1 ;;; calc.el --- the GNU Emacs calculator
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <belanger@truman.edu>
7 ;; Keywords: convenience, extensions
10 ;; This file is part of GNU Emacs.
12 ;; GNU Emacs is distributed in the hope that it will be useful,
13 ;; but WITHOUT ANY WARRANTY. No author or distributor
14 ;; accepts responsibility to anyone for the consequences of using it
15 ;; or for whether it serves any particular purpose or works at all,
16 ;; unless he says so in writing. Refer to the GNU Emacs General Public
17 ;; License for full details.
19 ;; Everyone is granted permission to copy, modify and redistribute
20 ;; GNU Emacs, but only under the conditions described in the
21 ;; GNU Emacs General Public License. A copy of this license is
22 ;; supposed to have been given to you along with GNU Emacs so you
23 ;; can know your rights and responsibilities. It should be in a
24 ;; file named COPYING. Among other things, the copyright notice
25 ;; and this notice must be preserved on all copies.
29 ;; Calc is split into many files. This file is the main entry point.
30 ;; This file includes autoload commands for various other basic Calc
31 ;; facilities. The more advanced features are based in calc-ext, which
32 ;; in turn contains autoloads for the rest of the Calc files. This
33 ;; odd set of interactions is designed to make Calc's loading time
34 ;; be as short as possible when only simple calculations are needed.
36 ;; Original author's address:
37 ;; Dave Gillespie, daveg@synaptics.com, uunet!synaptx!daveg.
38 ;; Synaptics, Inc., 2698 Orchard Parkway, San Jose, CA 95134.
40 ;; The old address daveg@csvax.cs.caltech.edu will continue to
41 ;; work for the foreseeable future.
43 ;; Bug reports and suggestions are always welcome! (Type M-x
44 ;; report-calc-bug to send them).
46 ;; All functions, macros, and Lisp variables defined here begin with one
47 ;; of the prefixes "math", "Math", or "calc", with the exceptions of
48 ;; "full-calc", "full-calc-keypad", "another-calc", "quick-calc",
49 ;; "report-calc-bug", and "defmath". User-accessible variables begin
54 ;; Fix rewrite mechanism to do less gratuitous rearrangement of terms.
55 ;; Implement a pattern-based "refers" predicate.
57 ;; Make it possible to Undo a selection command.
58 ;; Figure out how to allow selecting rows of matrices.
59 ;; If cursor was in selection before, move it after j n, j p, j L, etc.
60 ;; Consider reimplementing calc-delete-selection using rewrites.
62 ;; Implement line-breaking in non-flat compositions (is this desirable?).
63 ;; Implement matrix formatting with multi-line components.
65 ;; Have "Z R" define a user command based on a set of rewrite rules.
66 ;; Support "incf" and "decf" in defmath definitions.
67 ;; Have defmath generate calls to calc-binary-op or calc-unary-op.
68 ;; Make some way to define algebraic functions using keyboard macros.
70 ;; Allow calc-word-size=0 => Common Lisp-style signed bitwise arithmetic.
71 ;; Consider digamma function (and thus arb. prec. Euler's gamma constant).
72 ;; May as well make continued-fractions stuff available to the user.
74 ;; How about matrix eigenvalues, SVD, pseudo-inverse, etc.?
75 ;; Should cache matrix inverses as well as decompositions.
76 ;; If dividing by a non-square matrix, use least-squares automatically.
77 ;; Consider supporting matrix exponentials.
79 ;; Have ninteg detect and work around singularities at the endpoints.
80 ;; Use an adaptive subdivision algorithm for ninteg.
81 ;; Provide nsum and nprod to go along with ninteg.
83 ;; Handle TeX-mode parsing of \matrix{ ... } where ... contains braces.
84 ;; Support AmS-TeX's \{d,t,}frac, \{d,t,}binom notations.
85 ;; Format and parse sums and products in Eqn and Math modes.
87 ;; Get math-read-big-expr to read sums, products, etc.
88 ;; Change calc-grab-region to use math-read-big-expr.
89 ;; Have a way to define functions using := in Embedded Mode.
91 ;; Support polar plotting with GNUPLOT.
92 ;; Make a calc-graph-histogram function.
94 ;; Replace hokey formulas for complex functions with formulas designed
95 ;; to minimize roundoff while maintaining the proper branch cuts.
96 ;; Test accuracy of advanced math functions over whole complex plane.
97 ;; Extend Bessel functions to provide arbitrary precision.
98 ;; Extend advanced math functions to handle error forms and intervals.
99 ;; Provide a better implementation for math-sin-cos-raw.
100 ;; Provide a better implementation for math-hypot.
101 ;; Provide a better implementation for math-make-frac.
102 ;; Provide a better implementation for calcFunc-prfac.
103 ;; Provide a better implementation for calcFunc-factor.
105 ;; Provide more examples in the tutorial section of the manual.
106 ;; Cover in the tutorial: simplification modes, declarations,
107 ;; bitwise stuff, selections, matrix mapping, financial functions.
108 ;; Provide more Lisp programming examples in the manual.
109 ;; Finish the Internals section of the manual (and bring it up to date).
111 ;; Tim suggests adding spreadsheet-like features.
112 ;; Implement language modes for Gnuplot, Lisp, Ada, APL, ...?
114 ;; For atan series, if x > tan(pi/12) (about 0.268) reduce using the identity
115 ;; atan(x) = atan((x * sqrt(3) - 1) / (sqrt(3) + x)) + pi/6.
117 ;; A better integration algorithm:
118 ;; Use breadth-first instead of depth-first search, as follows:
119 ;; The integral cache allows unfinished integrals in symbolic notation
120 ;; on the righthand side. An entry with no unfinished integrals on the
121 ;; RHS is "complete"; references to it elsewhere are replaced by the
122 ;; integrated value. More than one cache entry for the same integral
123 ;; may exist, though if one becomes complete, the others may be deleted.
124 ;; The integrator works by using every applicable rule (such as
125 ;; substitution, parts, linearity, etc.) to generate possible righthand
126 ;; sides, all of which are entered into the cache. Now, as long as the
127 ;; target integral is not complete (and the time limit has not run out)
128 ;; choose an incomplete integral from the cache and, for every integral
129 ;; appearing in its RHS's, add those integrals to the cache using the
130 ;; same substitition, parts, etc. rules. The cache should be organized
131 ;; as a priority queue, choosing the "simplest" incomplete integral at
132 ;; each step, or choosing randomly among equally simple integrals.
133 ;; Simplicity equals small size, and few steps removed from the original
134 ;; target integral. Note that when the integrator finishes, incomplete
135 ;; integrals can be left in the cache, so the algorithm can start where
136 ;; it left off if another similar integral is later requested.
137 ;; Breadth-first search would avoid the nagging problem of, e.g., whether
138 ;; to use parts or substitution first, and which decomposition is best.
139 ;; All are tried, and any path that diverges will quickly be put on the
140 ;; back burner by the priority queue.
141 ;; Note: Probably a good idea to call math-simplify-extended before
142 ;; measuring a formula's simplicity.
144 ;; From: "Robert J. Chassell" <bob@rattlesnake.com>
145 ;; Subject: Re: fix for `Cannot open load file: calc-alg-3'
146 ;; To: walters@debian.org
147 ;; Date: Sat, 24 Nov 2001 21:44:21 +0000 (UTC)
149 ;; Could you add logistic curve fitting to the current list?
151 ;; (I guess the key binding for a logistic curve would have to be `s'
152 ;; since a logistic curve is an `s' curve; both `l' and `L' are already
153 ;; taken for logarithms.)
155 ;; Here is the current list for curve fitting;
158 ;; Linear or multilinear. a + b x + c y + d z.
161 ;; Polynomials. a + b x + c x^2 + d x^3.
164 ;; Exponential. a exp(b x) exp(c y).
167 ;; Base-10 exponential. a 10^(b x) 10^(c y).
170 ;; Exponential (alternate notation). exp(a + b x + c y).
173 ;; Base-10 exponential (alternate). 10^(a + b x + c y).
176 ;; Logarithmic. a + b ln(x) + c ln(y).
179 ;; Base-10 logarithmic. a + b log10(x) + c log10(y).
182 ;; General exponential. a b^x c^y.
185 ;; Power law. a x^b y^c.
188 ;; Quadratic. a + b (x-c)^2 + d (x-e)^2.
191 ;; Gaussian. (a / b sqrt(2 pi)) exp(-0.5*((x-c)/b)^2).
194 ;; Logistic curves are used a great deal in ecology, and in predicting
195 ;; human actions, such as use of different kinds of energy in a country
196 ;; (wood, coal, oil, natural gas, etc.) or the number of scientific
197 ;; papers a person publishes, or the number of movies made.
199 ;; (The less information on which to base the curve, the higher the error
200 ;; rate. Theodore Modis ran some Monte Carlo simulations and produced
201 ;; what may be useful set of confidence levels for different amounts of
202 ;; initial information.)
209 (defvar calc-settings-file user-init-file
210 "*File in which to record permanent settings; default is `user-init-file'.")
212 (defvar calc-bug-address "belanger@truman.edu"
213 "Address of the author of Calc, for use by `report-calc-bug'.")
215 (defvar calc-scan-for-dels t
216 "If t, scan keymaps to find all DEL-like keys.
217 if nil, only DEL itself is mapped to calc-pop.")
219 (defvar calc-stack '((top-of-stack 1 nil))
221 Entries are 3-lists: Formula, Height (in lines), Selection (or nil).")
223 (defvar calc-stack-top 1
224 "Index into `calc-stack' of \"top\" of stack.
225 This is 1 unless `calc-truncate-stack' has been used.")
227 (defvar calc-display-sci-high 0
228 "Floating-point numbers with this positive exponent or higher above the
229 current precision are displayed in scientific notation in calc-mode.")
231 (defvar calc-display-sci-low -3
232 "Floating-point numbers with this negative exponent or lower are displayed
233 scientific notation in calc-mode.")
235 (defvar calc-other-modes nil
236 "List of used-defined strings to append to Calculator mode line.")
238 (defvar calc-Y-help-msgs nil
239 "List of strings for Y prefix help.")
241 (defvar calc-loaded-settings-file nil
242 "t if `calc-settings-file' has been loaded yet.")
244 (defvar calc-always-load-extensions)
245 (defvar calc-line-numbering)
246 (defvar calc-line-breaking)
247 (defvar calc-display-just)
248 (defvar calc-display-origin)
249 (defvar calc-number-radix)
250 (defvar calc-leading-zeros)
251 (defvar calc-group-digits)
252 (defvar calc-group-char)
253 (defvar calc-point-char)
254 (defvar calc-frac-format)
255 (defvar calc-prefer-frac)
256 (defvar calc-hms-format)
257 (defvar calc-date-format)
258 (defvar calc-float-format)
259 (defvar calc-full-float-format)
260 (defvar calc-complex-format)
261 (defvar calc-complex-mode)
262 (defvar calc-infinite-mode)
263 (defvar calc-display-strings)
264 (defvar calc-matrix-just)
265 (defvar calc-break-vectors)
266 (defvar calc-full-vectors)
267 (defvar calc-full-trail-vectors)
268 (defvar calc-vector-commas)
269 (defvar calc-vector-brackets)
270 (defvar calc-matrix-brackets)
271 (defvar calc-language)
272 (defvar calc-language-option)
273 (defvar calc-left-label)
274 (defvar calc-right-label)
275 (defvar calc-word-size)
276 (defvar calc-previous-modulo)
277 (defvar calc-simplify-mode)
278 (defvar calc-auto-recompute)
279 (defvar calc-display-raw)
280 (defvar calc-internal-prec)
281 (defvar calc-angle-mode)
282 (defvar calc-algebraic-mode)
283 (defvar calc-incomplete-algebraic-mode)
284 (defvar calc-symbolic-mode)
285 (defvar calc-matrix-mode)
286 (defvar calc-shift-prefix)
287 (defvar calc-window-height)
288 (defvar calc-display-trail)
289 (defvar calc-show-selections)
290 (defvar calc-use-selections)
291 (defvar calc-assoc-selections)
292 (defvar calc-display-working-message)
293 (defvar calc-auto-why)
295 (defvar calc-mode-save-mode)
296 (defvar calc-standard-date-formats)
297 (defvar calc-autorange-units)
298 (defvar calc-was-keypad-mode)
299 (defvar calc-full-mode)
300 (defvar calc-user-parse-tables)
301 (defvar calc-gnuplot-default-device)
302 (defvar calc-gnuplot-default-output)
303 (defvar calc-gnuplot-print-device)
304 (defvar calc-gnuplot-print-output)
305 (defvar calc-gnuplot-geometry)
306 (defvar calc-graph-default-resolution)
307 (defvar calc-graph-default-resolution-3d)
308 (defvar calc-invocation-macro)
309 (defvar calc-show-banner)
311 (defconst calc-mode-var-list '(
312 (calc-always-load-extensions nil
313 "If non-nil, load the calc-ext module automatically when calc is loaded.")
315 (calc-line-numbering t
316 "If non-nil, display line numbers in Calculator stack.")
318 (calc-line-breaking t
319 "If non-nil, break long values across multiple lines in Calculator stack.")
321 (calc-display-just nil
322 "If nil, stack display is left-justified.
323 If `right', stack display is right-justified.
324 If `center', stack display is centered.")
326 (calc-display-origin nil
327 "Horizontal origin of displayed stack entries.
328 In left-justified mode, this is effectively indentation. (Default 0).
329 In right-justified mode, this is effectively window width.
330 In centered mode, center of stack entry is placed here.")
332 (calc-number-radix 10
333 "Radix for entry and display of numbers in calc-mode, 2-36.")
335 (calc-leading-zeros nil
336 "If non-nil, leading zeros are provided to pad integers to calc-word-size.")
338 (calc-group-digits nil
339 "If non-nil, group digits in large displayed integers by inserting spaces.
340 If an integer, group that many digits at a time.
341 If t, use 4 for binary and hex, 3 otherwise.")
344 "The character (in the form of a string) to be used for grouping digits.
345 This is used only when calc-group-digits mode is on.")
348 "The character (in the form of a string) to be used as a decimal point.")
350 (calc-frac-format (":" nil)
351 "Format of displayed fractions; a string of one or two of \":\" or \"/\".")
353 (calc-prefer-frac nil
354 "If non-nil, prefer fractional over floating-point results.")
356 (calc-hms-format "%s@ %s' %s\""
357 "Format of displayed hours-minutes-seconds angles, a format string.
358 String must contain three %s marks for hours, minutes, seconds respectively.")
360 (calc-date-format ((H ":" mm C SS pp " ")
361 Www " " Mmm " " D ", " YYYY)
362 "Format of displayed date forms.")
364 (calc-float-format (float 0)
365 "Format to use for display of floating-point numbers in calc-mode.
366 Must be a list of one of the following forms:
367 (float 0) Floating point format, display full precision.
368 (float N) N > 0: Floating point format, at most N significant figures.
369 (float -N) -N < 0: Floating point format, calc-internal-prec - N figs.
370 (fix N) N >= 0: Fixed point format, N places after decimal point.
371 (sci 0) Scientific notation, full precision.
372 (sci N) N > 0: Scientific notation, N significant figures.
373 (sci -N) -N < 0: Scientific notation, calc-internal-prec - N figs.
374 (eng 0) Engineering notation, full precision.
375 (eng N) N > 0: Engineering notation, N significant figures.
376 (eng -N) -N < 0: Engineering notation, calc-internal-prec - N figs.")
378 (calc-full-float-format (float 0)
379 "Format to use when full precision must be displayed.")
381 (calc-complex-format nil
382 "Format to use for display of complex numbers in calc-mode. Must be one of:
387 (calc-complex-mode cplx
388 "Preferred form, either `cplx' or `polar', for complex numbers.")
390 (calc-infinite-mode nil
391 "If nil, 1 / 0 is left unsimplified.
392 If 0, 1 / 0 is changed to inf (zeros are considered positive).
393 Otherwise, 1 / 0 is changed to uinf (undirected infinity).")
395 (calc-display-strings nil
396 "If non-nil, display vectors of byte-sized integers as strings.")
398 (calc-matrix-just center
399 "If nil, vector elements are left-justified.
400 If `right', vector elements are right-justified.
401 If `center', vector elements are centered.")
403 (calc-break-vectors nil
404 "If non-nil, display vectors one element per line.")
407 "If non-nil, display long vectors in full. If nil, use abbreviated form.")
409 (calc-full-trail-vectors t
410 "If non-nil, display long vectors in full in the trail.")
412 (calc-vector-commas ","
413 "If non-nil, separate elements of displayed vectors with this string.")
415 (calc-vector-brackets "[]"
416 "If non-nil, surround displayed vectors with these characters.")
418 (calc-matrix-brackets (R O)
419 "A list of code-letter symbols that control \"big\" matrix display.
420 If `R' is present, display inner brackets for matrices.
421 If `O' is present, display outer brackets for matrices (above/below).
422 If `C' is present, display outer brackets for matrices (centered).")
425 "Language or format for entry and display of stack values. Must be one of:
426 nil Use standard Calc notation.
427 flat Use standard Calc notation, one-line format.
428 big Display formulas in 2-d notation (enter w/std notation).
429 unform Use unformatted display: add(a, mul(b,c)).
430 c Use C language notation.
431 pascal Use Pascal language notation.
432 fortran Use Fortran language notation.
433 tex Use TeX notation.
434 eqn Use eqn notation.
435 math Use Mathematica(tm) notation.
436 maple Use Maple notation.")
438 (calc-language-option nil
439 "Numeric prefix argument for the command that set `calc-language'.")
442 "Label to display at left of formula.")
445 "Label to display at right of formula.")
448 "Minimum number of bits per word, if any, for binary operations in calc-mode.")
450 (calc-previous-modulo nil
451 "Most recently used value of M in a modulo form.")
453 (calc-simplify-mode nil
454 "Type of simplification applied to results.
455 If `none', results are not simplified when pushed on the stack.
456 If `num', functions are simplified only when args are constant.
457 If nil, only fast simplifications are applied.
458 If `binary', `math-clip' is applied if appropriate.
459 If `alg', `math-simplify' is applied.
460 If `ext', `math-simplify-extended' is applied.
461 If `units', `math-simplify-units' is applied.")
463 (calc-auto-recompute t
464 "If non-nil, recompute evalto's automatically when necessary.")
466 (calc-display-raw nil
467 "If non-nil, display shows unformatted Lisp exprs. (For debugging)")
469 (calc-internal-prec 12
470 "Number of digits of internal precision for calc-mode calculations.")
473 "If deg, angles are in degrees; if rad, angles are in radians.
474 If hms, angles are in degrees-minutes-seconds.")
476 (calc-algebraic-mode nil
477 "If non-nil, numeric entry accepts whole algebraic expressions.
478 If nil, algebraic expressions must be preceded by \"'\".")
480 (calc-incomplete-algebraic-mode nil
481 "Like calc-algebraic-mode except only affects ( and [ keys.")
483 (calc-symbolic-mode nil
484 "If non-nil, inexact numeric computations like sqrt(2) are postponed.
485 If nil, computations on numbers always yield numbers where possible.")
487 (calc-matrix-mode nil
488 "If `matrix', variables are assumed to be matrix-valued.
489 If a number, variables are assumed to be NxN matrices.
490 If `scalar', variables are assumed to be scalar-valued.
491 If nil, symbolic math routines make no assumptions about variables.")
493 (calc-shift-prefix nil
494 "If non-nil, shifted letter keys are prefix keys rather than normal meanings.")
496 (calc-window-height 7
497 "Initial height of Calculator window.")
499 (calc-display-trail t
500 "If non-nil, M-x calc creates a window to display Calculator trail.")
502 (calc-show-selections t
503 "If non-nil, selected sub-formulas are shown by obscuring rest of formula.
504 If nil, selected sub-formulas are highlighted by obscuring the sub-formulas.")
506 (calc-use-selections t
507 "If non-nil, commands operate only on selected portions of formulas.
508 If nil, selections displayed but ignored.")
510 (calc-assoc-selections t
511 "If non-nil, selection hides deep structure of associative formulas.")
513 (calc-display-working-message lots
514 "If non-nil, display \"Working...\" for potentially slow Calculator commands.")
517 "If non-nil, automatically execute a \"why\" command to explain odd results.")
520 "If non-nil, display timing information on each slow command.")
522 (calc-mode-save-mode local)
524 (calc-standard-date-formats
526 "<H:mm:SSpp >Www Mmm D, YYYY"
527 "D Mmm YYYY<, h:mm:SS>"
528 "Www Mmm BD< hh:mm:ss> YYYY"
536 (calc-autorange-units nil)
538 (calc-was-keypad-mode nil)
542 (calc-user-parse-tables nil)
544 (calc-gnuplot-default-device "default")
546 (calc-gnuplot-default-output "STDOUT")
548 (calc-gnuplot-print-device "postscript")
550 (calc-gnuplot-print-output "auto")
552 (calc-gnuplot-geometry nil)
554 (calc-graph-default-resolution 15)
556 (calc-graph-default-resolution-3d 5)
558 (calc-invocation-macro nil)
561 "*If non-nil, show a friendly greeting above the stack."))
562 "List of variables (and default values) used in customizing GNU Calc.")
564 (mapcar (function (lambda (v)
566 (set (car v) (nth 1 v)))
568 (put (car v) 'variable-documentation (nth 2 v)))))
571 (defconst calc-local-var-list '(calc-stack
575 calc-always-load-extensions
586 calc-incomplete-algebraic-mode
602 calc-standard-date-formats
604 calc-full-float-format
608 calc-full-trail-vectors
622 calc-assoc-selections
626 (defvar calc-mode-hook nil
627 "Hook run when entering calc-mode.")
629 (defvar calc-trail-mode-hook nil
630 "Hook run when entering calc-trail-mode.")
632 (defvar calc-start-hook nil
633 "Hook run when calc is started.")
635 (defvar calc-end-hook nil
636 "Hook run when calc is quit.")
638 (defvar calc-load-hook nil
639 "Hook run when calc.el is loaded.")
641 ;; Verify that Calc is running on the right kind of system.
642 (defvar calc-emacs-type-lucid (not (not (string-match "Lucid" emacs-version))))
644 ;; Set up the standard keystroke (M-#) to run the Calculator, if that key
645 ;; has not yet been bound to anything. For best results, the user should
646 ;; do this before Calc is even loaded, so that M-# can auto-load Calc.
647 (or (global-key-binding "\e#") (global-set-key "\e#" 'calc-dispatch))
649 ;; Set up the autoloading linkage.
650 (let ((name (and (fboundp 'calc-dispatch)
651 (eq (car-safe (symbol-function 'calc-dispatch)) 'autoload)
652 (nth 1 (symbol-function 'calc-dispatch))))
655 ;; If Calc files exist on the load-path, we're all set.
656 (while (and p (not (file-exists-p
657 (expand-file-name "calc-misc.elc" (car p)))))
661 ;; If Calc is autoloaded using a path name, look there for Calc files.
662 ;; This works for both relative ("calc/calc.elc") and absolute paths.
663 (and name (file-name-directory name)
665 (name2 (concat (file-name-directory name)
667 (while (and p2 (not (file-exists-p
668 (expand-file-name name2 (car p2)))))
671 (setq load-path (nconc load-path
676 name (car p2))))))))))))
678 ;; The following modes use specially-formatted data.
679 (put 'calc-mode 'mode-class 'special)
680 (put 'calc-trail-mode 'mode-class 'special)
682 ;; Define "inexact-result" as an e-lisp error symbol.
683 (put 'inexact-result 'error-conditions '(error inexact-result calc-error))
684 (put 'inexact-result 'error-message "Calc internal error (inexact-result)")
686 ;; Define "math-overflow" and "math-underflow" as e-lisp error symbols.
687 (put 'math-overflow 'error-conditions '(error math-overflow calc-error))
688 (put 'math-overflow 'error-message "Floating-point overflow occurred")
689 (put 'math-underflow 'error-conditions '(error math-underflow calc-error))
690 (put 'math-underflow 'error-message "Floating-point underflow occurred")
692 (defconst calc-version "2.02g")
693 (defconst calc-version-date "Mon Nov 19 2001")
694 (defvar calc-trail-pointer nil) ; "Current" entry in trail buffer.
695 (defvar calc-trail-overlay nil) ; Value of overlay-arrow-string.
696 (defvar calc-undo-list nil) ; List of previous operations for undo.
697 (defvar calc-redo-list nil) ; List of recent undo operations.
698 (defvar calc-main-buffer nil) ; Pointer to Calculator buffer.
699 (defvar calc-trail-buffer nil) ; Pointer to Calc Trail buffer.
700 (defvar calc-why nil) ; Explanations of most recent errors.
701 (defvar calc-next-why nil)
702 (defvar calc-inverse-flag nil
703 "If non-nil, next operation is Inverse.")
704 (defvar calc-hyperbolic-flag nil
705 "If non-nil, next operation is Hyperbolic.")
706 (defvar calc-keep-args-flag nil
707 "If non-nil, next operation should not remove its arguments from stack.")
708 (defvar calc-function-open "("
709 "Open-parenthesis string for function call notation.")
710 (defvar calc-function-close ")"
711 "Close-parenthesis string for function call notation.")
712 (defvar calc-language-output-filter nil
713 "Function through which to pass strings after formatting.")
714 (defvar calc-language-input-filter nil
715 "Function through which to pass strings before parsing.")
716 (defvar calc-radix-formatter nil
717 "Formatting function used for non-decimal numbers.")
719 (defvar calc-last-kill nil) ; Last number killed in calc-mode.
720 (defvar calc-previous-alg-entry nil) ; Previous algebraic entry.
721 (defvar calc-dollar-values nil) ; Values to be used for '$'.
722 (defvar calc-dollar-used nil) ; Highest order of '$' that occurred.
723 (defvar calc-hashes-used nil) ; Highest order of '#' that occurred.
724 (defvar calc-quick-prev-results nil) ; Previous results from Quick Calc.
725 (defvar calc-said-hello nil) ; Has welcome message been said yet?
726 (defvar calc-executing-macro nil) ; Kbd macro executing from "K" key.
727 (defvar calc-any-selections nil) ; Nil means no selections present.
728 (defvar calc-help-phase 0) ; Count of consecutive "?" keystrokes.
729 (defvar calc-full-help-flag nil) ; Executing calc-full-help?
730 (defvar calc-refresh-count 0) ; Count of calc-refresh calls.
731 (defvar calc-display-dirty nil)
732 (defvar calc-prepared-composition nil)
733 (defvar calc-selection-cache-default-entry nil)
734 (defvar calc-embedded-info nil)
735 (defvar calc-embedded-active nil)
736 (defvar calc-standalone-flag nil)
737 (defvar var-EvalRules nil)
738 (defvar math-eval-rules-cache-tag t)
739 (defvar math-radix-explicit-format t)
740 (defvar math-expr-function-mapping nil)
741 (defvar math-expr-variable-mapping nil)
742 (defvar math-read-expr-quotes nil)
743 (defvar math-working-step nil)
744 (defvar math-working-step-2 nil)
745 (defvar var-i '(special-const (math-imaginary 1)))
746 (defvar var-pi '(special-const (math-pi)))
747 (defvar var-e '(special-const (math-e)))
748 (defvar var-phi '(special-const (math-phi)))
749 (defvar var-gamma '(special-const (math-gamma-const)))
750 (defvar var-Modes '(special-const (math-get-modes-vec)))
752 (mapcar (lambda (v) (or (boundp v) (set v nil)))
755 (defvar calc-mode-map
756 (let ((map (make-keymap)))
757 (suppress-keymap map t)
758 (define-key map "+" 'calc-plus)
759 (define-key map "-" 'calc-minus)
760 (define-key map "*" 'calc-times)
761 (define-key map "/" 'calc-divide)
762 (define-key map "%" 'calc-mod)
763 (define-key map "&" 'calc-inv)
764 (define-key map "^" 'calc-power)
765 (define-key map "\M-%" 'calc-percent)
766 (define-key map "e" 'calcDigit-start)
767 (define-key map "i" 'calc-info)
768 (define-key map "n" 'calc-change-sign)
769 (define-key map "q" 'calc-quit)
770 (define-key map "Y" 'nil)
771 (define-key map "Y?" 'calc-shift-Y-prefix-help)
772 (define-key map "?" 'calc-help)
773 (define-key map " " 'calc-enter)
774 (define-key map "'" 'calc-algebraic-entry)
775 (define-key map "$" 'calc-auto-algebraic-entry)
776 (define-key map "\"" 'calc-auto-algebraic-entry)
777 (define-key map "\t" 'calc-roll-down)
778 (define-key map "\M-\t" 'calc-roll-up)
779 (define-key map "\C-m" 'calc-enter)
780 (define-key map "\M-\C-m" 'calc-last-args-stub)
781 (define-key map "\C-j" 'calc-over)
783 (mapc (lambda (x) (define-key map (char-to-string x) 'undefined))
785 (mapc (lambda (x) (define-key map (char-to-string x) 'calc-missing-key))
786 (concat "ABCDEFGHIJKLMNPQRSTUVXZabcdfghjkmoprstuvwxyz"
787 ":\\|!()[]<>{},;=~`\C-k\M-k\C-w\M-w\C-y\C-_"))
788 (mapc (lambda (x) (define-key map (char-to-string x) 'calcDigit-start))
792 (defvar calc-digit-map
793 (let ((map (make-keymap)))
794 (if calc-emacs-type-lucid
795 (map-keymap (function
798 (if (eq bind 'undefined)
799 'undefined 'calcDigit-nondigit))))
801 (let ((cmap (nth 1 calc-mode-map))
806 (if (eq (aref cmap i) 'undefined)
807 'undefined 'calcDigit-nondigit))
809 (mapcar (lambda (x) (define-key map (char-to-string x) 'calcDigit-key))
810 "_0123456789.e+-:n#@oh'\"mspM")
811 (mapcar (lambda (x) (define-key map (char-to-string x) 'calcDigit-letter))
812 "abcdfgijklqrtuvwxyzABCDEFGHIJKLNOPQRSTUVWXYZ")
813 (define-key map "'" 'calcDigit-algebraic)
814 (define-key map "`" 'calcDigit-edit)
815 (define-key map "\C-g" 'abort-recursive-edit)
821 (define-key calc-digit-map x 'calcDigit-backspace)
822 (define-key calc-mode-map x 'calc-pop)
823 (define-key calc-mode-map
825 (if calc-emacs-type-lucid
827 (vector (if (consp (aref x 0))
828 (cons 'meta (aref x 0))
829 (list 'meta (aref x 0))))
835 (if calc-scan-for-dels
836 (append (where-is-internal 'delete-backward-char global-map)
837 (where-is-internal 'backward-delete-char global-map)
841 (defvar calc-dispatch-map
842 (let ((map (make-keymap)))
844 (define-key map (char-to-string (car x)) (cdr x))
845 (when (string-match "abcdefhijklnopqrstuwxyz"
846 (char-to-string (car x)))
847 (define-key map (char-to-string (- (car x) ?a -1)) (cdr x)))
848 (define-key map (format "\e%c" (car x)) (cdr x)))
849 '( ( ?a . calc-embedded-activate )
850 ( ?b . calc-big-or-small )
852 ( ?d . calc-embedded-duplicate )
853 ( ?e . calc-embedded )
854 ( ?f . calc-embedded-new-formula )
855 ( ?g . calc-grab-region )
856 ( ?h . calc-dispatch-help )
858 ( ?j . calc-embedded-select )
860 ( ?l . calc-load-everything )
861 ( ?m . read-kbd-macro )
862 ( ?n . calc-embedded-next )
863 ( ?o . calc-other-window )
864 ( ?p . calc-embedded-previous )
866 ( ?r . calc-grab-rectangle )
867 ( ?s . calc-info-summary )
868 ( ?t . calc-tutorial )
869 ( ?u . calc-embedded-update-formula )
870 ( ?w . calc-embedded-word )
872 ( ?y . calc-copy-to-buffer )
873 ( ?z . calc-user-invocation )
874 ( ?= . calc-embedded-update-formula )
875 ( ?\' . calc-embedded-new-formula )
876 ( ?\` . calc-embedded-edit )
877 ( ?: . calc-grab-sum-down )
878 ( ?_ . calc-grab-sum-across )
880 ( ?# . calc-same-interface )
881 ( ?? . calc-dispatch-help ) ))
884 ;;;; (Autoloads here)
886 (lambda (x) (dolist (func (cdr x)) (autoload func (car x))))
889 ("calc-aent" calc-alg-digit-entry calc-alg-entry
890 calc-check-user-syntax calc-do-alg-entry calc-do-calc-eval
891 calc-do-quick-calc calc-match-user-syntax math-build-parse-table
892 math-find-user-tokens math-read-expr-list math-read-exprs math-read-if
893 math-read-token math-remove-dashes math-read-preprocess-string)
895 ("calc-embed" calc-do-embedded-activate)
898 calc-do-handle-whys calc-do-refresh calc-num-prefix-name
899 calc-record-list calc-record-why calc-report-bug calc-roll-down-stack
900 calc-roll-up-stack calc-temp-minibuffer-message calcFunc-floor
901 calcFunc-inv calcFunc-trunc math-concat math-constp math-div2
902 math-div2-bignum math-do-working math-evenp math-fixnatnump
903 math-fixnump math-floor math-imod math-ipow math-looks-negp math-mod
904 math-negp math-posp math-pow math-read-radix-digit math-reject-arg
905 math-trunc math-zerop)))
908 (lambda (x) (dolist (cmd (cdr x)) (autoload cmd (car x) nil t)))
911 ("calc-aent" calc-algebraic-entry calc-auto-algebraic-entry
912 calcDigit-algebraic calcDigit-edit)
914 ("calc-misc" another-calc calc-big-or-small calc-dispatch-help
915 calc-help calc-info calc-info-goto-node calc-info-summary calc-inv
917 calc-missing-key calc-mod calc-other-window calc-over calc-percent
918 calc-pop-above calc-power calc-roll-down calc-roll-up
919 calc-shift-Y-prefix-help calc-tutorial calcDigit-letter
923 ;;;###autoload (global-set-key "\e#" 'calc-dispatch)
926 (defun calc-dispatch (&optional arg)
927 "Invoke the GNU Emacs Calculator. See `calc-dispatch-help' for details."
929 (sit-for echo-keystrokes)
930 (condition-case err ; look for other keys bound to calc-dispatch
931 (let ((keys (this-command-keys)))
932 (unless (or (not (stringp keys))
933 (string-match "\\`\C-u\\|\\`\e[-0-9#]\\|`[\M--\M-0-\M-9]" keys)
934 (eq (lookup-key calc-dispatch-map keys) 'calc-same-interface))
935 (when (and (string-match "\\`[\C-@-\C-_]" keys)
937 (lookup-key calc-dispatch-map (substring keys 0 1))))
938 (define-key calc-dispatch-map (substring keys 0 1) nil))
939 (define-key calc-dispatch-map keys 'calc-same-interface)))
941 (calc-do-dispatch arg))
943 (defvar calc-dispatch-help nil)
944 (defun calc-do-dispatch (arg)
945 (let ((key (calc-read-key-sequence
946 (if calc-dispatch-help
947 "Calc options: Calc, Keypad, Quick, Embed; eXit; Info, Tutorial; Grab; ?=more"
948 (format "%s (Type ? for a list of Calc options)"
949 (key-description (this-command-keys))))
951 (setq key (lookup-key calc-dispatch-map key))
955 (or (commandp key) (require 'calc-ext))
956 (call-interactively key))
959 (defun calc-read-key-sequence (prompt map)
960 (let ((prompt2 (format "%s " (key-description (this-command-keys))))
961 (glob (current-global-map))
962 (loc (current-local-map)))
963 (or (input-pending-p) (message prompt))
964 (let ((key (calc-read-key t)))
965 (calc-unread-command (cdr key))
970 (read-key-sequence nil))
971 (use-global-map glob)
972 (use-local-map loc)))))
977 "Calculator major mode.
979 This is an RPN calculator featuring arbitrary-precision integer, rational,
980 floating-point, complex, matrix, and symbolic arithmetic.
982 RPN calculation: 2 RET 3 + produces 5.
983 Algebraic style: ' 2+3 RET produces 5.
985 Basic operators are +, -, *, /, ^, & (reciprocal), % (modulo), n (change-sign).
987 Press ? repeatedly for more complete help. Press `h i' to read the
988 Calc manual on-line, `h s' to read the summary, or `h t' for the tutorial.
990 Notations: 3.14e6 3.14 * 10^6
991 _23 negative number -23 (or type `23 n')
992 17:3 the fraction 17/3
993 5:2:3 the fraction 5 and 2/3
994 16#12C the integer 12C base 16 = 300 base 10
995 8#177:100 the fraction 177:100 base 8 = 127:64 base 10
996 (2, 4) complex number 2 + 4i
997 (2; 4) polar complex number (r; theta)
998 [1, 2, 3] vector ([[1, 2], [3, 4]] is a matrix)
999 [1 .. 4) semi-open interval, 1 <= x < 4
1000 2 +/- 3 (p key) number with mean 2, standard deviation 3
1001 2 mod 3 (M key) number 2 computed modulo 3
1002 <1 jan 91> Date form (enter using ' key)
1009 (lambda (v) (set-default v (symbol-value v)))) calc-local-var-list)
1010 (kill-all-local-variables)
1011 (use-local-map (if (eq calc-algebraic-mode 'total)
1012 (progn (require 'calc-ext) calc-alg-map) calc-mode-map))
1013 (mapcar (function (lambda (v) (make-local-variable v))) calc-local-var-list)
1014 (make-local-variable 'overlay-arrow-position)
1015 (make-local-variable 'overlay-arrow-string)
1016 (add-hook 'change-major-mode-hook 'font-lock-defontify nil t)
1017 (setq truncate-lines t)
1018 (setq buffer-read-only t)
1019 (setq major-mode 'calc-mode)
1020 (setq mode-name "Calculator")
1021 (setq calc-stack-top (length (or (memq (assq 'top-of-stack calc-stack)
1023 (setq calc-stack (list (list 'top-of-stack
1025 (setq calc-stack-top (- (length calc-stack) calc-stack-top -1))
1026 (or calc-loaded-settings-file
1027 (null calc-settings-file)
1028 (equal calc-settings-file user-init-file)
1030 (setq calc-loaded-settings-file t)
1031 (load calc-settings-file t))) ; t = missing-ok
1032 (let ((p command-line-args))
1034 (and (equal (car p) "-f")
1035 (string-match "calc" (nth 1 p))
1036 (string-match "full" (nth 1 p))
1037 (setq calc-standalone-flag t))
1039 (run-hooks 'calc-mode-hook)
1041 (calc-set-mode-line)
1042 (calc-check-defines))
1044 (defvar calc-check-defines 'calc-check-defines) ; suitable for run-hooks
1045 (defun calc-check-defines ()
1046 (if (symbol-plist 'calc-define)
1047 (let ((plist (copy-sequence (symbol-plist 'calc-define))))
1048 (while (and plist (null (nth 1 plist)))
1049 (setq plist (cdr (cdr plist))))
1053 (require 'calc-macs)
1054 (set-buffer "*Calculator*")
1056 (put 'calc-define (car plist) nil)
1057 (eval (nth 1 plist))
1058 (setq plist (cdr (cdr plist))))
1059 ;; See if this has added any more calc-define properties.
1060 (calc-check-defines))
1061 (setplist 'calc-define nil)))))
1063 (defun calc-trail-mode (&optional buf)
1065 This mode is used by the *Calc Trail* buffer, which records all results
1066 obtained by the GNU Emacs Calculator.
1068 Calculator commands beginning with the `t' key are used to manipulate
1071 This buffer uses the same key map as the *Calculator* buffer; calculator
1072 commands given here will actually operate on the *Calculator* stack."
1075 (use-local-map calc-mode-map)
1076 (setq major-mode 'calc-trail-mode)
1077 (setq mode-name "Calc Trail")
1078 (setq truncate-lines t)
1079 (setq buffer-read-only t)
1080 (make-local-variable 'overlay-arrow-position)
1081 (make-local-variable 'overlay-arrow-string)
1082 (set (make-local-variable 'font-lock-defaults)
1083 '(nil t nil nil nil (font-lock-core-only . t)))
1085 (set (make-local-variable 'calc-main-buffer) buf))
1086 (when (= (buffer-size) 0)
1087 (let ((buffer-read-only nil))
1088 (insert (propertize (concat "Emacs Calculator v" calc-version
1089 " by Dave Gillespie\n")
1090 'font-lock-face 'italic))))
1091 (run-hooks 'calc-trail-mode-hook))
1093 (defun calc-create-buffer ()
1094 (set-buffer (get-buffer-create "*Calculator*"))
1095 (or (eq major-mode 'calc-mode)
1097 (setq max-lisp-eval-depth (max max-lisp-eval-depth 1000))
1098 (when calc-always-load-extensions
1099 (require 'calc-ext))
1102 (calc-set-language calc-language calc-language-option t)))
1105 (defun calc (&optional arg full-display interactive)
1106 "The Emacs Calculator. Full documentation is listed under \"calc-mode\"."
1107 (interactive "P\ni\np")
1111 (if (= (prefix-numeric-value arg) -1)
1112 (calc-grab-region (region-beginning) (region-end) nil)
1113 (when (= (prefix-numeric-value arg) -2)
1115 (when (get-buffer-window "*Calc Keypad*")
1117 (set-buffer (window-buffer (selected-window))))
1118 (if (eq major-mode 'calc-mode)
1120 (let ((oldbuf (current-buffer)))
1121 (calc-create-buffer)
1122 (setq calc-was-keypad-mode nil)
1123 (if (or (eq full-display t)
1124 (and (null full-display) calc-full-mode))
1125 (switch-to-buffer (current-buffer) t)
1126 (if (get-buffer-window (current-buffer))
1127 (select-window (get-buffer-window (current-buffer)))
1128 (let ((w (get-largest-window)))
1129 (if (and pop-up-windows
1130 (> (window-height w)
1131 (+ window-min-height calc-window-height 2)))
1133 (setq w (split-window w
1134 (- (window-height w)
1135 calc-window-height 2)
1137 (set-window-buffer w (current-buffer))
1139 (pop-to-buffer (current-buffer))))))
1141 (set-buffer (calc-trail-buffer))
1142 (and calc-display-trail
1143 (= (window-width) (frame-width))
1144 (calc-trail-display 1 t)))
1145 (message "Welcome to the GNU Emacs Calculator! Press `?' or `h' for help, `q' to quit")
1146 (run-hooks 'calc-start-hook)
1147 (and (windowp full-display)
1148 (window-point full-display)
1149 (select-window full-display))
1150 (calc-check-defines)
1151 (when (and calc-said-hello interactive)
1154 (setq calc-said-hello t)))))
1157 (defun full-calc (&optional interactive)
1158 "Invoke the Calculator and give it a full-sized window."
1160 (calc nil t interactive))
1162 (defun calc-same-interface (arg)
1163 "Invoke the Calculator using the most recent interface (calc or calc-keypad)."
1165 (if (and (equal (buffer-name) "*Gnuplot Trail*")
1166 (> (recursion-depth) 0))
1167 (exit-recursive-edit)
1168 (if (eq major-mode 'calc-edit-mode)
1169 (calc-edit-finish arg)
1170 (if calc-was-keypad-mode
1172 (calc arg calc-full-mode t)))))
1174 (defun calc-quit (&optional non-fatal interactive)
1175 (interactive "i\np")
1176 (and calc-standalone-flag (not non-fatal)
1177 (save-buffers-kill-emacs nil))
1178 (if (and (equal (buffer-name) "*Gnuplot Trail*")
1179 (> (recursion-depth) 0))
1180 (exit-recursive-edit))
1181 (if (eq major-mode 'calc-edit-mode)
1183 (if (and interactive
1185 (eq (current-buffer) (aref calc-embedded-info 0)))
1187 (unless (eq major-mode 'calc-mode)
1188 (calc-create-buffer))
1189 (run-hooks 'calc-end-hook)
1190 (setq calc-undo-list nil calc-redo-list nil)
1191 (mapcar (function (lambda (v) (set-default v (symbol-value v))))
1192 calc-local-var-list)
1193 (let ((buf (current-buffer))
1194 (win (get-buffer-window (current-buffer)))
1195 (kbuf (get-buffer "*Calc Keypad*")))
1196 (delete-windows-on (calc-trail-buffer))
1198 (< (window-height win) (1- (frame-height)))
1199 (= (window-width win) (frame-width)) ; avoid calc-keypad
1200 (not (get-buffer-window "*Calc Keypad*")))
1201 (setq calc-window-height (- (window-height win) 2)))
1203 (delete-windows-on buf)
1204 (delete-windows-on kbuf))
1206 (bury-buffer calc-trail-buffer)
1207 (and kbuf (bury-buffer kbuf))))))
1210 (defun quick-calc ()
1211 "Do a quick calculation in the minibuffer without invoking full Calculator."
1213 (calc-do-quick-calc))
1216 (defun calc-eval (str &optional separator &rest args)
1217 "Do a quick calculation and return the result as a string.
1218 Return value will either be the formatted result in string form,
1219 or a list containing a character position and an error message in string form."
1220 (calc-do-calc-eval str separator args))
1223 (defun calc-keypad (&optional interactive)
1224 "Invoke the Calculator in \"visual keypad\" mode.
1225 This is most useful in the X window system.
1226 In this mode, click on the Calc \"buttons\" using the left mouse button.
1227 Or, position the cursor manually and do M-x calc-keypad-press."
1230 (calc-do-keypad calc-full-mode interactive))
1233 (defun full-calc-keypad (&optional interactive)
1234 "Invoke the Calculator in full-screen \"visual keypad\" mode.
1235 See calc-keypad for details."
1238 (calc-do-keypad t interactive))
1241 (defvar calc-aborted-prefix nil)
1242 (defvar calc-start-time nil)
1243 (defvar calc-command-flags)
1244 (defvar calc-final-point-line)
1245 (defvar calc-final-point-column)
1246 ;;; Note that modifications to this function may break calc-pass-errors.
1247 (defun calc-do (do-body &optional do-slow)
1248 (calc-check-defines)
1249 (let* ((calc-command-flags nil)
1250 (calc-start-time (and calc-timing (not calc-start-time)
1252 (current-time-string)))
1253 (gc-cons-threshold (max gc-cons-threshold
1254 (if calc-timing 2000000 100000)))
1255 calc-final-point-line calc-final-point-column)
1256 (setq calc-aborted-prefix "")
1260 (if calc-embedded-info
1261 (calc-embedded-select-buffer)
1262 (calc-select-buffer))
1263 (and (eq calc-algebraic-mode 'total)
1265 (use-local-map calc-alg-map))
1266 (when (and do-slow calc-display-working-message)
1267 (message "Working...")
1268 (calc-set-command-flag 'clear-message))
1270 (setq calc-aborted-prefix nil)
1271 (when (memq 'renum-stack calc-command-flags)
1272 (calc-renumber-stack))
1273 (when (memq 'clear-message calc-command-flags)
1276 (if (and (eq (car err) 'error)
1277 (stringp (nth 1 err))
1278 (string-match "max-specpdl-size\\|max-lisp-eval-depth"
1280 (error "Computation got stuck or ran too long. Type `M' to increase the limit")
1281 (setq calc-aborted-prefix nil)
1282 (signal (car err) (cdr err)))))
1283 (when calc-aborted-prefix
1284 (calc-record "<Aborted>" calc-aborted-prefix))
1285 (and calc-start-time
1286 (let* ((calc-internal-prec 12)
1287 (calc-date-format nil)
1288 (end-time (current-time-string))
1289 (time (if (equal calc-start-time end-time)
1292 (calcFunc-unixtime (math-parse-date end-time) 0)
1293 (calcFunc-unixtime (math-parse-date calc-start-time)
1295 (if (math-lessp 1 time)
1296 (calc-record time "(t)"))))
1297 (or (memq 'no-align calc-command-flags)
1298 (eq major-mode 'calc-trail-mode)
1299 (calc-align-stack-window))
1300 (and (memq 'position-point calc-command-flags)
1301 (if (eq major-mode 'calc-mode)
1303 (goto-line calc-final-point-line)
1304 (move-to-column calc-final-point-column))
1305 (save-current-buffer
1306 (calc-select-buffer)
1307 (goto-line calc-final-point-line)
1308 (move-to-column calc-final-point-column))))
1309 (unless (memq 'keep-flags calc-command-flags)
1311 (calc-select-buffer)
1312 (setq calc-inverse-flag nil
1313 calc-hyperbolic-flag nil
1314 calc-keep-args-flag nil)))
1315 (when (memq 'do-edit calc-command-flags)
1316 (switch-to-buffer (get-buffer-create "*Calc Edit*")))
1317 (calc-set-mode-line)
1318 (when calc-embedded-info
1319 (calc-embedded-finish-command))))
1320 (identity nil)) ; allow a GC after timing is done
1323 (defun calc-set-command-flag (f)
1324 (unless (memq f calc-command-flags)
1325 (setq calc-command-flags (cons f calc-command-flags))))
1327 (defun calc-select-buffer ()
1328 (or (eq major-mode 'calc-mode)
1329 (if calc-main-buffer
1330 (set-buffer calc-main-buffer)
1331 (let ((buf (get-buffer "*Calculator*")))
1334 (error "Calculator buffer not available"))))))
1336 (defun calc-cursor-stack-index (&optional index)
1337 (goto-char (point-max))
1338 (forward-line (- (calc-substack-height (or index 1)))))
1340 (defun calc-stack-size ()
1341 (- (length calc-stack) calc-stack-top))
1343 (defun calc-substack-height (n)
1346 (setq n (+ n calc-stack-top))
1347 (while (and (> n 0) stack)
1348 (setq sum (+ sum (nth 1 (car stack)))
1353 (defun calc-set-mode-line ()
1355 (calc-select-buffer)
1356 (let* ((fmt (car calc-float-format))
1357 (figs (nth 1 calc-float-format))
1359 (format "Calc%s%s: %d %s %-14s"
1360 (if calc-embedded-info "Embed" "")
1361 (if (and (> (length (buffer-name)) 12)
1362 (equal (substring (buffer-name) 0 12)
1364 (substring (buffer-name) 12)
1367 (capitalize (symbol-name calc-angle-mode))
1370 ;; Input-related modes
1371 (if (eq calc-algebraic-mode 'total) "Alg* "
1372 (if calc-algebraic-mode "Alg "
1373 (if calc-incomplete-algebraic-mode "Alg[( " "")))
1375 ;; Computational modes
1376 (if calc-symbolic-mode "Symb " "")
1377 (cond ((eq calc-matrix-mode 'matrix) "Matrix ")
1378 ((integerp calc-matrix-mode)
1379 (format "Matrix%d " calc-matrix-mode))
1380 ((eq calc-matrix-mode 'scalar) "Scalar ")
1382 (if (eq calc-complex-mode 'polar) "Polar " "")
1383 (if calc-prefer-frac "Frac " "")
1384 (cond ((null calc-infinite-mode) "")
1385 ((eq calc-infinite-mode 1) "+Inf ")
1387 (cond ((eq calc-simplify-mode 'none) "NoSimp ")
1388 ((eq calc-simplify-mode 'num) "NumSimp ")
1389 ((eq calc-simplify-mode 'binary)
1390 (format "BinSimp%d " calc-word-size))
1391 ((eq calc-simplify-mode 'alg) "AlgSimp ")
1392 ((eq calc-simplify-mode 'ext) "ExtSimp ")
1393 ((eq calc-simplify-mode 'units) "UnitSimp ")
1397 (cond ((= calc-number-radix 10) "")
1398 ((= calc-number-radix 2) "Bin ")
1399 ((= calc-number-radix 8) "Oct ")
1400 ((= calc-number-radix 16) "Hex ")
1401 (t (format "Radix%d " calc-number-radix)))
1402 (if calc-leading-zeros "Zero " "")
1403 (cond ((null calc-language) "")
1404 ((eq calc-language 'tex) "TeX ")
1406 (capitalize (symbol-name calc-language))
1408 (cond ((eq fmt 'float)
1409 (if (zerop figs) "" (format "Norm%d " figs)))
1410 ((eq fmt 'fix) (format "Fix%d " figs))
1412 (if (zerop figs) "Sci " (format "Sci%d " figs)))
1414 (if (zerop figs) "Eng " (format "Eng%d " figs))))
1415 (cond ((not calc-display-just)
1416 (if calc-display-origin
1417 (format "Left%d " calc-display-origin) ""))
1418 ((eq calc-display-just 'right)
1419 (if calc-display-origin
1420 (format "Right%d " calc-display-origin)
1423 (if calc-display-origin
1424 (format "Center%d " calc-display-origin)
1426 (cond ((integerp calc-line-breaking)
1427 (format "Wid%d " calc-line-breaking))
1428 (calc-line-breaking "")
1431 ;; Miscellaneous other modes/indicators
1432 (if calc-assoc-selections "" "Break ")
1433 (cond ((eq calc-mode-save-mode 'save) "Save ")
1434 ((not calc-embedded-info) "")
1435 ((eq calc-mode-save-mode 'local) "Local ")
1436 ((eq calc-mode-save-mode 'edit) "LocEdit ")
1437 ((eq calc-mode-save-mode 'perm) "LocPerm ")
1438 ((eq calc-mode-save-mode 'global) "Global ")
1440 (if calc-auto-recompute "" "Manual ")
1441 (if (and (fboundp 'calc-gnuplot-alive)
1442 (calc-gnuplot-alive)) "Graph " "")
1443 (if (and calc-embedded-info
1444 (> (calc-stack-size) 0)
1445 (calc-top 1 'sel)) "Sel " "")
1446 (if calc-display-dirty "Dirty " "")
1447 (if calc-inverse-flag "Inv " "")
1448 (if calc-hyperbolic-flag "Hyp " "")
1449 (if calc-keep-args-flag "Keep " "")
1450 (if (/= calc-stack-top 1) "Narrow " "")
1451 (apply 'concat calc-other-modes)))))
1452 (if (equal new-mode-string mode-line-buffer-identification)
1454 (setq mode-line-buffer-identification new-mode-string)
1455 (set-buffer-modified-p (buffer-modified-p))
1456 (and calc-embedded-info (calc-embedded-mode-line-change))))))
1458 (defun calc-align-stack-window ()
1459 (if (eq major-mode 'calc-mode)
1461 (let ((win (get-buffer-window (current-buffer))))
1464 (calc-cursor-stack-index 0)
1465 (vertical-motion (- 2 (window-height win)))
1466 (set-window-start win (point)))))
1467 (calc-cursor-stack-index 0)
1468 (if (looking-at " *\\.$")
1469 (goto-char (1- (match-end 0)))))
1471 (calc-select-buffer)
1472 (calc-align-stack-window))))
1474 (defun calc-check-stack (n)
1475 (if (> n (calc-stack-size))
1476 (error "Too few elements on stack"))
1478 (error "Invalid argument")))
1480 (defun calc-push-list (vals &optional m sels)
1482 (if calc-executing-macro
1483 (calc-push-list-in-macro vals m sels)
1485 (calc-select-buffer)
1486 (let* ((val (car vals))
1487 (entry (list val 1 (car sels)))
1488 (mm (+ (or m 1) calc-stack-top)))
1489 (calc-cursor-stack-index (1- (or m 1)))
1491 (setcdr (nthcdr (- mm 2) calc-stack)
1492 (cons entry (nthcdr (1- mm) calc-stack)))
1493 (setq calc-stack (cons entry calc-stack)))
1494 (let ((buffer-read-only nil))
1495 (insert (math-format-stack-value entry) "\n"))
1496 (calc-record-undo (list 'push mm))
1497 (calc-set-command-flag 'renum-stack))))
1498 (setq vals (cdr vals)
1501 (defun calc-pop-push-list (n vals &optional m sels)
1502 (if (and calc-any-selections (null sels))
1503 (calc-replace-selections n vals m)
1504 (calc-pop-stack n m sels)
1505 (calc-push-list vals m sels)))
1507 (defun calc-pop-push-record-list (n prefix vals &optional m sels)
1508 (or (and (consp vals)
1509 (or (integerp (car vals))
1510 (consp (car vals))))
1511 (and vals (setq vals (list vals)
1512 sels (and sels (list sels)))))
1513 (calc-check-stack (+ n (or m 1) -1))
1516 (calc-record-list vals prefix)
1517 (calc-record (car vals) prefix)))
1518 (calc-pop-push-list n vals m sels))
1520 (defun calc-enter-result (n prefix vals &optional m)
1521 (setq calc-aborted-prefix prefix)
1522 (if (and (consp vals)
1523 (or (integerp (car vals))
1524 (consp (car vals))))
1525 (setq vals (mapcar 'calc-normalize vals))
1526 (setq vals (calc-normalize vals)))
1527 (or (and (consp vals)
1528 (or (integerp (car vals))
1529 (consp (car vals))))
1530 (setq vals (list vals)))
1531 (if (equal vals '((nil)))
1533 (calc-pop-push-record-list n prefix vals m)
1536 (defun calc-normalize (val)
1537 (if (memq calc-simplify-mode '(nil none num))
1538 (math-normalize val)
1540 (calc-normalize-fancy val)))
1542 (defun calc-handle-whys ()
1544 (calc-do-handle-whys)))
1547 (defun calc-pop-stack (&optional n m sel-ok) ; pop N objs at level M of stack.
1550 (or calc-keep-args-flag
1551 (let ((mm (+ m calc-stack-top)))
1552 (if (and calc-any-selections (not sel-ok)
1553 (calc-top-selected n m))
1555 (if calc-executing-macro
1556 (calc-pop-stack-in-macro n mm)
1557 (calc-record-undo (list 'pop mm (calc-top-list n m 'full)))
1559 (calc-select-buffer)
1560 (let ((buffer-read-only nil))
1563 (calc-cursor-stack-index (1- m))
1564 (let ((bot (point)))
1565 (calc-cursor-stack-index (+ n m -1))
1566 (delete-region (point) bot))
1567 (setcdr (nthcdr (- mm 2) calc-stack)
1568 (nthcdr (+ n mm -1) calc-stack)))
1569 (calc-cursor-stack-index n)
1570 (setq calc-stack (nthcdr n calc-stack))
1571 (delete-region (point) (point-max))))
1572 (calc-set-command-flag 'renum-stack))))))
1575 (defun calc-get-stack-element (x)
1576 (cond ((eq sel-mode 'entry)
1580 ((or (null (nth 2 x))
1582 (not calc-use-selections))
1588 ;; Get the Nth element of the stack (N=1 is the top element).
1589 (defun calc-top (&optional n sel-mode)
1591 (calc-check-stack n)
1592 (calc-get-stack-element (nth (+ n calc-stack-top -1) calc-stack)))
1594 (defun calc-top-n (&optional n sel-mode) ; in case precision has changed
1595 (math-check-complete (calc-normalize (calc-top n sel-mode))))
1597 (defun calc-top-list (&optional n m sel-mode)
1600 (calc-check-stack (+ n m -1))
1602 (let ((top (copy-sequence (nthcdr (+ m calc-stack-top -1)
1604 (setcdr (nthcdr (1- n) top) nil)
1605 (nreverse (mapcar 'calc-get-stack-element top)))))
1607 (defun calc-top-list-n (&optional n m sel-mode)
1608 (mapcar 'math-check-complete
1609 (mapcar 'calc-normalize (calc-top-list n m sel-mode))))
1612 (defun calc-renumber-stack ()
1613 (if calc-line-numbering
1615 (calc-cursor-stack-index 0)
1617 (buffer-read-only nil)
1618 (stack (nthcdr calc-stack-top calc-stack)))
1619 (if (re-search-forward "^[0-9]+[:*]" nil t)
1622 (while (re-search-forward "^[0-9]+[:*]" nil t)
1623 (let ((buffer-read-only nil))
1627 (calc-cursor-stack-index 0)))
1628 (while (re-search-backward "^[0-9]+[:*]" nil t)
1631 (insert (format "%03d%s" (% lnum 1000)
1632 (if (and (nth 2 (car stack))
1633 calc-use-selections) "*" ":")))
1634 (let ((prefix (int-to-string lnum)))
1635 (insert prefix (if (and (nth 2 (car stack))
1636 calc-use-selections) "*" ":")
1637 (make-string (- 3 (length prefix)) 32))))
1639 (setq lnum (1+ lnum)
1640 stack (cdr stack))))))
1641 (and calc-embedded-info (calc-embedded-stack-change)))
1643 (defvar calc-any-evaltos nil)
1644 (defun calc-refresh (&optional align)
1646 (and (eq major-mode 'calc-mode)
1647 (not calc-executing-macro)
1648 (let* ((buffer-read-only nil)
1649 (save-point (point))
1650 (save-mark (condition-case err (mark) (error nil)))
1651 (save-aligned (looking-at "\\.$"))
1653 (calc-any-evaltos nil))
1654 (setq calc-any-selections nil)
1656 (when calc-show-banner
1657 (insert (propertize "--- Emacs Calculator Mode ---\n"
1658 'font-lock-face 'italic)))
1660 (goto-char (point-min))
1661 (when calc-show-banner
1663 (insert (math-format-stack-value (car thing)) "\n")
1664 (setq thing (cdr thing)))
1665 (calc-renumber-stack)
1666 (if calc-display-dirty
1667 (calc-wrapper (setq calc-display-dirty nil)))
1668 (and calc-any-evaltos calc-auto-recompute
1669 (calc-wrapper (calc-refresh-evaltos)))
1670 (if (or align save-aligned)
1671 (calc-align-stack-window)
1672 (goto-char save-point))
1673 (if save-mark (set-mark save-mark))))
1674 (and calc-embedded-info (not (eq major-mode 'calc-mode))
1676 (set-buffer (aref calc-embedded-info 1))
1677 (calc-refresh align)))
1678 (setq calc-refresh-count (1+ calc-refresh-count)))
1680 ;;;; The Calc Trail buffer.
1682 (defun calc-check-trail-aligned ()
1684 (let ((win (get-buffer-window (current-buffer))))
1686 (pos-visible-in-window-p (1- (point-max)) win)))))
1688 (defun calc-trail-buffer ()
1689 (and (or (null calc-trail-buffer)
1690 (null (buffer-name calc-trail-buffer)))
1692 (setq calc-trail-buffer (get-buffer-create "*Calc Trail*"))
1693 (let ((buf (or (and (not (eq major-mode 'calc-mode))
1694 (get-buffer "*Calculator*"))
1696 (set-buffer calc-trail-buffer)
1697 (or (eq major-mode 'calc-trail-mode)
1698 (calc-trail-mode buf)))))
1699 (or (and calc-trail-pointer
1700 (eq (marker-buffer calc-trail-pointer) calc-trail-buffer))
1702 (set-buffer calc-trail-buffer)
1704 (setq calc-trail-pointer (point-marker))))
1707 (defun calc-record (val &optional prefix)
1708 (setq calc-aborted-prefix nil)
1709 (or calc-executing-macro
1710 (let* ((mainbuf (current-buffer))
1711 (buf (calc-trail-buffer))
1712 (calc-display-raw nil)
1713 (calc-can-abbrev-vectors t)
1717 (math-showing-full-precision
1718 (math-format-flat-expr val 0)))
1722 (let ((aligned (calc-check-trail-aligned))
1723 (buffer-read-only nil))
1724 (goto-char (point-max))
1725 (cond ((null prefix) (insert " "))
1726 ((and (> (length prefix) 4)
1727 (string-match " " prefix 4))
1728 (insert (substring prefix 0 4) " "))
1729 (t (insert (format "%4s " prefix))))
1731 (let ((win (get-buffer-window buf)))
1732 (if (and aligned win (not (memq 'hold-trail calc-command-flags)))
1734 (goto-char (1- (point-max))))))))
1738 (defun calc-trail-display (flag &optional no-refresh interactive)
1739 (interactive "P\ni\np")
1740 (let ((win (get-buffer-window (calc-trail-buffer))))
1741 (if (setq calc-display-trail
1742 (not (if flag (memq flag '(nil 0)) win)))
1745 (let ((w (split-window nil (/ (* (window-width) 2) 3) t)))
1746 (set-window-buffer w calc-trail-buffer))
1748 (setq overlay-arrow-string calc-trail-overlay
1749 overlay-arrow-position calc-trail-pointer)
1761 (calc-refresh))))))))
1764 (defun calc-trail-here ()
1766 (if (eq major-mode 'calc-trail-mode)
1773 (if (or (bobp) (eobp))
1774 (setq overlay-arrow-position nil) ; trail is empty
1775 (set-marker calc-trail-pointer (point) (current-buffer))
1776 (setq calc-trail-overlay (concat (buffer-substring (point)
1779 overlay-arrow-string calc-trail-overlay
1780 overlay-arrow-position calc-trail-pointer)
1782 (let ((win (get-buffer-window (current-buffer))))
1785 (forward-line (/ (window-height win) 2))
1786 (forward-line (- 1 (window-height win)))
1787 (set-window-start win (point))
1788 (set-window-point win (+ calc-trail-pointer 4))
1789 (set-buffer calc-main-buffer)
1790 (setq overlay-arrow-string calc-trail-overlay
1791 overlay-arrow-position calc-trail-pointer))))))
1792 (error "Not in Calc Trail buffer")))
1799 (defun calc-record-undo (rec)
1800 (or calc-executing-macro
1801 (if (memq 'undo calc-command-flags)
1802 (setq calc-undo-list (cons (cons rec (car calc-undo-list))
1803 (cdr calc-undo-list)))
1804 (setq calc-undo-list (cons (list rec) calc-undo-list)
1806 (calc-set-command-flag 'undo))))
1811 ;;; Arithmetic commands.
1813 (defun calc-binary-op (name func arg &optional ident unary func2)
1814 (setq calc-aborted-prefix name)
1816 (calc-enter-result 2 name (cons (or func2 func)
1817 (mapcar 'math-check-complete
1818 (calc-top-list 2))))
1820 (calc-binary-op-fancy name func arg ident unary)))
1822 (defun calc-unary-op (name func arg &optional func2)
1823 (setq calc-aborted-prefix name)
1825 (calc-enter-result 1 name (list (or func2 func)
1826 (math-check-complete (calc-top 1))))
1828 (calc-unary-op-fancy name func arg)))
1831 (defun calc-plus (arg)
1834 (calc-binary-op "+" 'calcFunc-add arg 0 nil '+)))
1836 (defun calc-minus (arg)
1839 (calc-binary-op "-" 'calcFunc-sub arg 0 'neg '-)))
1841 (defun calc-times (arg)
1844 (calc-binary-op "*" 'calcFunc-mul arg 1 nil '*)))
1846 (defun calc-divide (arg)
1849 (calc-binary-op "/" 'calcFunc-div arg 0 'calcFunc-inv '/)))
1852 (defun calc-change-sign (arg)
1855 (calc-unary-op "chs" 'neg arg)))
1859 ;;; Stack management commands.
1861 (defun calc-enter (n)
1865 (calc-push-list (calc-top-list 1 (- n))))
1867 (calc-push-list (calc-top-list (calc-stack-size))))
1869 (calc-push-list (calc-top-list n))))))
1875 (let* ((nn (prefix-numeric-value n))
1876 (top (and (null n) (calc-top 1))))
1877 (cond ((and (null n)
1878 (eq (car-safe top) 'incomplete)
1879 (> (length top) (if (eq (nth 1 top) 'intv) 3 2)))
1880 (calc-pop-push-list 1 (let ((tt (copy-sequence top)))
1881 (setcdr (nthcdr (- (length tt) 2) tt) nil)
1884 (if (and calc-any-selections
1885 (calc-top-selected 1 (- nn)))
1886 (calc-delete-selection (- nn))
1887 (calc-pop-stack 1 (- nn) t)))
1889 (calc-pop-stack (calc-stack-size) 1 t))
1891 (if (and calc-any-selections
1893 (calc-top-selected 1 1))
1894 (calc-delete-selection 1)
1895 (calc-pop-stack nn)))))))
1900 ;;;; Reading a number using the minibuffer.
1901 (defvar calc-buffer)
1902 (defvar calc-prev-char)
1903 (defvar calc-prev-prev-char)
1904 (defvar calc-digit-value)
1905 (defun calcDigit-start ()
1908 (if (or calc-algebraic-mode
1909 (and (> calc-number-radix 14) (eq last-command-char ?e)))
1910 (calc-alg-digit-entry)
1911 (calc-unread-command)
1912 (setq calc-aborted-prefix nil)
1913 (let* ((calc-digit-value nil)
1914 (calc-prev-char nil)
1915 (calc-prev-prev-char nil)
1916 (calc-buffer (current-buffer))
1917 (buf (if calc-emacs-type-lucid
1919 (catch 'execute-kbd-macro
1921 (read-from-minibuffer
1922 "Calc: " "" calc-digit-map)))
1923 (error "Lucid Emacs requires RET after %s"
1924 "digit entry in kbd macro"))
1925 (let ((old-esc (lookup-key global-map "\e")))
1928 (define-key global-map "\e" nil)
1929 (read-from-minibuffer "Calc: " "" calc-digit-map))
1930 (define-key global-map "\e" old-esc))))))
1931 (or calc-digit-value (setq calc-digit-value (math-read-number buf)))
1932 (if (stringp calc-digit-value)
1933 (calc-alg-entry calc-digit-value)
1934 (if calc-digit-value
1935 (calc-push-list (list (calc-record (calc-normalize
1936 calc-digit-value))))))
1937 (if (eq calc-prev-char 'dots)
1942 (defsubst calc-minibuffer-size ()
1943 (- (point-max) (minibuffer-prompt-end)))
1945 (defun calcDigit-nondigit ()
1947 ;; Exercise for the reader: Figure out why this is a good precaution!
1948 (or (boundp 'calc-buffer)
1949 (use-local-map minibuffer-local-map))
1950 (let ((str (minibuffer-contents)))
1951 (setq calc-digit-value (save-excursion
1952 (set-buffer calc-buffer)
1953 (math-read-number str))))
1954 (if (and (null calc-digit-value) (> (calc-minibuffer-size) 0))
1957 (calc-temp-minibuffer-message " [Bad format]"))
1958 (or (memq last-command-char '(32 13))
1959 (progn (setq prefix-arg current-prefix-arg)
1960 (calc-unread-command (if (and (eq last-command-char 27)
1961 (>= last-input-char 128))
1967 (defun calc-minibuffer-contains (rex)
1969 (goto-char (minibuffer-prompt-end))
1972 (defun calcDigit-key ()
1974 (goto-char (point-max))
1975 (if (or (and (memq last-command-char '(?+ ?-))
1977 (/= (preceding-char) ?e))
1978 (and (memq last-command-char '(?m ?s))
1979 (not (calc-minibuffer-contains "[-+]?[0-9]+\\.?0*[@oh].*"))
1980 (not (calc-minibuffer-contains "[-+]?\\(1[1-9]\\|[2-9][0-9]\\)#.*"))))
1981 (calcDigit-nondigit)
1982 (if (calc-minibuffer-contains "\\([-+]?\\|.* \\)\\'")
1983 (cond ((memq last-command-char '(?. ?@)) (insert "0"))
1984 ((and (memq last-command-char '(?o ?h ?m))
1985 (not (calc-minibuffer-contains ".*#.*"))) (insert "0"))
1986 ((memq last-command-char '(?: ?e)) (insert "1"))
1987 ((eq last-command-char ?#)
1988 (insert (int-to-string calc-number-radix)))))
1989 (if (and (calc-minibuffer-contains "\\([-+]?[0-9]+#\\|[^:]*:\\)\\'")
1990 (eq last-command-char ?:))
1992 (if (and (calc-minibuffer-contains "[-+]?[0-9]+#\\'")
1993 (eq last-command-char ?.))
1995 (if (and (calc-minibuffer-contains "[-+]?0*\\([2-9]\\|1[0-4]\\)#\\'")
1996 (eq last-command-char ?e))
1998 (if (or (and (memq last-command-char '(?h ?o ?m ?s ?p))
1999 (calc-minibuffer-contains ".*#.*"))
2000 (and (eq last-command-char ?e)
2001 (calc-minibuffer-contains "[-+]?\\(1[5-9]\\|[2-9][0-9]\\)#.*"))
2002 (and (eq last-command-char ?n)
2003 (calc-minibuffer-contains "[-+]?\\(2[4-9]\\|[3-9][0-9]\\)#.*")))
2004 (setq last-command-char (upcase last-command-char)))
2006 ((memq last-command-char '(?_ ?n))
2007 (goto-char (minibuffer-prompt-end))
2008 (if (and (search-forward " +/- " nil t)
2009 (not (search-forward "e" nil t)))
2011 (and (not (calc-minibuffer-contains "[-+]?\\(1[5-9]\\|[2-9][0-9]\\)#.*"))
2012 (search-forward "e" nil t))
2013 (if (looking-at "+")
2015 (if (looking-at "-")
2018 (goto-char (point-max)))
2019 ((eq last-command-char ?p)
2020 (if (or (calc-minibuffer-contains ".*\\+/-.*")
2021 (calc-minibuffer-contains ".*mod.*")
2022 (calc-minibuffer-contains ".*#.*")
2023 (calc-minibuffer-contains ".*[-+e:]\\'"))
2025 (if (not (calc-minibuffer-contains ".* \\'"))
2028 ((and (eq last-command-char ?M)
2029 (not (calc-minibuffer-contains
2030 "[-+]?\\(2[3-9]\\|[3-9][0-9]\\)#.*")))
2031 (if (or (calc-minibuffer-contains ".*\\+/-.*")
2032 (calc-minibuffer-contains ".*mod *[^ ]+")
2033 (calc-minibuffer-contains ".*[-+e:]\\'"))
2035 (if (calc-minibuffer-contains ".*mod \\'")
2036 (if calc-previous-modulo
2037 (insert (math-format-flat-expr calc-previous-modulo 0))
2039 (if (not (calc-minibuffer-contains ".* \\'"))
2043 (insert (char-to-string last-command-char))
2044 (if (or (and (calc-minibuffer-contains "[-+]?\\(.*\\+/- *\\|.*mod *\\)?\\([0-9][0-9]?\\)#[0-9a-zA-Z]*\\(:[0-9a-zA-Z]*\\(:[0-9a-zA-Z]*\\)?\\|.[0-9a-zA-Z]*\\(e[-+]?[0-9]*\\)?\\)?\\'")
2045 (let ((radix (string-to-int
2047 (match-beginning 2) (match-end 2)))))
2050 (or (memq last-command-char '(?# ?: ?. ?e ?+ ?-))
2051 (let ((dig (math-read-radix-digit
2052 (upcase last-command-char))))
2055 (calc-minibuffer-contains
2056 "[-+]?\\(.*\\+/- *\\|.*mod *\\)?\\([0-9]+\\.?0*[@oh] *\\)?\\([0-9]+\\.?0*['m] *\\)?[0-9]*\\(\\.?[0-9]*\\(e[-+]?[0-3]?[0-9]?[0-9]?[0-9]?[0-9]?[0-9]?[0-9]?\\)?\\|[0-9]:\\([0-9]+:\\)?[0-9]*\\)?[\"s]?\\'"))
2057 (if (and (memq last-command-char '(?@ ?o ?h ?\' ?m))
2058 (string-match " " calc-hms-format))
2060 (if (and (eq this-command last-command)
2061 (eq last-command-char ?.))
2065 (delete-backward-char 1)
2067 (calc-temp-minibuffer-message " [Bad format]"))))))
2068 (setq calc-prev-prev-char calc-prev-char
2069 calc-prev-char last-command-char))
2072 (defun calcDigit-backspace ()
2074 (goto-char (point-max))
2075 (cond ((calc-minibuffer-contains ".* \\+/- \\'")
2076 (backward-delete-char 5))
2077 ((calc-minibuffer-contains ".* mod \\'")
2078 (backward-delete-char 5))
2079 ((calc-minibuffer-contains ".* \\'")
2080 (backward-delete-char 2))
2081 ((eq last-command 'calcDigit-start)
2083 (t (backward-delete-char 1)))
2084 (if (= (calc-minibuffer-size) 0)
2086 (setq last-command-char 13)
2087 (calcDigit-nondigit))))
2095 ;;;; Arithmetic routines.
2097 ;;; An object as manipulated by one of these routines may take any of the
2098 ;;; following forms:
2100 ;;; integer An integer. For normalized numbers, this format
2101 ;;; is used only for -999999 ... 999999.
2103 ;;; (bigpos N0 N1 N2 ...) A big positive integer, N0 + N1*1000 + N2*10^6 ...
2104 ;;; (bigneg N0 N1 N2 ...) A big negative integer, - N0 - N1*1000 ...
2105 ;;; Each digit N is in the range 0 ... 999.
2106 ;;; Normalized, always at least three N present,
2107 ;;; and the most significant N is nonzero.
2109 ;;; (frac NUM DEN) A fraction. NUM and DEN are small or big integers.
2110 ;;; Normalized, DEN > 1.
2112 ;;; (float NUM EXP) A floating-point number, NUM * 10^EXP;
2113 ;;; NUM is a small or big integer, EXP is a small int.
2114 ;;; Normalized, NUM is not a multiple of 10, and
2115 ;;; abs(NUM) < 10^calc-internal-prec.
2116 ;;; Normalized zero is stored as (float 0 0).
2118 ;;; (cplx REAL IMAG) A complex number; REAL and IMAG are any of above.
2119 ;;; Normalized, IMAG is nonzero.
2121 ;;; (polar R THETA) Polar complex number. Normalized, R > 0 and THETA
2122 ;;; is neither zero nor 180 degrees (pi radians).
2124 ;;; (vec A B C ...) Vector of objects A, B, C, ... A matrix is a
2125 ;;; vector of vectors.
2127 ;;; (hms H M S) Angle in hours-minutes-seconds form. All three
2128 ;;; components have the same sign; H and M must be
2129 ;;; numerically integers; M and S are expected to
2130 ;;; lie in the range [0,60).
2132 ;;; (date N) A date or date/time object. N is an integer to
2133 ;;; store a date only, or a fraction or float to
2134 ;;; store a date and time.
2136 ;;; (sdev X SIGMA) Error form, X +/- SIGMA. When normalized,
2137 ;;; SIGMA > 0. X is any complex number and SIGMA
2138 ;;; is real numbers; or these may be symbolic
2139 ;;; expressions where SIGMA is assumed real.
2141 ;;; (intv MASK LO HI) Interval form. MASK is 0=(), 1=(], 2=[), or 3=[].
2142 ;;; LO and HI are any real numbers, or symbolic
2143 ;;; expressions which are assumed real, and LO < HI.
2144 ;;; For [LO..HI], if LO = HI normalization produces LO,
2145 ;;; and if LO > HI normalization produces [LO..LO).
2146 ;;; For other intervals, if LO > HI normalization
2147 ;;; sets HI equal to LO.
2149 ;;; (mod N M) Number modulo M. When normalized, 0 <= N < M.
2150 ;;; N and M are real numbers.
2152 ;;; (var V S) Symbolic variable. V is a Lisp symbol which
2153 ;;; represents the variable's visible name. S is
2154 ;;; the symbol which actually stores the variable's
2155 ;;; value: (var pi var-pi).
2157 ;;; In general, combining rational numbers in a calculation always produces
2158 ;;; a rational result, but if either argument is a float, result is a float.
2160 ;;; In the following comments, [x y z] means result is x, args must be y, z,
2161 ;;; respectively, where the code letters are:
2163 ;;; O Normalized object (vector or number)
2164 ;;; V Normalized vector
2165 ;;; N Normalized number of any type
2166 ;;; N Normalized complex number
2167 ;;; R Normalized real number (float or rational)
2168 ;;; F Normalized floating-point number
2169 ;;; T Normalized rational number
2170 ;;; I Normalized integer
2171 ;;; B Normalized big integer
2172 ;;; S Normalized small integer
2173 ;;; D Digit (small integer, 0..999)
2174 ;;; L Normalized bignum digit list (without "bigpos" or "bigneg" symbol)
2175 ;;; or normalized vector element list (without "vec")
2176 ;;; P Predicate (truth value)
2177 ;;; X Any Lisp object
2180 ;;; Lower-case letters signify possibly un-normalized values.
2181 ;;; "L.D" means a cons of an L and a D.
2182 ;;; [N N; n n] means result will be normalized if argument is.
2183 ;;; Also, [Public] marks routines intended to be called from outside.
2184 ;;; [This notation has been neglected in many recent routines.]
2186 (defvar math-eval-rules-cache)
2187 (defvar math-eval-rules-cache-other)
2188 ;;; Reduce an object to canonical (normalized) form. [O o; Z Z] [Public]
2190 (defvar math-normalize-a)
2191 (defun math-normalize (math-normalize-a)
2193 ((not (consp math-normalize-a))
2194 (if (integerp math-normalize-a)
2195 (if (or (>= math-normalize-a 1000000) (<= math-normalize-a -1000000))
2196 (math-bignum math-normalize-a)
2199 ((eq (car math-normalize-a) 'bigpos)
2200 (if (eq (nth (1- (length math-normalize-a)) math-normalize-a) 0)
2201 (let* ((last (setq math-normalize-a
2202 (copy-sequence math-normalize-a))) (digs math-normalize-a))
2203 (while (setq digs (cdr digs))
2204 (or (eq (car digs) 0) (setq last digs)))
2206 (if (cdr (cdr (cdr math-normalize-a)))
2209 ((cdr (cdr math-normalize-a)) (+ (nth 1 math-normalize-a)
2210 (* (nth 2 math-normalize-a) 1000)))
2211 ((cdr math-normalize-a) (nth 1 math-normalize-a))
2213 ((eq (car math-normalize-a) 'bigneg)
2214 (if (eq (nth (1- (length math-normalize-a)) math-normalize-a) 0)
2215 (let* ((last (setq math-normalize-a (copy-sequence math-normalize-a)))
2216 (digs math-normalize-a))
2217 (while (setq digs (cdr digs))
2218 (or (eq (car digs) 0) (setq last digs)))
2220 (if (cdr (cdr (cdr math-normalize-a)))
2223 ((cdr (cdr math-normalize-a)) (- (+ (nth 1 math-normalize-a)
2224 (* (nth 2 math-normalize-a) 1000))))
2225 ((cdr math-normalize-a) (- (nth 1 math-normalize-a)))
2227 ((eq (car math-normalize-a) 'float)
2228 (math-make-float (math-normalize (nth 1 math-normalize-a))
2229 (nth 2 math-normalize-a)))
2230 ((or (memq (car math-normalize-a)
2231 '(frac cplx polar hms date mod sdev intv vec var quote
2232 special-const calcFunc-if calcFunc-lambda
2233 calcFunc-quote calcFunc-condition
2235 (integerp (car math-normalize-a))
2236 (and (consp (car math-normalize-a))
2237 (not (eq (car (car math-normalize-a)) 'lambda))))
2239 (math-normalize-fancy math-normalize-a))
2241 (or (and calc-simplify-mode
2243 (math-normalize-nonstandard))
2244 (let ((args (mapcar 'math-normalize (cdr math-normalize-a))))
2245 (or (condition-case err
2247 (assq (car math-normalize-a) '( ( + . math-add )
2254 ( | . math-concat ) ))))
2255 (or (and var-EvalRules
2257 (or (eq var-EvalRules math-eval-rules-cache-tag)
2260 (math-recompile-eval-rules)))
2261 (and (or math-eval-rules-cache-other
2262 (assq (car math-normalize-a)
2263 math-eval-rules-cache))
2264 (math-apply-rewrites
2265 (cons (car math-normalize-a) args)
2266 (cdr math-eval-rules-cache)
2267 nil math-eval-rules-cache))))
2269 (apply (cdr func) args)
2270 (and (or (consp (car math-normalize-a))
2271 (fboundp (car math-normalize-a))
2272 (and (not (featurep 'calc-ext))
2274 (fboundp (car math-normalize-a))))
2275 (apply (car math-normalize-a) args)))))
2276 (wrong-number-of-arguments
2277 (calc-record-why "*Wrong number of arguments"
2278 (cons (car math-normalize-a) args))
2280 (wrong-type-argument
2282 (calc-record-why "Wrong type of argument"
2283 (cons (car math-normalize-a) args)))
2286 (calc-record-why "*Argument out of range"
2287 (cons (car math-normalize-a) args))
2290 (calc-record-why "No exact representation for result"
2291 (cons (car math-normalize-a) args))
2294 (calc-record-why "*Floating-point overflow occurred"
2295 (cons (car math-normalize-a) args))
2298 (calc-record-why "*Floating-point underflow occurred"
2299 (cons (car math-normalize-a) args))
2302 (if (eq (nth 1 err) 'var-EvalRules)
2304 (setq var-EvalRules nil)
2305 (math-normalize (cons (car math-normalize-a) args)))
2306 (calc-record-why "*Variable is void" (nth 1 err)))))
2307 (if (consp (car math-normalize-a))
2308 (math-dimension-error)
2309 (cons (car math-normalize-a) args))))))))
2313 ;;; True if A is a floating-point real or complex number. [P x] [Public]
2314 (defun math-floatp (a)
2315 (cond ((eq (car-safe a) 'float) t)
2316 ((memq (car-safe a) '(cplx polar mod sdev intv))
2317 (or (math-floatp (nth 1 a))
2318 (math-floatp (nth 2 a))
2319 (and (eq (car a) 'intv) (math-floatp (nth 3 a)))))
2320 ((eq (car-safe a) 'date)
2321 (math-floatp (nth 1 a)))))
2325 ;;; Verify that A is a complete object and return A. [x x] [Public]
2326 (defun math-check-complete (a)
2327 (cond ((integerp a) a)
2328 ((eq (car-safe a) 'incomplete)
2329 (calc-incomplete-error a))
2331 (t (error "Invalid data object encountered"))))
2335 ;;; Coerce integer A to be a bignum. [B S]
2336 (defun math-bignum (a)
2338 (cons 'bigpos (math-bignum-big a))
2339 (cons 'bigneg (math-bignum-big (- a)))))
2341 (defun math-bignum-big (a) ; [L s]
2344 (cons (% a 1000) (math-bignum-big (/ a 1000)))))
2347 ;;; Build a normalized floating-point number. [F I S]
2348 (defun math-make-float (mant exp)
2351 (let* ((ldiff (- calc-internal-prec (math-numdigs mant))))
2353 (setq mant (math-scale-rounding mant ldiff)
2354 exp (- exp ldiff))))
2356 (let ((digs (cdr mant)))
2357 (if (= (% (car digs) 10) 0)
2359 (while (= (car digs) 0)
2360 (setq digs (cdr digs)
2362 (while (= (% (car digs) 10) 0)
2363 (setq digs (math-div10-bignum digs)
2365 (setq mant (math-normalize (cons (car mant) digs))))))
2366 (while (= (% mant 10) 0)
2367 (setq mant (/ mant 10)
2369 (if (and (<= exp -4000000)
2370 (<= (+ exp (math-numdigs mant) -1) -4000000))
2371 (signal 'math-underflow nil)
2372 (if (and (>= exp 3000000)
2373 (>= (+ exp (math-numdigs mant) -1) 4000000))
2374 (signal 'math-overflow nil)
2375 (list 'float mant exp)))))
2377 (defun math-div10-bignum (a) ; [l l]
2379 (cons (+ (/ (car a) 10) (* (% (nth 1 a) 10) 100))
2380 (math-div10-bignum (cdr a)))
2381 (list (/ (car a) 10))))
2383 ;;; Coerce A to be a float. [F N; V V] [Public]
2384 (defun math-float (a)
2385 (cond ((Math-integerp a) (math-make-float a 0))
2386 ((eq (car a) 'frac) (math-div (math-float (nth 1 a)) (nth 2 a)))
2387 ((eq (car a) 'float) a)
2388 ((memq (car a) '(cplx polar vec hms date sdev mod))
2389 (cons (car a) (mapcar 'math-float (cdr a))))
2390 (t (math-float-fancy a))))
2394 (cond ((not (consp a)) (- a))
2395 ((eq (car a) 'bigpos) (cons 'bigneg (cdr a)))
2396 ((eq (car a) 'bigneg) (cons 'bigpos (cdr a)))
2397 ((memq (car a) '(frac float))
2398 (list (car a) (Math-integer-neg (nth 1 a)) (nth 2 a)))
2399 ((memq (car a) '(cplx vec hms date calcFunc-idn))
2400 (cons (car a) (mapcar 'math-neg (cdr a))))
2401 (t (math-neg-fancy a))))
2404 ;;; Compute the number of decimal digits in integer A. [S I]
2405 (defun math-numdigs (a)
2408 (let* ((len (1- (length a)))
2410 (+ (* len 3) (cond ((>= top 100) 0) ((>= top 10) -1) (t -2))))
2412 (cond ((>= a 100) (+ (math-numdigs (/ a 1000)) 3))
2418 (t (math-numdigs (- a))))))
2420 ;;; Multiply (with truncation toward 0) the integer A by 10^N. [I i S]
2421 (defun math-scale-int (a n)
2423 ((> n 0) (math-scale-left a n))
2424 (t (math-normalize (math-scale-right a (- n))))))
2426 (defun math-scale-left (a n) ; [I I S]
2430 (cons (car a) (math-scale-left-bignum (cdr a) n))
2432 (if (or (>= a 1000) (<= a -1000))
2433 (math-scale-left (math-bignum a) n)
2434 (math-scale-left (* a 1000) (- n 3)))
2436 (if (or (>= a 10000) (<= a -10000))
2437 (math-scale-left (math-bignum a) 2)
2439 (if (or (>= a 100000) (<= a -100000))
2440 (math-scale-left (math-bignum a) 1)
2443 (defun math-scale-left-bignum (a n)
2445 (while (>= (setq a (cons 0 a)
2448 (math-mul-bignum-digit a (if (= n 2) 100 10) 0)
2451 (defun math-scale-right (a n) ; [i i S]
2455 (cons (car a) (math-scale-right-bignum (cdr a) n))
2459 (- (math-scale-right (- a) n)))
2461 (while (and (> (setq a (/ a 1000)) 0)
2462 (>= (setq n (- n 3)) 3))))
2469 (defun math-scale-right-bignum (a n) ; [L L S; l l S]
2471 (setq a (nthcdr (/ n 3) a)
2474 (cdr (math-mul-bignum-digit a (if (= n 2) 10 100) 0))
2477 ;;; Multiply (with rounding) the integer A by 10^N. [I i S]
2478 (defun math-scale-rounding (a n)
2480 (math-scale-left a n))
2484 (let ((val (if (< n -3)
2485 (math-scale-right-bignum (cdr a) (- -3 n))
2487 (math-mul-bignum-digit (cdr a) 10 0)
2489 (math-mul-bignum-digit (cdr a) 100 0)
2490 (cdr a)))))) ; n = -3
2491 (if (and val (>= (car val) 500))
2493 (if (eq (car (cdr val)) 999)
2494 (math-add-bignum (cdr val) '(1))
2495 (cons (1+ (car (cdr val))) (cdr (cdr val))))
2500 (- (math-scale-rounding (- a) n))
2503 (/ (+ (math-scale-right a (- -1 n)) 5) 10))))))
2506 ;;; Compute the sum of A and B. [O O O] [Public]
2507 (defun math-add (a b)
2509 (and (not (or (consp a) (consp b)))
2512 (if (or (<= a -1000000) (>= a 1000000))
2515 (and (Math-zerop a) (not (eq (car-safe a) 'mod))
2516 (if (and (math-floatp a) (Math-ratp b)) (math-float b) b))
2517 (and (Math-zerop b) (not (eq (car-safe b) 'mod))
2518 (if (and (math-floatp b) (Math-ratp a)) (math-float a) a))
2519 (and (Math-objvecp a) (Math-objvecp b)
2521 (and (Math-integerp a) (Math-integerp b)
2523 (or (consp a) (setq a (math-bignum a)))
2524 (or (consp b) (setq b (math-bignum b)))
2525 (if (eq (car a) 'bigneg)
2526 (if (eq (car b) 'bigneg)
2527 (cons 'bigneg (math-add-bignum (cdr a) (cdr b)))
2529 (let ((diff (math-sub-bignum (cdr b) (cdr a))))
2531 (cons 'bigneg (math-sub-bignum (cdr a) (cdr b)))
2532 (cons 'bigpos diff)))))
2533 (if (eq (car b) 'bigneg)
2535 (let ((diff (math-sub-bignum (cdr a) (cdr b))))
2537 (cons 'bigneg (math-sub-bignum (cdr b) (cdr a)))
2538 (cons 'bigpos diff))))
2539 (cons 'bigpos (math-add-bignum (cdr a) (cdr b)))))))
2540 (and (Math-ratp a) (Math-ratp b)
2542 (calc-add-fractions a b))
2543 (and (Math-realp a) (Math-realp b)
2545 (or (and (consp a) (eq (car a) 'float))
2546 (setq a (math-float a)))
2547 (or (and (consp b) (eq (car b) 'float))
2548 (setq b (math-float b)))
2549 (math-add-float a b)))
2550 (and (require 'calc-ext)
2551 (math-add-objects-fancy a b))))
2552 (and (require 'calc-ext)
2553 (math-add-symb-fancy a b))))
2555 (defun math-add-bignum (a b) ; [L L L; l l l]
2558 (let* ((a (copy-sequence a)) (aa a) (carry nil) sum)
2561 (if (< (setq sum (+ (car aa) (car b))) 999)
2563 (setcar aa (1+ sum))
2565 (setcar aa (+ sum -999)))
2566 (if (< (setq sum (+ (car aa) (car b))) 1000)
2568 (setcar aa (+ sum -1000))
2574 (nconc a (math-add-bignum b '(1)))
2575 (while (eq (car aa) 999)
2580 (setcar aa (1+ (car aa)))
2589 (defun math-sub-bignum (a b) ; [l l l]
2592 (let* ((a (copy-sequence a)) (aa a) (borrow nil) sum diff)
2595 (if (>= (setq diff (- (car aa) (car b))) 1)
2597 (setcar aa (1- diff))
2599 (setcar aa (+ diff 999)))
2600 (if (>= (setq diff (- (car aa) (car b))) 0)
2602 (setcar aa (+ diff 1000))
2608 (while (eq (car aa) 0)
2613 (setcar aa (1- (car aa)))
2616 (while (eq (car b) 0)
2621 (while (eq (car b) 0)
2627 (defun math-add-float (a b) ; [F F F]
2628 (let ((ediff (- (nth 2 a) (nth 2 b))))
2630 (if (>= ediff (+ calc-internal-prec calc-internal-prec))
2632 (math-make-float (math-add (nth 1 b)
2635 (math-scale-left (nth 1 a) ediff)))
2637 (if (>= (setq ediff (- ediff))
2638 (+ calc-internal-prec calc-internal-prec))
2640 (math-make-float (math-add (nth 1 a)
2641 (math-scale-left (nth 1 b) ediff))
2644 ;;; Compute the difference of A and B. [O O O] [Public]
2645 (defun math-sub (a b)
2646 (if (or (consp a) (consp b))
2647 (math-add a (math-neg b))
2649 (if (or (<= a -1000000) (>= a 1000000))
2653 (defun math-sub-float (a b) ; [F F F]
2654 (let ((ediff (- (nth 2 a) (nth 2 b))))
2656 (if (>= ediff (+ calc-internal-prec calc-internal-prec))
2658 (math-make-float (math-add (Math-integer-neg (nth 1 b))
2661 (math-scale-left (nth 1 a) ediff)))
2663 (if (>= (setq ediff (- ediff))
2664 (+ calc-internal-prec calc-internal-prec))
2666 (math-make-float (math-add (nth 1 a)
2668 (math-scale-left (nth 1 b) ediff)))
2672 ;;; Compute the product of A and B. [O O O] [Public]
2673 (defun math-mul (a b)
2675 (and (not (consp a)) (not (consp b))
2676 (< a 1000) (> a -1000) (< b 1000) (> b -1000)
2678 (and (Math-zerop a) (not (eq (car-safe b) 'mod))
2679 (if (Math-scalarp b)
2680 (if (and (math-floatp b) (Math-ratp a)) (math-float a) a)
2682 (math-mul-zero a b)))
2683 (and (Math-zerop b) (not (eq (car-safe a) 'mod))
2684 (if (Math-scalarp a)
2685 (if (and (math-floatp a) (Math-ratp b)) (math-float b) b)
2687 (math-mul-zero b a)))
2688 (and (Math-objvecp a) (Math-objvecp b)
2690 (and (Math-integerp a) (Math-integerp b)
2692 (or (consp a) (setq a (math-bignum a)))
2693 (or (consp b) (setq b (math-bignum b)))
2695 (cons (if (eq (car a) (car b)) 'bigpos 'bigneg)
2698 (math-mul-bignum (cdr a) (cdr b))
2699 (math-mul-bignum-digit (cdr a) (nth 1 b) 0))
2700 (math-mul-bignum-digit (cdr b) (nth 1 a) 0))))))
2701 (and (Math-ratp a) (Math-ratp b)
2703 (calc-mul-fractions a b))
2704 (and (Math-realp a) (Math-realp b)
2706 (or (and (consp a) (eq (car a) 'float))
2707 (setq a (math-float a)))
2708 (or (and (consp b) (eq (car b) 'float))
2709 (setq b (math-float b)))
2710 (math-make-float (math-mul (nth 1 a) (nth 1 b))
2711 (+ (nth 2 a) (nth 2 b)))))
2712 (and (require 'calc-ext)
2713 (math-mul-objects-fancy a b))))
2714 (and (require 'calc-ext)
2715 (math-mul-symb-fancy a b))))
2717 (defun math-infinitep (a &optional undir)
2718 (while (and (consp a) (memq (car a) '(* / neg)))
2719 (if (or (not (eq (car a) '*)) (math-infinitep (nth 1 a)))
2721 (setq a (nth 2 a))))
2724 (memq (nth 2 a) '(var-inf var-uinf var-nan))
2725 (if (and undir (eq (nth 2 a) 'var-inf))
2726 '(var uinf var-uinf)
2729 ;;; Multiply digit lists A and B. [L L L; l l l]
2730 (defun math-mul-bignum (a b)
2732 (let* ((sum (if (<= (car b) 1)
2736 (math-mul-bignum-digit a (car b) 0)))
2737 (sump sum) c d aa ss prod)
2738 (while (setq b (cdr b))
2739 (setq ss (setq sump (or (cdr sump) (setcdr sump (list 0))))
2744 (setcar ss (% (setq prod (+ (+ (car ss) (* (car aa) d))
2747 (setq c (/ prod 1000)
2748 ss (or (cdr ss) (setcdr ss (list 0)))))
2751 (setcar (cdr ss) (+ (/ prod 1000) (car (cdr ss))))
2752 (setcdr ss (list (/ prod 1000))))))
2755 ;;; Multiply digit list A by digit D. [L L D D; l l D D]
2756 (defun math-mul-bignum-digit (a d c)
2760 (let* ((a (copy-sequence a)) (aa a) prod)
2762 (setcar aa (% (setq prod (+ (* (car aa) d) c)) 1000))
2767 (setcdr aa (list (/ prod 1000))))
2773 ;;; Compute the integer (quotient . remainder) of A and B, which may be
2774 ;;; small or big integers. Type and consistency of truncation is undefined
2775 ;;; if A or B is negative. B must be nonzero. [I.I I I] [Public]
2776 (defun math-idivmod (a b)
2778 (math-reject-arg a "*Division by zero"))
2779 (if (or (consp a) (consp b))
2780 (if (and (natnump b) (< b 1000))
2781 (let ((res (math-div-bignum-digit (cdr a) b)))
2783 (math-normalize (cons (car a) (car res)))
2785 (or (consp a) (setq a (math-bignum a)))
2786 (or (consp b) (setq b (math-bignum b)))
2787 (let ((res (math-div-bignum (cdr a) (cdr b))))
2789 (math-normalize (cons (if (eq (car a) (car b)) 'bigpos 'bigneg)
2791 (math-normalize (cons (car a) (cdr res))))))
2792 (cons (/ a b) (% a b))))
2794 (defun math-quotient (a b) ; [I I I] [Public]
2795 (if (and (not (consp a)) (not (consp b)))
2797 (math-reject-arg a "*Division by zero")
2799 (if (and (natnump b) (< b 1000))
2801 (math-reject-arg a "*Division by zero")
2802 (math-normalize (cons (car a)
2803 (car (math-div-bignum-digit (cdr a) b)))))
2804 (or (consp a) (setq a (math-bignum a)))
2805 (or (consp b) (setq b (math-bignum b)))
2806 (let* ((alen (1- (length a)))
2807 (blen (1- (length b)))
2808 (d (/ 1000 (1+ (nth (1- blen) (cdr b)))))
2809 (res (math-div-bignum-big (math-mul-bignum-digit (cdr a) d 0)
2810 (math-mul-bignum-digit (cdr b) d 0)
2812 (math-normalize (cons (if (eq (car a) (car b)) 'bigpos 'bigneg)
2816 ;;; Divide a bignum digit list by another. [l.l l L]
2817 ;;; The following division algorithm is borrowed from Knuth vol. II, sec. 4.3.1
2818 (defun math-div-bignum (a b)
2820 (let* ((alen (length a))
2822 (d (/ 1000 (1+ (nth (1- blen) b))))
2823 (res (math-div-bignum-big (math-mul-bignum-digit a d 0)
2824 (math-mul-bignum-digit b d 0)
2829 (car (math-div-bignum-digit (cdr res) d)))))
2830 (let ((res (math-div-bignum-digit a (car b))))
2831 (cons (car res) (list (cdr res))))))
2833 ;;; Divide a bignum digit list by a digit. [l.D l D]
2834 (defun math-div-bignum-digit (a b)
2836 (let* ((res (math-div-bignum-digit (cdr a) b))
2837 (num (+ (* (cdr res) 1000) (car a))))
2839 (cons (/ num b) (car res))
2843 (defun math-div-bignum-big (a b alen blen) ; [l.l l L]
2846 (let* ((res (math-div-bignum-big (cdr a) b (1- alen) blen))
2847 (num (cons (car a) (cdr res)))
2848 (res2 (math-div-bignum-part num b blen)))
2850 (cons (car res2) (car res))
2853 (defun math-div-bignum-part (a b blen) ; a < b*1000 [D.l l L]
2854 (let* ((num (+ (* (or (nth blen a) 0) 1000) (or (nth (1- blen) a) 0)))
2855 (den (nth (1- blen) b))
2856 (guess (min (/ num den) 999)))
2857 (math-div-bignum-try a b (math-mul-bignum-digit b guess 0) guess)))
2859 (defun math-div-bignum-try (a b c guess) ; [D.l l l D]
2860 (let ((rem (math-sub-bignum a c)))
2862 (math-div-bignum-try a b (math-sub-bignum c b) (1- guess))
2866 ;;; Compute the quotient of A and B. [O O N] [Public]
2867 (defun math-div (a b)
2871 (math-div-by-zero a b))
2872 (and (Math-zerop a) (not (eq (car-safe b) 'mod))
2873 (if (Math-scalarp b)
2874 (if (and (math-floatp b) (Math-ratp a)) (math-float a) a)
2876 (math-div-zero a b)))
2877 (and (Math-objvecp a) (Math-objvecp b)
2879 (and (Math-integerp a) (Math-integerp b)
2880 (let ((q (math-idivmod a b)))
2883 (if calc-prefer-frac
2886 (math-make-frac a b))
2887 (math-div-float (math-make-float a 0)
2888 (math-make-float b 0))))))
2889 (and (Math-ratp a) (Math-ratp b)
2891 (calc-div-fractions a b))
2892 (and (Math-realp a) (Math-realp b)
2894 (or (and (consp a) (eq (car a) 'float))
2895 (setq a (math-float a)))
2896 (or (and (consp b) (eq (car b) 'float))
2897 (setq b (math-float b)))
2898 (math-div-float a b)))
2899 (and (require 'calc-ext)
2900 (math-div-objects-fancy a b))))
2901 (and (require 'calc-ext)
2902 (math-div-symb-fancy a b))))
2904 (defun math-div-float (a b) ; [F F F]
2905 (let ((ldiff (max (- (1+ calc-internal-prec)
2906 (- (math-numdigs (nth 1 a)) (math-numdigs (nth 1 b))))
2908 (math-make-float (math-quotient (math-scale-int (nth 1 a) ldiff) (nth 1 b))
2909 (- (- (nth 2 a) (nth 2 b)) ldiff))))
2914 (defvar calc-selection-cache-entry)
2915 ;;; Format the number A as a string. [X N; X Z] [Public]
2916 (defun math-format-stack-value (entry)
2917 (setq calc-selection-cache-entry calc-selection-cache-default-entry)
2918 (let* ((a (car entry))
2919 (math-comp-selected (nth 2 entry))
2920 (c (cond ((null a) "<nil>")
2921 ((eq calc-display-raw t) (format "%s" a))
2923 ((eq a 'top-of-stack) (propertize "." 'font-lock-face 'bold))
2924 (calc-prepared-composition
2925 calc-prepared-composition)
2926 ((and (Math-scalarp a)
2927 (memq calc-language '(nil flat unform))
2928 (null math-comp-selected))
2929 (math-format-number a))
2930 (t (require 'calc-ext)
2931 (math-compose-expr a 0))))
2932 (off (math-stack-value-offset c))
2934 (and math-comp-selected (setq calc-any-selections t))
2938 (setq c (math-comp-concat (make-string off ? ) c)))
2939 (or (equal calc-left-label "")
2940 (setq c (math-comp-concat (if (eq a 'top-of-stack)
2941 (make-string (length calc-left-label) ? )
2944 (when calc-line-numbering
2945 (setq c (math-comp-concat (if (eq calc-language 'big)
2946 (if math-comp-selected
2951 (unless (or (equal calc-right-label "")
2952 (eq a 'top-of-stack))
2954 (setq c (list 'horiz c
2955 (make-string (max (- w (math-comp-width c)
2956 (length calc-right-label)) 0) ? )
2959 (setq s (if (stringp c)
2960 (if calc-display-raw
2963 (math-composition-to-string c w)))
2964 (when calc-language-output-filter
2965 (setq s (funcall calc-language-output-filter s)))
2966 (if (eq calc-language 'big)
2967 (setq s (concat s "\n"))
2968 (when calc-line-numbering
2969 (setq s (concat "1:" (substring s 2)))))
2970 (setcar (cdr entry) (calc-count-lines s))
2973 ;; The variables math-svo-c, math-svo-wid and math-svo-off are local
2974 ;; to math-stack-value-offset, but are used by math-stack-value-offset-fancy
2977 (defun math-stack-value-offset (math-svo-c)
2978 (let* ((num (if calc-line-numbering 4 0))
2979 (math-svo-wid (calc-window-width))
2981 (if calc-display-just
2984 (math-stack-value-offset-fancy))
2985 (setq math-svo-off (or calc-display-origin 0))
2986 (when (integerp calc-line-breaking)
2987 (setq math-svo-wid calc-line-breaking)))
2988 (cons (max (- math-svo-off (length calc-left-label)) 0)
2989 (+ math-svo-wid num))))
2991 (defun calc-count-lines (s)
2994 (while (setq pos (string-match "\n" s pos))
2999 (defun math-format-value (a &optional w)
3000 (if (and (Math-scalarp a)
3001 (memq calc-language '(nil flat unform)))
3002 (math-format-number a)
3004 (let ((calc-line-breaking nil))
3005 (math-composition-to-string (math-compose-expr a 0) w))))
3007 (defun calc-window-width ()
3008 (if calc-embedded-info
3009 (let ((win (get-buffer-window (aref calc-embedded-info 0))))
3010 (1- (if win (window-width win) (frame-width))))
3011 (- (window-width (get-buffer-window (current-buffer)))
3012 (if calc-line-numbering 5 1))))
3014 (defun math-comp-concat (c1 c2)
3015 (if (and (stringp c1) (stringp c2))
3017 (list 'horiz c1 c2)))
3021 ;;; Format an expression as a one-line string suitable for re-reading.
3023 (defun math-format-flat-expr (a prec)
3025 ((or (not (or (consp a) (integerp a)))
3026 (eq calc-display-raw t))
3027 (let ((print-escape-newlines t))
3028 (concat "'" (prin1-to-string a))))
3030 (let ((calc-group-digits nil)
3031 (calc-point-char ".")
3032 (calc-frac-format (if (> (length (car calc-frac-format)) 1)
3033 '("::" nil) '(":" nil)))
3034 (calc-complex-format nil)
3035 (calc-hms-format "%s@ %s' %s\"")
3036 (calc-language nil))
3037 (math-format-number a)))
3040 (math-format-flat-expr-fancy a prec))))
3044 ;;; Format a number as a string.
3045 (defun math-format-number (a &optional prec) ; [X N] [Public]
3047 ((eq calc-display-raw t) (format "%s" a))
3048 ((and (nth 1 calc-frac-format) (Math-integerp a))
3050 (math-format-number (math-adjust-fraction a)))
3052 (if (not (or calc-group-digits calc-leading-zeros))
3053 (if (= calc-number-radix 10)
3056 (concat "-" (math-format-number (- a)))
3058 (if math-radix-explicit-format
3059 (if calc-radix-formatter
3060 (funcall calc-radix-formatter
3062 (if (= calc-number-radix 2)
3063 (math-format-binary a)
3064 (math-format-radix a)))
3065 (format "%d#%s" calc-number-radix
3066 (if (= calc-number-radix 2)
3067 (math-format-binary a)
3068 (math-format-radix a))))
3069 (math-format-radix a))))
3070 (math-format-number (math-bignum a))))
3072 ((not (consp a)) (prin1-to-string a))
3073 ((eq (car a) 'bigpos) (math-format-bignum (cdr a)))
3074 ((eq (car a) 'bigneg) (concat "-" (math-format-bignum (cdr a))))
3075 ((and (eq (car a) 'float) (= calc-number-radix 10))
3076 (if (Math-integer-negp (nth 1 a))
3077 (concat "-" (math-format-number (math-neg a)))
3078 (let ((mant (nth 1 a))
3080 (fmt (car calc-float-format))
3081 (figs (nth 1 calc-float-format))
3082 (point calc-point-char)
3084 (if (and (eq fmt 'fix)
3085 (or (and (< figs 0) (setq figs (- figs)))
3086 (> (+ exp (math-numdigs mant)) (- figs))))
3088 (setq mant (math-scale-rounding mant (+ exp figs))
3089 str (if (integerp mant)
3090 (int-to-string mant)
3091 (math-format-bignum-decimal (cdr mant))))
3092 (if (<= (length str) figs)
3093 (setq str (concat (make-string (1+ (- figs (length str))) ?0)
3096 (setq str (concat (substring str 0 (- figs)) point
3097 (substring str (- figs))))
3098 (setq str (concat str point)))
3099 (when calc-group-digits
3101 (setq str (math-group-float str))))
3103 (setq figs (+ calc-internal-prec figs)))
3105 (let ((adj (- figs (math-numdigs mant))))
3107 (setq mant (math-scale-rounding mant adj)
3109 (setq str (if (integerp mant)
3110 (int-to-string mant)
3111 (math-format-bignum-decimal (cdr mant))))
3112 (let* ((len (length str))
3114 (if (and (eq fmt 'float)
3115 (<= dpos (+ calc-internal-prec calc-display-sci-high))
3116 (>= dpos (+ calc-display-sci-low 2)))
3120 (setq str (concat "0" point str)))
3121 ((and (<= exp 0) (> dpos 0))
3122 (setq str (concat (substring str 0 dpos) point
3123 (substring str dpos))))
3125 (setq str (concat str (make-string exp ?0) point)))
3127 (setq str (concat "0" point
3128 (make-string (- dpos) ?0) str))))
3129 (when calc-group-digits
3131 (setq str (math-group-float str))))
3132 (let* ((eadj (+ exp len))
3133 (scale (if (eq fmt 'eng)
3134 (1+ (math-mod (+ eadj 300002) 3))
3136 (if (> scale (length str))
3137 (setq str (concat str (make-string (- scale (length str))
3139 (if (< scale (length str))
3140 (setq str (concat (substring str 0 scale) point
3141 (substring str scale))))
3142 (when calc-group-digits
3144 (setq str (math-group-float str)))
3145 (setq str (format (if (memq calc-language '(math maple))
3146 (if (and prec (> prec 191))
3147 "(%s*10.^%d)" "%s*10.^%d")
3149 str (- eadj scale)))))))
3153 (math-format-number-fancy a prec))))
3155 (defun math-format-bignum (a) ; [X L]
3156 (if (and (= calc-number-radix 10)
3157 (not calc-leading-zeros)
3158 (not calc-group-digits))
3159 (math-format-bignum-decimal a)
3161 (math-format-bignum-fancy a)))
3163 (defun math-format-bignum-decimal (a) ; [X L]
3166 (while (cdr (cdr a))
3167 (setq s (concat (format "%06d" (+ (* (nth 1 a) 1000) (car a))) s)
3169 (concat (int-to-string (+ (* (or (nth 1 a) 0) 1000) (car a))) s))
3174 ;;; Parse a simple number in string form. [N X] [Public]
3175 (defun math-read-number (s)
3179 ;; Integers (most common case)
3180 ((string-match "\\` *\\([0-9]+\\) *\\'" s)
3181 (let ((digs (math-match-substring s 1)))
3182 (if (and (eq calc-language 'c)
3184 (eq (aref digs 0) ?0))
3185 (math-read-number (concat "8#" digs))
3186 (if (<= (length digs) 6)
3187 (string-to-int digs)
3188 (cons 'bigpos (math-read-bignum digs))))))
3190 ;; Clean up the string if necessary
3191 ((string-match "\\`\\(.*\\)[ \t\n]+\\([^\001]*\\)\\'" s)
3192 (math-read-number (concat (math-match-substring s 1)
3193 (math-match-substring s 2))))
3195 ;; Plus and minus signs
3196 ((string-match "^[-_+]\\(.*\\)$" s)
3197 (let ((val (math-read-number (math-match-substring s 1))))
3198 (and val (if (eq (aref s 0) ?+) val (math-neg val)))))
3200 ;; Forms that require extensions module
3201 ((string-match "[^-+0-9eE.]" s)
3203 (math-read-number-fancy s))
3206 ((string-match "^\\([0-9]*\\)\\.\\([0-9]*\\)$" s)
3207 (let ((int (math-match-substring s 1))
3208 (frac (math-match-substring s 2)))
3209 (let ((ilen (length int))
3210 (flen (length frac)))
3211 (let ((int (if (> ilen 0) (math-read-number int) 0))
3212 (frac (if (> flen 0) (math-read-number frac) 0)))
3213 (and int frac (or (> ilen 0) (> flen 0))
3215 (math-add (math-scale-int int flen) frac)
3219 ((string-match "^\\(.*\\)[eE]\\([-+]?[0-9]+\\)$" s)
3220 (let ((mant (math-match-substring s 1))
3221 (exp (math-match-substring s 2)))
3222 (let ((mant (if (> (length mant) 0) (math-read-number mant) 1))
3223 (exp (if (<= (length exp) (if (memq (aref exp 0) '(?+ ?-)) 8 7))
3224 (string-to-int exp))))
3225 (and mant exp (Math-realp mant) (> exp -4000000) (< exp 4000000)
3226 (let ((mant (math-float mant)))
3227 (list 'float (nth 1 mant) (+ (nth 2 mant) exp)))))))
3232 (defun math-match-substring (s n)
3233 (if (match-beginning n)
3234 (substring s (match-beginning n) (match-end n))
3237 (defun math-read-bignum (s) ; [l X]
3238 (if (> (length s) 3)
3239 (cons (string-to-int (substring s -3))
3240 (math-read-bignum (substring s 0 -3)))
3241 (list (string-to-int s))))
3244 (defconst math-tex-ignore-words
3245 '( ("\\hbox") ("\\mbox") ("\\text") ("\\left") ("\\right")
3246 ("\\,") ("\\>") ("\\:") ("\\;") ("\\!") ("\\ ")
3247 ("\\quad") ("\\qquad") ("\\hfil") ("\\hfill")
3248 ("\\displaystyle") ("\\textstyle") ("\\dsize") ("\\tsize")
3249 ("\\scriptstyle") ("\\scriptscriptstyle") ("\\ssize") ("\\sssize")
3250 ("\\rm") ("\\bf") ("\\it") ("\\sl")
3251 ("\\roman") ("\\bold") ("\\italic") ("\\slanted")
3252 ("\\cal") ("\\mit") ("\\Cal") ("\\Bbb") ("\\frak") ("\\goth")
3254 ("\\matrix" mat) ("\\bmatrix" mat) ("\\pmatrix" mat)
3255 ("\\cr" punc ";") ("\\\\" punc ";") ("\\*" punc "*")
3256 ("\\{" punc "[") ("\\}" punc "]")
3259 (defconst math-eqn-ignore-words
3260 '( ("roman") ("bold") ("italic") ("mark") ("lineup") ("evalto")
3261 ("left" ("floor") ("ceil"))
3262 ("right" ("floor") ("ceil"))
3263 ("arc" ("sin") ("cos") ("tan") ("sinh") ("cosh") ("tanh"))
3264 ("size" n) ("font" n) ("fwd" n) ("back" n) ("up" n) ("down" n)
3268 (defconst math-standard-opers
3269 '( ( "_" calcFunc-subscr 1200 1201 )
3270 ( "%" calcFunc-percent 1100 -1 )
3271 ( "u+" ident -1 1000 )
3272 ( "u-" neg -1 1000 197 )
3273 ( "u!" calcFunc-lnot -1 1000 )
3274 ( "mod" mod 400 400 185 )
3275 ( "+/-" sdev 300 300 185 )
3276 ( "!!" calcFunc-dfact 210 -1 )
3277 ( "!" calcFunc-fact 210 -1 )
3284 ( "\\" calcFunc-idiv 190 191 )
3288 ( "<" calcFunc-lt 160 161 )
3289 ( ">" calcFunc-gt 160 161 )
3290 ( "<=" calcFunc-leq 160 161 )
3291 ( ">=" calcFunc-geq 160 161 )
3292 ( "=" calcFunc-eq 160 161 )
3293 ( "==" calcFunc-eq 160 161 )
3294 ( "!=" calcFunc-neq 160 161 )
3295 ( "&&" calcFunc-land 110 111 )
3296 ( "||" calcFunc-lor 100 101 )
3297 ( "?" (math-read-if) 91 90 )
3298 ( "!!!" calcFunc-pnot -1 85 )
3299 ( "&&&" calcFunc-pand 80 81 )
3300 ( "|||" calcFunc-por 75 76 )
3301 ( ":=" calcFunc-assign 51 50 )
3302 ( "::" calcFunc-condition 45 46 )
3303 ( "=>" calcFunc-evalto 40 41 )
3304 ( "=>" calcFunc-evalto 40 -1 )))
3305 (defvar math-expr-opers math-standard-opers)
3308 (defun calc-grab-region (top bot arg)
3309 "Parse the region as a vector of numbers and push it on the Calculator stack."
3310 (interactive "r\nP")
3312 (calc-do-grab-region top bot arg))
3315 (defun calc-grab-rectangle (top bot arg)
3316 "Parse a rectangle as a matrix of numbers and push it on the Calculator stack."
3317 (interactive "r\nP")
3319 (calc-do-grab-rectangle top bot arg))
3321 (defun calc-grab-sum-down (top bot arg)
3322 "Parse a rectangle as a matrix of numbers and sum its columns."
3323 (interactive "r\nP")
3325 (calc-do-grab-rectangle top bot arg 'calcFunc-reduced))
3327 (defun calc-grab-sum-across (top bot arg)
3328 "Parse a rectangle as a matrix of numbers and sum its rows."
3329 (interactive "r\nP")
3331 (calc-do-grab-rectangle top bot arg 'calcFunc-reducea))
3335 (defun calc-embedded (arg &optional end obeg oend)
3336 "Start Calc Embedded mode on the formula surrounding point."
3339 (calc-do-embedded arg end obeg oend))
3342 (defun calc-embedded-activate (&optional arg cbuf)
3343 "Scan the current editing buffer for all embedded := and => formulas.
3344 Also looks for the equivalent TeX words, \\gets and \\evalto."
3346 (calc-do-embedded-activate arg cbuf))
3348 (defun calc-user-invocation ()
3350 (unless (stringp calc-invocation-macro)
3351 (error "Use `Z I' inside Calc to define a `M-# Z' keyboard macro"))
3352 (execute-kbd-macro calc-invocation-macro nil))
3354 ;;; User-programmability.
3357 (defmacro defmath (func args &rest body) ; [Public]
3359 (math-do-defmath func args body))
3361 ;;; Functions needed for Lucid Emacs support.
3363 (defun calc-read-key (&optional optkey)
3364 (cond (calc-emacs-type-lucid
3365 (let ((event (next-command-event)))
3366 (let ((key (event-to-character event t t)))
3367 (or key optkey (error "Expected a plain keystroke"))
3370 (let ((key (read-event)))
3373 (defun calc-unread-command (&optional input)
3374 (if (featurep 'xemacs)
3375 (setq unread-command-event
3376 (if (integerp input) (character-to-event input)
3377 (or input last-command-event)))
3378 (push (or input last-command-event) unread-command-events)))
3380 (defun calc-clear-unread-commands ()
3381 (if (featurep 'xemacs)
3382 (calc-emacs-type-lucid (setq unread-command-event nil))
3383 (setq unread-command-events nil)))
3385 (when calc-always-load-extensions
3387 (calc-load-everything))
3390 (run-hooks 'calc-load-hook)
3394 ;;; arch-tag: 0c3b170c-4ce6-4eaf-8d9b-5834d1fe938f
3395 ;;; calc.el ends here