | (math-clip (logior a b) w)) | |
317 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
318 | (math-binary-modulo-args 'calcFunc-or a b w)) | |
319 | ((not (Math-num-integerp a)) | |
320 | (math-reject-arg a 'integerp)) | |
321 | ((not (Math-num-integerp b)) | |
322 | (math-reject-arg b 'integerp)) | |
323 | (t (math-clip (cons 'bigpos | |
324 | (math-or-bignum (math-binary-arg a w) | |
325 | (math-binary-arg b w))) | |
7d70a3ba | 326 | w)))) |
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327 | |
328 | (defun math-or-bignum (a b) ; [l l l] | |
329 | (and (or a b) | |
330 | (let ((qa (math-div-bignum-digit a 512)) | |
331 | (qb (math-div-bignum-digit b 512))) | |
332 | (math-mul-bignum-digit (math-or-bignum (math-norm-bignum (car qa)) | |
333 | (math-norm-bignum (car qb))) | |
334 | 512 | |
7d70a3ba | 335 | (logior (cdr qa) (cdr qb)))))) |
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336 | |
337 | (defun calcFunc-xor (a b &optional w) ; [I I I] [Public] | |
338 | (cond ((Math-messy-integerp w) | |
339 | (calcFunc-xor a b (math-trunc w))) | |
340 | ((and w (not (integerp w))) | |
341 | (math-reject-arg w 'fixnump)) | |
342 | ((and (integerp a) (integerp b)) | |
343 | (math-clip (logxor a b) w)) | |
344 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
345 | (math-binary-modulo-args 'calcFunc-xor a b w)) | |
346 | ((not (Math-num-integerp a)) | |
347 | (math-reject-arg a 'integerp)) | |
348 | ((not (Math-num-integerp b)) | |
349 | (math-reject-arg b 'integerp)) | |
350 | (t (math-clip (cons 'bigpos | |
351 | (math-xor-bignum (math-binary-arg a w) | |
352 | (math-binary-arg b w))) | |
7d70a3ba | 353 | w)))) |
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354 | |
355 | (defun math-xor-bignum (a b) ; [l l l] | |
356 | (and (or a b) | |
357 | (let ((qa (math-div-bignum-digit a 512)) | |
358 | (qb (math-div-bignum-digit b 512))) | |
359 | (math-mul-bignum-digit (math-xor-bignum (math-norm-bignum (car qa)) | |
360 | (math-norm-bignum (car qb))) | |
361 | 512 | |
7d70a3ba | 362 | (logxor (cdr qa) (cdr qb)))))) |
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363 | |
364 | (defun calcFunc-diff (a b &optional w) ; [I I I] [Public] | |
365 | (cond ((Math-messy-integerp w) | |
366 | (calcFunc-diff a b (math-trunc w))) | |
367 | ((and w (not (integerp w))) | |
368 | (math-reject-arg w 'fixnump)) | |
369 | ((and (integerp a) (integerp b)) | |
370 | (math-clip (logand a (lognot b)) w)) | |
371 | ((or (eq (car-safe a) 'mod) (eq (car-safe b) 'mod)) | |
372 | (math-binary-modulo-args 'calcFunc-diff a b w)) | |
373 | ((not (Math-num-integerp a)) | |
374 | (math-reject-arg a 'integerp)) | |
375 | ((not (Math-num-integerp b)) | |
376 | (math-reject-arg b 'integerp)) | |
377 | (t (math-clip (cons 'bigpos | |
378 | (math-diff-bignum (math-binary-arg a w) | |
379 | (math-binary-arg b w))) | |
7d70a3ba | 380 | w)))) |
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381 | |
382 | (defun math-diff-bignum (a b) ; [l l l] | |
383 | (and a | |
384 | (let ((qa (math-div-bignum-digit a 512)) | |
385 | (qb (math-div-bignum-digit b 512))) | |
386 | (math-mul-bignum-digit (math-diff-bignum (math-norm-bignum (car qa)) | |
387 | (math-norm-bignum (car qb))) | |
388 | 512 | |
7d70a3ba | 389 | (logand (cdr qa) (lognot (cdr qb))))))) |
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390 | |
391 | (defun calcFunc-not (a &optional w) ; [I I] [Public] | |
392 | (cond ((Math-messy-integerp w) | |
393 | (calcFunc-not a (math-trunc w))) | |
394 | ((eq (car-safe a) 'mod) | |
395 | (math-binary-modulo-args 'calcFunc-not a nil w)) | |
396 | ((and w (not (integerp w))) | |
397 | (math-reject-arg w 'fixnump)) | |
398 | ((not (Math-num-integerp a)) | |
399 | (math-reject-arg a 'integerp)) | |
400 | ((< (or w (setq w calc-word-size)) 0) | |
401 | (math-clip (calcFunc-not a (- w)) w)) | |
402 | (t (math-normalize | |
403 | (cons 'bigpos | |
404 | (math-not-bignum (math-binary-arg a w) | |
7d70a3ba | 405 | w)))))) |
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406 | |
407 | (defun math-not-bignum (a w) ; [l l] | |
408 | (let ((q (math-div-bignum-digit a 512))) | |
409 | (if (<= w 9) | |
410 | (list (logand (lognot (cdr q)) | |
411 | (1- (lsh 1 w)))) | |
412 | (math-mul-bignum-digit (math-not-bignum (math-norm-bignum (car q)) | |
413 | (- w 9)) | |
414 | 512 | |
7d70a3ba | 415 | (logxor (cdr q) 511))))) |
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416 | |
417 | (defun calcFunc-lsh (a &optional n w) ; [I I] [Public] | |
418 | (setq a (math-trunc a) | |
419 | n (if n (math-trunc n) 1)) | |
420 | (if (eq (car-safe a) 'mod) | |
421 | (math-binary-modulo-args 'calcFunc-lsh a n w) | |
422 | (setq w (if w (math-trunc w) calc-word-size)) | |
423 | (or (integerp w) | |
424 | (math-reject-arg w 'fixnump)) | |
425 | (or (Math-integerp a) | |
426 | (math-reject-arg a 'integerp)) | |
427 | (or (Math-integerp n) | |
428 | (math-reject-arg n 'integerp)) | |
429 | (if (< w 0) | |
430 | (math-clip (calcFunc-lsh a n (- w)) w) | |
431 | (if (Math-integer-negp a) | |
432 | (setq a (math-clip a w))) | |
433 | (cond ((or (Math-lessp n (- w)) | |
434 | (Math-lessp w n)) | |
435 | 0) | |
436 | ((< n 0) | |
437 | (math-quotient (math-clip a w) (math-power-of-2 (- n)))) | |
438 | (t | |
7d70a3ba | 439 | (math-clip (math-mul a (math-power-of-2 n)) w)))))) |
136211a9 EZ |
440 | |
441 | (defun calcFunc-rsh (a &optional n w) ; [I I] [Public] | |
7d70a3ba | 442 | (calcFunc-lsh a (math-neg (or n 1)) w)) |
136211a9 EZ |
443 | |
444 | (defun calcFunc-ash (a &optional n w) ; [I I] [Public] | |
445 | (if (or (null n) | |
446 | (not (Math-negp n))) | |
447 | (calcFunc-lsh a n w) | |
448 | (setq a (math-trunc a) | |
449 | n (if n (math-trunc n) 1)) | |
450 | (if (eq (car-safe a) 'mod) | |
451 | (math-binary-modulo-args 'calcFunc-ash a n w) | |
452 | (setq w (if w (math-trunc w) calc-word-size)) | |
453 | (or (integerp w) | |
454 | (math-reject-arg w 'fixnump)) | |
455 | (or (Math-integerp a) | |
456 | (math-reject-arg a 'integerp)) | |
457 | (or (Math-integerp n) | |
458 | (math-reject-arg n 'integerp)) | |
459 | (if (< w 0) | |
460 | (math-clip (calcFunc-ash a n (- w)) w) | |
461 | (if (Math-integer-negp a) | |
462 | (setq a (math-clip a w))) | |
463 | (let ((two-to-sizem1 (math-power-of-2 (1- w))) | |
464 | (sh (calcFunc-lsh a n w))) | |
465 | (cond ((Math-natnum-lessp a two-to-sizem1) | |
466 | sh) | |
467 | ((Math-lessp n (- 1 w)) | |
468 | (math-add (math-mul two-to-sizem1 2) -1)) | |
469 | (t (let ((two-to-n (math-power-of-2 (- n)))) | |
470 | (math-add (calcFunc-lsh (math-add two-to-n -1) | |
471 | (+ w n) w) | |
7d70a3ba | 472 | sh))))))))) |
136211a9 EZ |
473 | |
474 | (defun calcFunc-rash (a &optional n w) ; [I I] [Public] | |
7d70a3ba | 475 | (calcFunc-ash a (math-neg (or n 1)) w)) |
136211a9 EZ |
476 | |
477 | (defun calcFunc-rot (a &optional n w) ; [I I] [Public] | |
478 | (setq a (math-trunc a) | |
479 | n (if n (math-trunc n) 1)) | |
480 | (if (eq (car-safe a) 'mod) | |
481 | (math-binary-modulo-args 'calcFunc-rot a n w) | |
482 | (setq w (if w (math-trunc w) calc-word-size)) | |
483 | (or (integerp w) | |
484 | (math-reject-arg w 'fixnump)) | |
485 | (or (Math-integerp a) | |
486 | (math-reject-arg a 'integerp)) | |
487 | (or (Math-integerp n) | |
488 | (math-reject-arg n 'integerp)) | |
489 | (if (< w 0) | |
490 | (math-clip (calcFunc-rot a n (- w)) w) | |
491 | (if (Math-integer-negp a) | |
492 | (setq a (math-clip a w))) | |
493 | (cond ((or (Math-integer-negp n) | |
494 | (not (Math-natnum-lessp n w))) | |
495 | (calcFunc-rot a (math-mod n w) w)) | |
496 | (t | |
497 | (math-add (calcFunc-lsh a (- n w) w) | |
7d70a3ba | 498 | (calcFunc-lsh a n w))))))) |
136211a9 EZ |
499 | |
500 | (defun math-clip (a &optional w) ; [I I] [Public] | |
501 | (cond ((Math-messy-integerp w) | |
502 | (math-clip a (math-trunc w))) | |
503 | ((eq (car-safe a) 'mod) | |
504 | (math-binary-modulo-args 'math-clip a nil w)) | |
505 | ((and w (not (integerp w))) | |
506 | (math-reject-arg w 'fixnump)) | |
507 | ((not (Math-num-integerp a)) | |
508 | (math-reject-arg a 'integerp)) | |
509 | ((< (or w (setq w calc-word-size)) 0) | |
510 | (setq a (math-clip a (- w))) | |
511 | (if (Math-natnum-lessp a (math-power-of-2 (- -1 w))) | |
512 | a | |
513 | (math-sub a (math-power-of-2 (- w))))) | |
514 | ((Math-negp a) | |
515 | (math-normalize (cons 'bigpos (math-binary-arg a w)))) | |
516 | ((and (integerp a) (< a 1000000)) | |
517 | (if (>= w 20) | |
518 | a | |
519 | (logand a (1- (lsh 1 w))))) | |
520 | (t | |
521 | (math-normalize | |
522 | (cons 'bigpos | |
523 | (math-clip-bignum (cdr (math-bignum-test (math-trunc a))) | |
7d70a3ba CW |
524 | w)))))) |
525 | ||
526 | (defalias 'calcFunc-clip 'math-clip) | |
136211a9 EZ |
527 | |
528 | (defun math-clip-bignum (a w) ; [l l] | |
529 | (let ((q (math-div-bignum-digit a 512))) | |
530 | (if (<= w 9) | |
531 | (list (logand (cdr q) | |
532 | (1- (lsh 1 w)))) | |
533 | (math-mul-bignum-digit (math-clip-bignum (math-norm-bignum (car q)) | |
534 | (- w 9)) | |
535 | 512 | |
7d70a3ba | 536 | (cdr q))))) |
136211a9 EZ |
537 | |
538 | (defvar math-max-digits-cache nil) | |
539 | (defun math-compute-max-digits (w r) | |
540 | (let* ((pair (+ (* r 100000) w)) | |
541 | (res (assq pair math-max-digits-cache))) | |
542 | (if res | |
543 | (cdr res) | |
544 | (let* ((calc-command-flags nil) | |
545 | (digs (math-ceiling (math-div w (math-real-log2 r))))) | |
546 | (setq math-max-digits-cache (cons (cons pair digs) | |
547 | math-max-digits-cache)) | |
7d70a3ba | 548 | digs)))) |
136211a9 EZ |
549 | |
550 | (defvar math-log2-cache (list '(2 . 1) | |
551 | '(4 . 2) | |
552 | '(8 . 3) | |
553 | '(10 . (float 332193 -5)) | |
554 | '(16 . 4) | |
555 | '(32 . 5))) | |
556 | (defun math-real-log2 (x) ;;; calc-internal-prec must be 6 | |
557 | (let ((res (assq x math-log2-cache))) | |
558 | (if res | |
559 | (cdr res) | |
560 | (let* ((calc-symbolic-mode nil) | |
561 | (calc-display-working-message nil) | |
562 | (log (calcFunc-log x 2))) | |
563 | (setq math-log2-cache (cons (cons x log) math-log2-cache)) | |
7d70a3ba | 564 | log)))) |
136211a9 EZ |
565 | |
566 | (defconst math-radix-digits ["0" "1" "2" "3" "4" "5" "6" "7" "8" "9" | |
567 | "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" | |
568 | "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T" | |
569 | "U" "V" "W" "X" "Y" "Z"]) | |
570 | ||
3132f345 CW |
571 | (defsubst math-format-radix-digit (a) ; [X D] |
572 | (aref math-radix-digits a)) | |
573 | ||
136211a9 EZ |
574 | (defun math-format-radix (a) ; [X S] |
575 | (if (< a calc-number-radix) | |
576 | (if (< a 0) | |
577 | (concat "-" (math-format-radix (- a))) | |
578 | (math-format-radix-digit a)) | |
579 | (let ((s "")) | |
580 | (while (> a 0) | |
581 | (setq s (concat (math-format-radix-digit (% a calc-number-radix)) s) | |
582 | a (/ a calc-number-radix))) | |
7d70a3ba | 583 | s))) |
136211a9 EZ |
584 | |
585 | (defconst math-binary-digits ["000" "001" "010" "011" | |
586 | "100" "101" "110" "111"]) | |
587 | (defun math-format-binary (a) ; [X S] | |
588 | (if (< a 8) | |
589 | (if (< a 0) | |
590 | (concat "-" (math-format-binary (- a))) | |
591 | (math-format-radix a)) | |
592 | (let ((s "")) | |
593 | (while (> a 7) | |
594 | (setq s (concat (aref math-binary-digits (% a 8)) s) | |
595 | a (/ a 8))) | |
7d70a3ba | 596 | (concat (math-format-radix a) s)))) |
136211a9 EZ |
597 | |
598 | (defun math-format-bignum-radix (a) ; [X L] | |
599 | (cond ((null a) "0") | |
600 | ((and (null (cdr a)) | |
601 | (< (car a) calc-number-radix)) | |
602 | (math-format-radix-digit (car a))) | |
603 | (t | |
604 | (let ((q (math-div-bignum-digit a calc-number-radix))) | |
605 | (concat (math-format-bignum-radix (math-norm-bignum (car q))) | |
7d70a3ba | 606 | (math-format-radix-digit (cdr q))))))) |
136211a9 EZ |
607 | |
608 | (defun math-format-bignum-binary (a) ; [X L] | |
609 | (cond ((null a) "0") | |
610 | ((null (cdr a)) | |
611 | (math-format-binary (car a))) | |
612 | (t | |
613 | (let ((q (math-div-bignum-digit a 512))) | |
614 | (concat (math-format-bignum-binary (math-norm-bignum (car q))) | |
615 | (aref math-binary-digits (/ (cdr q) 64)) | |
616 | (aref math-binary-digits (% (/ (cdr q) 8) 8)) | |
7d70a3ba | 617 | (aref math-binary-digits (% (cdr q) 8))))))) |
136211a9 EZ |
618 | |
619 | (defun math-format-bignum-octal (a) ; [X L] | |
620 | (cond ((null a) "0") | |
621 | ((null (cdr a)) | |
622 | (math-format-radix (car a))) | |
623 | (t | |
624 | (let ((q (math-div-bignum-digit a 512))) | |
625 | (concat (math-format-bignum-octal (math-norm-bignum (car q))) | |
626 | (math-format-radix-digit (/ (cdr q) 64)) | |
627 | (math-format-radix-digit (% (/ (cdr q) 8) 8)) | |
7d70a3ba | 628 | (math-format-radix-digit (% (cdr q) 8))))))) |
136211a9 EZ |
629 | |
630 | (defun math-format-bignum-hex (a) ; [X L] | |
631 | (cond ((null a) "0") | |
632 | ((null (cdr a)) | |
633 | (math-format-radix (car a))) | |
634 | (t | |
635 | (let ((q (math-div-bignum-digit a 256))) | |
636 | (concat (math-format-bignum-hex (math-norm-bignum (car q))) | |
637 | (math-format-radix-digit (/ (cdr q) 16)) | |
7d70a3ba | 638 | (math-format-radix-digit (% (cdr q) 16))))))) |
136211a9 EZ |
639 | |
640 | ;;; Decompose into integer and fractional parts, without depending | |
641 | ;;; on calc-internal-prec. | |
642 | (defun math-float-parts (a need-frac) ; returns ( int frac fracdigs ) | |
643 | (if (>= (nth 2 a) 0) | |
644 | (list (math-scale-rounding (nth 1 a) (nth 2 a)) '(float 0 0) 0) | |
645 | (let* ((d (math-numdigs (nth 1 a))) | |
646 | (n (- (nth 2 a)))) | |
647 | (if need-frac | |
648 | (if (>= n d) | |
649 | (list 0 a n) | |
650 | (let ((qr (math-idivmod (nth 1 a) (math-scale-int 1 n)))) | |
651 | (list (car qr) (math-make-float (cdr qr) (- n)) n))) | |
652 | (list (math-scale-rounding (nth 1 a) (nth 2 a)) | |
7d70a3ba | 653 | '(float 0 0) 0))))) |
136211a9 EZ |
654 | |
655 | (defun math-format-radix-float (a prec) | |
656 | (let ((fmt (car calc-float-format)) | |
657 | (figs (nth 1 calc-float-format)) | |
658 | (point calc-point-char) | |
659 | (str nil)) | |
660 | (if (eq fmt 'fix) | |
661 | (let* ((afigs (math-abs figs)) | |
662 | (fp (math-float-parts a (> afigs 0))) | |
663 | (calc-internal-prec (+ 3 (max (nth 2 fp) | |
664 | (math-convert-radix-digits | |
665 | afigs t)))) | |
666 | (int (car fp)) | |
667 | (frac (math-round (math-mul (math-normalize (nth 1 fp)) | |
668 | (math-radix-float-power afigs))))) | |
669 | (if (not (and (math-zerop frac) (math-zerop int) (< figs 0))) | |
670 | (let ((math-radix-explicit-format nil)) | |
671 | (let ((calc-group-digits nil)) | |
672 | (setq str (if (> afigs 0) (math-format-number frac) "")) | |
673 | (if (< (length str) afigs) | |
674 | (setq str (concat (make-string (- afigs (length str)) ?0) | |
675 | str)) | |
676 | (if (> (length str) afigs) | |
677 | (setq str (substring str 1) | |
678 | int (math-add int 1)))) | |
679 | (setq str (concat (math-format-number int) point str))) | |
23cbf556 | 680 | (when calc-group-digits |
23cbf556 | 681 | (setq str (math-group-float str)))) |
136211a9 EZ |
682 | (setq figs 0)))) |
683 | (or str | |
684 | (let* ((prec calc-internal-prec) | |
685 | (afigs (if (> figs 0) | |
686 | figs | |
687 | (max 1 (+ figs | |
688 | (1- (math-convert-radix-digits | |
689 | (max prec | |
690 | (math-numdigs (nth 1 a))))))))) | |
691 | (calc-internal-prec (+ 3 (math-convert-radix-digits afigs t))) | |
692 | (explo -1) (vlo (math-radix-float-power explo)) | |
693 | (exphi 1) (vhi (math-radix-float-power exphi)) | |
694 | expmid vmid eadj) | |
695 | (setq a (math-normalize a)) | |
696 | (if (Math-zerop a) | |
697 | (setq explo 0) | |
698 | (if (math-lessp-float '(float 1 0) a) | |
699 | (while (not (math-lessp-float a vhi)) | |
700 | (setq explo exphi vlo vhi | |
701 | exphi (math-mul exphi 2) | |
702 | vhi (math-radix-float-power exphi))) | |
703 | (while (math-lessp-float a vlo) | |
704 | (setq exphi explo vhi vlo | |
705 | explo (math-mul explo 2) | |
706 | vlo (math-radix-float-power explo)))) | |
707 | (while (not (eq (math-sub exphi explo) 1)) | |
708 | (setq expmid (math-div2 (math-add explo exphi)) | |
709 | vmid (math-radix-float-power expmid)) | |
710 | (if (math-lessp-float a vmid) | |
711 | (setq exphi expmid vhi vmid) | |
712 | (setq explo expmid vlo vmid))) | |
713 | (setq a (math-div-float a vlo))) | |
714 | (let* ((sc (math-round (math-mul a (math-radix-float-power | |
715 | (1- afigs))))) | |
716 | (math-radix-explicit-format nil)) | |
717 | (let ((calc-group-digits nil)) | |
718 | (setq str (math-format-number sc)))) | |
719 | (if (> (length str) afigs) | |
720 | (setq str (substring str 0 -1) | |
721 | explo (1+ explo))) | |
722 | (if (and (eq fmt 'float) | |
723 | (math-lessp explo (+ (if (= figs 0) | |
724 | (1- (math-convert-radix-digits | |
725 | prec)) | |
726 | afigs) | |
727 | calc-display-sci-high 1)) | |
728 | (math-lessp calc-display-sci-low explo)) | |
729 | (let ((dpos (1+ explo))) | |
730 | (cond ((<= dpos 0) | |
731 | (setq str (concat "0" point (make-string (- dpos) ?0) | |
732 | str))) | |
733 | ((> dpos (length str)) | |
734 | (setq str (concat str (make-string (- dpos (length str)) | |
735 | ?0) point))) | |
736 | (t | |
737 | (setq str (concat (substring str 0 dpos) point | |
738 | (substring str dpos))))) | |
739 | (setq explo nil)) | |
740 | (setq eadj (if (eq fmt 'eng) | |
741 | (min (math-mod explo 3) (length str)) | |
742 | 0) | |
743 | str (concat (substring str 0 (1+ eadj)) point | |
744 | (substring str (1+ eadj))))) | |
745 | (setq pos (length str)) | |
746 | (while (eq (aref str (1- pos)) ?0) (setq pos (1- pos))) | |
747 | (and explo (eq (aref str (1- pos)) ?.) (setq pos (1- pos))) | |
748 | (setq str (substring str 0 pos)) | |
23cbf556 CW |
749 | (when calc-group-digits |
750 | (setq str (math-group-float str))) | |
136211a9 EZ |
751 | (if explo |
752 | (let ((estr (let ((calc-number-radix 10) | |
753 | (calc-group-digits nil)) | |
754 | (setq estr (math-format-number | |
755 | (math-sub explo eadj)))))) | |
756 | (setq str (if (or (memq calc-language '(math maple)) | |
757 | (> calc-number-radix 14)) | |
758 | (format "%s*%d.^%s" str calc-number-radix estr) | |
759 | (format "%se%s" str estr))))))) | |
7d70a3ba | 760 | str)) |
136211a9 | 761 | |
3132f345 CW |
762 | (defvar math-radix-digits-cache nil) |
763 | ||
136211a9 EZ |
764 | (defun math-convert-radix-digits (n &optional to-dec) |
765 | (let ((key (cons n (cons to-dec calc-number-radix)))) | |
766 | (or (cdr (assoc key math-radix-digits-cache)) | |
767 | (let* ((calc-internal-prec 6) | |
768 | (log (math-div (math-real-log2 calc-number-radix) | |
769 | '(float 332193 -5)))) | |
770 | (cdr (car (setq math-radix-digits-cache | |
771 | (cons (cons key (math-ceiling (if to-dec | |
772 | (math-mul n log) | |
773 | (math-div n log)))) | |
7d70a3ba CW |
774 | math-radix-digits-cache)))))))) |
775 | ||
3132f345 | 776 | (defvar math-radix-float-cache-tag nil) |
136211a9 EZ |
777 | |
778 | (defun math-radix-float-power (n) | |
779 | (if (eq n 0) | |
780 | '(float 1 0) | |
781 | (or (and (eq calc-number-radix (car math-radix-float-cache-tag)) | |
782 | (<= calc-internal-prec (cdr math-radix-float-cache-tag))) | |
783 | (setq math-radix-float-cache-tag (cons calc-number-radix | |
784 | calc-internal-prec) | |
785 | math-radix-float-cache nil)) | |
786 | (math-normalize | |
787 | (or (cdr (assoc n math-radix-float-cache)) | |
788 | (cdr (car (setq math-radix-float-cache | |
789 | (cons (cons | |
790 | n | |
791 | (let ((calc-internal-prec | |
792 | (cdr math-radix-float-cache-tag))) | |
793 | (if (math-negp n) | |
794 | (math-div-float '(float 1 0) | |
795 | (math-radix-float-power | |
796 | (math-neg n))) | |
797 | (math-mul-float (math-sqr-float | |
798 | (math-radix-float-power | |
799 | (math-div2 n))) | |
800 | (if (math-evenp n) | |
801 | '(float 1 0) | |
802 | (math-float | |
803 | calc-number-radix)))))) | |
7d70a3ba CW |
804 | math-radix-float-cache)))))))) |
805 | ||
136211a9 | 806 | |
7d70a3ba | 807 | ;;; calc-bin.el ends here |