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[emacs.git] / lisp / calc / calc-units.el
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1 ;;; calc-units.el --- unit conversion functions for Calc
2
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005, 2006 Free Software Foundation, Inc.
5
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <belanger@truman.edu>
8
9 ;; This file is part of GNU Emacs.
10
11 ;; GNU Emacs is distributed in the hope that it will be useful,
12 ;; but WITHOUT ANY WARRANTY. No author or distributor
13 ;; accepts responsibility to anyone for the consequences of using it
14 ;; or for whether it serves any particular purpose or works at all,
15 ;; unless he says so in writing. Refer to the GNU Emacs General Public
16 ;; License for full details.
17
18 ;; Everyone is granted permission to copy, modify and redistribute
19 ;; GNU Emacs, but only under the conditions described in the
20 ;; GNU Emacs General Public License. A copy of this license is
21 ;; supposed to have been given to you along with GNU Emacs so you
22 ;; can know your rights and responsibilities. It should be in a
23 ;; file named COPYING. Among other things, the copyright notice
24 ;; and this notice must be preserved on all copies.
25
26 ;;; Commentary:
27
28 ;;; Code:
29
30 ;; This file is autoloaded from calc-ext.el.
31
32 (require 'calc-ext)
33 (require 'calc-macs)
34 (eval-when-compile
35 (require 'calc-alg))
36
37 ;;; Units operations.
38
39 ;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
40 ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)
41 ;;; Updated April 2002 by Jochen Küpper
42
43 ;;; for CODATA 1998 see one of
44 ;;; - Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999.
45 ;;; - Reviews of Modern Physics, 72(2), 351-495, 2000.
46 ;;; for CODATA 2005 see
47 ;;; - http://physics.nist.gov/cuu/Constants/index.html
48
49 (defvar math-standard-units
50 '( ;; Length
51 ( m nil "*Meter" )
52 ( in "2.54 cm" "Inch" )
53 ( ft "12 in" "Foot" )
54 ( yd "3 ft" "Yard" )
55 ( mi "5280 ft" "Mile" )
56 ( au "149597870691 m" "Astronomical Unit" ) ;; NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
57 ( lyr "9460536207068016 m" "Light Year" )
58 ( pc "206264.80625 au" "Parsec" )
59 ( nmi "1852 m" "Nautical Mile" )
60 ( fath "6 ft" "Fathom" )
61 ( mu "1 um" "Micron" )
62 ( mil "in/1000" "Mil" )
63 ( point "in/72" "Point (1/72 inch)" )
64 ( Ang "1e-10 m" "Angstrom" )
65 ( mfi "mi+ft+in" "Miles + feet + inches" )
66 ;; TeX lengths
67 ( texpt "in/72.27" "Point (TeX conventions)" )
68 ( texpc "12 texpt" "Pica" )
69 ( texbp "point" "Big point (TeX conventions)" )
70 ( texdd "1238/1157 texpt" "Didot point" )
71 ( texcc "12 texdd" "Cicero" )
72 ( texsp "1/66536 texpt" "Scaled TeX point" )
73
74 ;; Area
75 ( hect "10000 m^2" "*Hectare" )
76 ( a "100 m^2" "Are")
77 ( acre "mi^2 / 640" "Acre" )
78 ( b "1e-28 m^2" "Barn" )
79
80 ;; Volume
81 ( L "1e-3 m^3" "*Liter" )
82 ( l "L" "Liter" )
83 ( gal "4 qt" "US Gallon" )
84 ( qt "2 pt" "Quart" )
85 ( pt "2 cup" "Pint" )
86 ( cup "8 ozfl" "Cup" )
87 ( ozfl "2 tbsp" "Fluid Ounce" )
88 ( floz "2 tbsp" "Fluid Ounce" )
89 ( tbsp "3 tsp" "Tablespoon" )
90 ( tsp "4.92892159375 ml" "Teaspoon" )
91 ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" )
92 ( galC "4.54609 L" "Canadian Gallon" )
93 ( galUK "4.546092 L" "UK Gallon" )
94
95 ;; Time
96 ( s nil "*Second" )
97 ( sec "s" "Second" )
98 ( min "60 s" "Minute" )
99 ( hr "60 min" "Hour" )
100 ( day "24 hr" "Day" )
101 ( wk "7 day" "Week" )
102 ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" )
103 ( yr "365.25 day" "Year" )
104 ( Hz "1/s" "Hertz" )
105
106 ;; Speed
107 ( mph "mi/hr" "*Miles per hour" )
108 ( kph "km/hr" "Kilometers per hour" )
109 ( knot "nmi/hr" "Knot" )
110 ( c "299792458 m/s" "Speed of light" ) ;;; CODATA 2005
111
112 ;; Acceleration
113 ( ga "9.80665 m/s^2" "*\"g\" acceleration" ) ;; CODATA 2005
114
115 ;; Mass
116 ( g nil "*Gram" )
117 ( lb "16 oz" "Pound (mass)" )
118 ( oz "28.349523125 g" "Ounce (mass)" )
119 ( ton "2000 lb" "Ton" )
120 ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
121 ( t "1000 kg" "Metric ton" )
122 ( tonUK "1016.0469088 kg" "UK ton" )
123 ( lbt "12 ozt" "Troy pound" )
124 ( ozt "31.103475 g" "Troy ounce" )
125 ( ct ".2 g" "Carat" )
126 ( u "1.66053886e-27 kg" "Unified atomic mass" ) ;; CODATA 2005
127
128 ;; Force
129 ( N "m kg/s^2" "*Newton" )
130 ( dyn "1e-5 N" "Dyne" )
131 ( gf "ga g" "Gram (force)" )
132 ( lbf "4.44822161526 N" "Pound (force)" )
133 ( kip "1000 lbf" "Kilopound (force)" )
134 ( pdl "0.138255 N" "Poundal" )
135
136 ;; Energy
137 ( J "N m" "*Joule" )
138 ( erg "1e-7 J" "Erg" )
139 ( cal "4.1868 J" "International Table Calorie" )
140 ( Btu "1055.05585262 J" "International Table Btu" )
141 ( eV "ech V" "Electron volt" )
142 ( ev "eV" "Electron volt" )
143 ( therm "105506000 J" "EEC therm" )
144 ( invcm "h c/cm" "Energy in inverse centimeters" )
145 ( Kayser "invcm" "Kayser (inverse centimeter energy)" )
146 ( men "100/invcm" "Inverse energy in meters" )
147 ( Hzen "h Hz" "Energy in Hertz")
148 ( Ken "k K" "Energy in Kelvins")
149 ( Wh "W hr" "Watt hour")
150 ( Ws "W s" "Watt second")
151
152 ;; Power
153 ( W "J/s" "*Watt" )
154 ( hp "745.7 W" "Horsepower" )
155
156 ;; Temperature
157 ( K nil "*Degree Kelvin" K )
158 ( dK "K" "Degree Kelvin" K )
159 ( degK "K" "Degree Kelvin" K )
160 ( dC "K" "Degree Celsius" C )
161 ( degC "K" "Degree Celsius" C )
162 ( dF "(5/9) K" "Degree Fahrenheit" F )
163 ( degF "(5/9) K" "Degree Fahrenheit" F )
164
165 ;; Pressure
166 ( Pa "N/m^2" "*Pascal" )
167 ( bar "1e5 Pa" "Bar" )
168 ( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA 2005
169 ( Torr " 1.333224e2 Pa" "Torr" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
170 ( mHg "1000 Torr" "Meter of mercury" )
171 ( inHg "25.4 mmHg" "Inch of mercury" )
172 ( inH2O "2.490889e2 Pa" "Inch of water" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
173 ( psi "6894.75729317 Pa" "Pound per square inch" )
174
175 ;; Viscosity
176 ( P "0.1 Pa s" "*Poise" )
177 ( St "1e-4 m^2/s" "Stokes" )
178
179 ;; Electromagnetism
180 ( A nil "*Ampere" )
181 ( C "A s" "Coulomb" )
182 ( Fdy "ech Nav" "Faraday" )
183 ( e "1.60217653e-19 C" "Elementary charge" ) ;; CODATA 2005
184 ( ech "1.60217653e-19 C" "Elementary charge" ) ;; CODATA 2005
185 ( V "W/A" "Volt" )
186 ( ohm "V/A" "Ohm" )
187 ( mho "A/V" "Mho" )
188 ( S "A/V" "Siemens" )
189 ( F "C/V" "Farad" )
190 ( H "Wb/A" "Henry" )
191 ( T "Wb/m^2" "Tesla" )
192 ( Gs "1e-4 T" "Gauss" )
193 ( Wb "V s" "Weber" )
194
195 ;; Luminous intensity
196 ( cd nil "*Candela" )
197 ( sb "1e4 cd/m^2" "Stilb" )
198 ( lm "cd sr" "Lumen" )
199 ( lx "lm/m^2" "Lux" )
200 ( ph "1e4 lx" "Phot" )
201 ( fc "10.76391 lx" "Footcandle" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
202 ( lam "1e4 lm/m^2" "Lambert" )
203 ( flam "3.426259 cd/m^2" "Footlambert" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
204
205 ;; Radioactivity
206 ( Bq "1/s" "*Becquerel" )
207 ( Ci "3.7e10 Bq" "Curie" )
208 ( Gy "J/kg" "Gray" )
209 ( Sv "Gy" "Sievert" )
210 ( R "2.58e-4 C/kg" "Roentgen" )
211 ( rd ".01 Gy" "Rad" )
212 ( rem "rd" "Rem" )
213
214 ;; Amount of substance
215 ( mol nil "*Mole" )
216
217 ;; Plane angle
218 ( rad nil "*Radian" )
219 ( circ "2 pi rad" "Full circle" )
220 ( rev "circ" "Full revolution" )
221 ( deg "circ/360" "Degree" )
222 ( arcmin "deg/60" "Arc minute" )
223 ( arcsec "arcmin/60" "Arc second" )
224 ( grad "circ/400" "Grade" )
225 ( rpm "rev/min" "Revolutions per minute" )
226
227 ;; Solid angle
228 ( sr nil "*Steradian" )
229
230 ;; Other physical quantities
231 ( h "6.6260693e-34 J s" "*Planck's constant" ) ;; CODATA 2005
232 ( hbar "h / 2 pi" "Planck's constant" )
233 ( mu0 "4 pi 1e-7 H/m" "Permeability of vacuum" )
234 ( G "6.6742e-11 m^3/kg^1/s^2" "Gravitational constant" ) ;; CODATA 2005
235 ( Nav "6.02214115e23 / mol" "Avagadro's constant" ) ;; CODATA 2005
236 ( me "9.1093826e-31 kg" "Electron rest mass" ) ;; CODATA 2005
237 ( mp "1.67262171e-27 kg" "Proton rest mass" ) ;; CODATA 2005
238 ( mn "1.67492728e-27 kg" "Neutron rest mass" ) ;; CODATA 2005
239 ( mmu "1.88353140e-28 kg" "Muon rest mass" ) ;; CODATA 2005
240 ( Ryd "10973731.568525 /m" "Rydberg's constant" ) ;; CODATA 2005
241 ( k "1.3806505e-23 J/K" "Boltzmann's constant" ) ;; CODATA 2005
242 ( alpha "7.297352568e-3" "Fine structure constant" ) ;; CODATA 2005
243 ( muB "927.400949e-26 J/T" "Bohr magneton" ) ;; CODATA 2005
244 ( muN "5.05078343e-27 J/T" "Nuclear magneton" ) ;; CODATA 2005
245 ( mue "-928.476412e-26 J/T" "Electron magnetic moment" ) ;; CODATA 2005
246 ( mup "1.41060671e-26 J/T" "Proton magnetic moment" ) ;; CODATA 2005
247 ( R0 "8.314472 J/mol/K" "Molar gas constant" ) ;; CODATA 2005
248 ( V0 "22.710981e-3 m^3/mol" "Standard volume of ideal gas" )))
249
250
251 (defvar math-additional-units nil
252 "*Additional units table for user-defined units.
253 Must be formatted like math-standard-units.
254 If this is changed, be sure to set math-units-table to nil to ensure
255 that the combined units table will be rebuilt.")
256
257 (defvar math-unit-prefixes
258 '( ( ?Y (float 1 24) "Yotta" )
259 ( ?Z (float 1 21) "Zetta" )
260 ( ?E (float 1 18) "Exa" )
261 ( ?P (float 1 15) "Peta" )
262 ( ?T (float 1 12) "Tera" )
263 ( ?G (float 1 9) "Giga" )
264 ( ?M (float 1 6) "Mega" )
265 ( ?k (float 1 3) "Kilo" )
266 ( ?K (float 1 3) "Kilo" )
267 ( ?h (float 1 2) "Hecto" )
268 ( ?H (float 1 2) "Hecto" )
269 ( ?D (float 1 1) "Deka" )
270 ( 0 (float 1 0) nil )
271 ( ?d (float 1 -1) "Deci" )
272 ( ?c (float 1 -2) "Centi" )
273 ( ?m (float 1 -3) "Milli" )
274 ( ?u (float 1 -6) "Micro" )
275 ( ?n (float 1 -9) "Nano" )
276 ( ?p (float 1 -12) "Pico" )
277 ( ?f (float 1 -15) "Femto" )
278 ( ?a (float 1 -18) "Atto" )
279 ( ?z (float 1 -21) "zepto" )
280 ( ?y (float 1 -24) "yocto" )))
281
282 (defvar math-standard-units-systems
283 '( ( base nil )
284 ( si ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
285 ( mks ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
286 ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
287
288 (defvar math-units-table nil
289 "Internal units table derived from math-defined-units.
290 Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
291
292 (defvar math-units-table-buffer-valid nil)
293
294 ;;; Units commands.
295
296 (defun calc-base-units ()
297 (interactive)
298 (calc-slow-wrapper
299 (let ((calc-autorange-units nil))
300 (calc-enter-result 1 "bsun" (math-simplify-units
301 (math-to-standard-units (calc-top-n 1)
302 nil))))))
303
304 (defun calc-quick-units ()
305 (interactive)
306 (calc-slow-wrapper
307 (let* ((num (- last-command-char ?0))
308 (pos (if (= num 0) 10 num))
309 (units (calc-var-value 'var-Units))
310 (expr (calc-top-n 1)))
311 (unless (and (>= num 0) (<= num 9))
312 (error "Bad unit number"))
313 (unless (math-vectorp units)
314 (error "No \"quick units\" are defined"))
315 (unless (< pos (length units))
316 (error "Unit number %d not defined" pos))
317 (if (math-units-in-expr-p expr nil)
318 (calc-enter-result 1 (format "cun%d" num)
319 (math-convert-units expr (nth pos units)))
320 (calc-enter-result 1 (format "*un%d" num)
321 (math-simplify-units
322 (math-mul expr (nth pos units))))))))
323
324 (defun calc-convert-units (&optional old-units new-units)
325 (interactive)
326 (calc-slow-wrapper
327 (let ((expr (calc-top-n 1))
328 (uoldname nil)
329 unew
330 units)
331 (unless (math-units-in-expr-p expr t)
332 (let ((uold (or old-units
333 (progn
334 (setq uoldname (read-string "Old units: "))
335 (if (equal uoldname "")
336 (progn
337 (setq uoldname "1")
338 1)
339 (if (string-match "\\` */" uoldname)
340 (setq uoldname (concat "1" uoldname)))
341 (math-read-expr uoldname))))))
342 (when (eq (car-safe uold) 'error)
343 (error "Bad format in units expression: %s" (nth 1 uold)))
344 (setq expr (math-mul expr uold))))
345 (unless new-units
346 (setq new-units (read-string (if uoldname
347 (concat "Old units: "
348 uoldname
349 ", new units: ")
350 "New units: "))))
351 (when (string-match "\\` */" new-units)
352 (setq new-units (concat "1" new-units)))
353 (setq units (math-read-expr new-units))
354 (when (eq (car-safe units) 'error)
355 (error "Bad format in units expression: %s" (nth 2 units)))
356 (let ((unew (math-units-in-expr-p units t))
357 (std (and (eq (car-safe units) 'var)
358 (assq (nth 1 units) math-standard-units-systems))))
359 (if std
360 (calc-enter-result 1 "cvun" (math-simplify-units
361 (math-to-standard-units expr
362 (nth 1 std))))
363 (unless unew
364 (error "No units specified"))
365 (calc-enter-result 1 "cvun"
366 (math-convert-units
367 expr units
368 (and uoldname (not (equal uoldname "1"))))))))))
369
370 (defun calc-autorange-units (arg)
371 (interactive "P")
372 (calc-wrapper
373 (calc-change-mode 'calc-autorange-units arg nil t)
374 (message (if calc-autorange-units
375 "Adjusting target unit prefix automatically"
376 "Using target units exactly"))))
377
378 (defun calc-convert-temperature (&optional old-units new-units)
379 (interactive)
380 (calc-slow-wrapper
381 (let ((expr (calc-top-n 1))
382 (uold nil)
383 (uoldname nil)
384 unew)
385 (setq uold (or old-units
386 (let ((units (math-single-units-in-expr-p expr)))
387 (if units
388 (if (consp units)
389 (list 'var (car units)
390 (intern (concat "var-"
391 (symbol-name
392 (car units)))))
393 (error "Not a pure temperature expression"))
394 (math-read-expr
395 (setq uoldname (read-string
396 "Old temperature units: ")))))))
397 (when (eq (car-safe uold) 'error)
398 (error "Bad format in units expression: %s" (nth 2 uold)))
399 (or (math-units-in-expr-p expr nil)
400 (setq expr (math-mul expr uold)))
401 (setq unew (or new-units
402 (math-read-expr
403 (read-string (if uoldname
404 (concat "Old temperature units: "
405 uoldname
406 ", new units: ")
407 "New temperature units: ")))))
408 (when (eq (car-safe unew) 'error)
409 (error "Bad format in units expression: %s" (nth 2 unew)))
410 (calc-enter-result 1 "cvtm" (math-simplify-units
411 (math-convert-temperature expr uold unew
412 uoldname))))))
413
414 (defun calc-remove-units ()
415 (interactive)
416 (calc-slow-wrapper
417 (calc-enter-result 1 "rmun" (math-simplify-units
418 (math-remove-units (calc-top-n 1))))))
419
420 (defun calc-extract-units ()
421 (interactive)
422 (calc-slow-wrapper
423 (calc-enter-result 1 "rmun" (math-simplify-units
424 (math-extract-units (calc-top-n 1))))))
425
426 ;; The variables calc-num-units and calc-den-units are local to
427 ;; calc-explain-units, but are used by calc-explain-units-rec,
428 ;; which is called by calc-explain-units.
429 (defvar calc-num-units)
430 (defvar calc-den-units)
431
432 (defun calc-explain-units ()
433 (interactive)
434 (calc-wrapper
435 (let ((calc-num-units nil)
436 (calc-den-units nil))
437 (calc-explain-units-rec (calc-top-n 1) 1)
438 (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
439 (setq calc-den-units (concat "(" calc-den-units ")")))
440 (if calc-num-units
441 (if calc-den-units
442 (message "%s per %s" calc-num-units calc-den-units)
443 (message "%s" calc-num-units))
444 (if calc-den-units
445 (message "1 per %s" calc-den-units)
446 (message "No units in expression"))))))
447
448 (defun calc-explain-units-rec (expr pow)
449 (let ((u (math-check-unit-name expr))
450 pos)
451 (if (and u (not (math-zerop pow)))
452 (let ((name (or (nth 2 u) (symbol-name (car u)))))
453 (if (eq (aref name 0) ?\*)
454 (setq name (substring name 1)))
455 (if (string-match "[^a-zA-Z0-9']" name)
456 (if (string-match "^[a-zA-Z0-9' ()]*$" name)
457 (while (setq pos (string-match "[ ()]" name))
458 (setq name (concat (substring name 0 pos)
459 (if (eq (aref name pos) 32) "-" "")
460 (substring name (1+ pos)))))
461 (setq name (concat "(" name ")"))))
462 (or (eq (nth 1 expr) (car u))
463 (setq name (concat (nth 2 (assq (aref (symbol-name
464 (nth 1 expr)) 0)
465 math-unit-prefixes))
466 (if (and (string-match "[^a-zA-Z0-9']" name)
467 (not (memq (car u) '(mHg gf))))
468 (concat "-" name)
469 (downcase name)))))
470 (cond ((or (math-equal-int pow 1)
471 (math-equal-int pow -1)))
472 ((or (math-equal-int pow 2)
473 (math-equal-int pow -2))
474 (if (equal (nth 4 u) '((m . 1)))
475 (setq name (concat "Square-" name))
476 (setq name (concat name "-squared"))))
477 ((or (math-equal-int pow 3)
478 (math-equal-int pow -3))
479 (if (equal (nth 4 u) '((m . 1)))
480 (setq name (concat "Cubic-" name))
481 (setq name (concat name "-cubed"))))
482 (t
483 (setq name (concat name "^"
484 (math-format-number (math-abs pow))))))
485 (if (math-posp pow)
486 (setq calc-num-units (if calc-num-units
487 (concat calc-num-units " " name)
488 name))
489 (setq calc-den-units (if calc-den-units
490 (concat calc-den-units " " name)
491 name))))
492 (cond ((eq (car-safe expr) '*)
493 (calc-explain-units-rec (nth 1 expr) pow)
494 (calc-explain-units-rec (nth 2 expr) pow))
495 ((eq (car-safe expr) '/)
496 (calc-explain-units-rec (nth 1 expr) pow)
497 (calc-explain-units-rec (nth 2 expr) (- pow)))
498 ((memq (car-safe expr) '(neg + -))
499 (calc-explain-units-rec (nth 1 expr) pow))
500 ((and (eq (car-safe expr) '^)
501 (math-realp (nth 2 expr)))
502 (calc-explain-units-rec (nth 1 expr)
503 (math-mul pow (nth 2 expr))))))))
504
505 (defun calc-simplify-units ()
506 (interactive)
507 (calc-slow-wrapper
508 (calc-with-default-simplification
509 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
510
511 (defun calc-view-units-table (n)
512 (interactive "P")
513 (and n (setq math-units-table-buffer-valid nil))
514 (let ((win (get-buffer-window "*Units Table*")))
515 (if (and win
516 math-units-table
517 math-units-table-buffer-valid)
518 (progn
519 (bury-buffer (window-buffer win))
520 (let ((curwin (selected-window)))
521 (select-window win)
522 (switch-to-buffer nil)
523 (select-window curwin)))
524 (math-build-units-table-buffer nil))))
525
526 (defun calc-enter-units-table (n)
527 (interactive "P")
528 (and n (setq math-units-table-buffer-valid nil))
529 (math-build-units-table-buffer t)
530 (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
531
532 (defun calc-define-unit (uname desc)
533 (interactive "SDefine unit name: \nsDescription: ")
534 (calc-wrapper
535 (let ((form (calc-top-n 1))
536 (unit (assq uname math-additional-units)))
537 (or unit
538 (setq math-additional-units
539 (cons (setq unit (list uname nil nil))
540 math-additional-units)
541 math-units-table nil))
542 (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
543 (eq (nth 1 form) uname)))
544 (not (math-equal-int form 1))
545 (math-format-flat-expr form 0)))
546 (setcar (cdr (cdr unit)) (and (not (equal desc ""))
547 desc))))
548 (calc-invalidate-units-table))
549
550 (defun calc-undefine-unit (uname)
551 (interactive "SUndefine unit name: ")
552 (calc-wrapper
553 (let ((unit (assq uname math-additional-units)))
554 (or unit
555 (if (assq uname math-standard-units)
556 (error "\"%s\" is a predefined unit name" uname)
557 (error "Unit name \"%s\" not found" uname)))
558 (setq math-additional-units (delq unit math-additional-units)
559 math-units-table nil)))
560 (calc-invalidate-units-table))
561
562 (defun calc-invalidate-units-table ()
563 (setq math-units-table nil)
564 (let ((buf (get-buffer "*Units Table*")))
565 (and buf
566 (save-excursion
567 (set-buffer buf)
568 (save-excursion
569 (goto-char (point-min))
570 (if (looking-at "Calculator Units Table")
571 (let ((inhibit-read-only t))
572 (insert "(Obsolete) "))))))))
573
574 (defun calc-get-unit-definition (uname)
575 (interactive "SGet definition for unit: ")
576 (calc-wrapper
577 (math-build-units-table)
578 (let ((unit (assq uname math-units-table)))
579 (or unit
580 (error "Unit name \"%s\" not found" uname))
581 (let ((msg (nth 2 unit)))
582 (if (stringp msg)
583 (if (string-match "^\\*" msg)
584 (setq msg (substring msg 1)))
585 (setq msg (symbol-name uname)))
586 (if (nth 1 unit)
587 (progn
588 (calc-enter-result 0 "ugdf" (nth 1 unit))
589 (message "Derived unit: %s" msg))
590 (calc-enter-result 0 "ugdf" (list 'var uname
591 (intern
592 (concat "var-"
593 (symbol-name uname)))))
594 (message "Base unit: %s" msg))))))
595
596 (defun calc-permanent-units ()
597 (interactive)
598 (calc-wrapper
599 (let (pos)
600 (set-buffer (find-file-noselect (substitute-in-file-name
601 calc-settings-file)))
602 (goto-char (point-min))
603 (if (and (search-forward ";;; Custom units stored by Calc" nil t)
604 (progn
605 (beginning-of-line)
606 (setq pos (point))
607 (search-forward "\n;;; End of custom units" nil t)))
608 (progn
609 (beginning-of-line)
610 (forward-line 1)
611 (delete-region pos (point)))
612 (goto-char (point-max))
613 (insert "\n\n")
614 (forward-char -1))
615 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
616 (if math-additional-units
617 (progn
618 (insert "(setq math-additional-units '(\n")
619 (let ((list math-additional-units))
620 (while list
621 (insert " (" (symbol-name (car (car list))) " "
622 (if (nth 1 (car list))
623 (if (stringp (nth 1 (car list)))
624 (prin1-to-string (nth 1 (car list)))
625 (prin1-to-string (math-format-flat-expr
626 (nth 1 (car list)) 0)))
627 "nil")
628 " "
629 (prin1-to-string (nth 2 (car list)))
630 ")\n")
631 (setq list (cdr list))))
632 (insert "))\n"))
633 (insert ";;; (no custom units defined)\n"))
634 (insert ";;; End of custom units\n")
635 (save-buffer))))
636
637
638 ;; The variable math-cu-unit-list is local to math-build-units-table,
639 ;; but is used by math-compare-unit-names, which is called (indirectly)
640 ;; by math-build-units-table.
641 ;; math-cu-unit-list is also local to math-convert-units, but is used
642 ;; by math-convert-units-rec, which is called by math-convert-units.
643 (defvar math-cu-unit-list)
644
645 (defun math-build-units-table ()
646 (or math-units-table
647 (let* ((combined-units (append math-additional-units
648 math-standard-units))
649 (math-cu-unit-list (mapcar 'car combined-units))
650 tab)
651 (message "Building units table...")
652 (setq math-units-table-buffer-valid nil)
653 (setq tab (mapcar (function
654 (lambda (x)
655 (list (car x)
656 (and (nth 1 x)
657 (if (stringp (nth 1 x))
658 (let ((exp (math-read-plain-expr
659 (nth 1 x))))
660 (if (eq (car-safe exp) 'error)
661 (error "Format error in definition of %s in units table: %s"
662 (car x) (nth 2 exp))
663 exp))
664 (nth 1 x)))
665 (nth 2 x)
666 (nth 3 x)
667 (and (not (nth 1 x))
668 (list (cons (car x) 1))))))
669 combined-units))
670 (let ((math-units-table tab))
671 (mapcar 'math-find-base-units tab))
672 (message "Building units table...done")
673 (setq math-units-table tab))))
674
675 ;; The variables math-fbu-base and math-fbu-entry are local to
676 ;; math-find-base-units, but are used by math-find-base-units-rec,
677 ;; which is called by math-find-base-units.
678 (defvar math-fbu-base)
679 (defvar math-fbu-entry)
680
681 (defun math-find-base-units (math-fbu-entry)
682 (if (eq (nth 4 math-fbu-entry) 'boom)
683 (error "Circular definition involving unit %s" (car math-fbu-entry)))
684 (or (nth 4 math-fbu-entry)
685 (let (math-fbu-base)
686 (setcar (nthcdr 4 math-fbu-entry) 'boom)
687 (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
688 '(or math-fbu-base
689 (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
690 (while (eq (cdr (car math-fbu-base)) 0)
691 (setq math-fbu-base (cdr math-fbu-base)))
692 (let ((b math-fbu-base))
693 (while (cdr b)
694 (if (eq (cdr (car (cdr b))) 0)
695 (setcdr b (cdr (cdr b)))
696 (setq b (cdr b)))))
697 (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
698 (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
699 math-fbu-base)))
700
701 (defun math-compare-unit-names (a b)
702 (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
703
704 (defun math-find-base-units-rec (expr pow)
705 (let ((u (math-check-unit-name expr)))
706 (cond (u
707 (let ((ulist (math-find-base-units u)))
708 (while ulist
709 (let ((p (* (cdr (car ulist)) pow))
710 (old (assq (car (car ulist)) math-fbu-base)))
711 (if old
712 (setcdr old (+ (cdr old) p))
713 (setq math-fbu-base
714 (cons (cons (car (car ulist)) p) math-fbu-base))))
715 (setq ulist (cdr ulist)))))
716 ((math-scalarp expr))
717 ((and (eq (car expr) '^)
718 (integerp (nth 2 expr)))
719 (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
720 ((eq (car expr) '*)
721 (math-find-base-units-rec (nth 1 expr) pow)
722 (math-find-base-units-rec (nth 2 expr) pow))
723 ((eq (car expr) '/)
724 (math-find-base-units-rec (nth 1 expr) pow)
725 (math-find-base-units-rec (nth 2 expr) (- pow)))
726 ((eq (car expr) 'neg)
727 (math-find-base-units-rec (nth 1 expr) pow))
728 ((eq (car expr) '+)
729 (math-find-base-units-rec (nth 1 expr) pow))
730 ((eq (car expr) 'var)
731 (or (eq (nth 1 expr) 'pi)
732 (error "Unknown name %s in defining expression for unit %s"
733 (nth 1 expr) (car math-fbu-entry))))
734 (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
735
736
737 (defun math-units-in-expr-p (expr sub-exprs)
738 (and (consp expr)
739 (if (eq (car expr) 'var)
740 (math-check-unit-name expr)
741 (and (or sub-exprs
742 (memq (car expr) '(* / ^)))
743 (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
744 (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
745
746 (defun math-only-units-in-expr-p (expr)
747 (and (consp expr)
748 (if (eq (car expr) 'var)
749 (math-check-unit-name expr)
750 (if (memq (car expr) '(* /))
751 (and (math-only-units-in-expr-p (nth 1 expr))
752 (math-only-units-in-expr-p (nth 2 expr)))
753 (and (eq (car expr) '^)
754 (and (math-only-units-in-expr-p (nth 1 expr))
755 (math-realp (nth 2 expr))))))))
756
757 (defun math-single-units-in-expr-p (expr)
758 (cond ((math-scalarp expr) nil)
759 ((eq (car expr) 'var)
760 (math-check-unit-name expr))
761 ((eq (car expr) '*)
762 (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
763 (u2 (math-single-units-in-expr-p (nth 2 expr))))
764 (or (and u1 u2 'wrong)
765 u1
766 u2)))
767 ((eq (car expr) '/)
768 (if (math-units-in-expr-p (nth 2 expr) nil)
769 'wrong
770 (math-single-units-in-expr-p (nth 1 expr))))
771 (t 'wrong)))
772
773 (defun math-check-unit-name (v)
774 (and (eq (car-safe v) 'var)
775 (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
776 (let ((name (symbol-name (nth 1 v))))
777 (and (> (length name) 1)
778 (assq (aref name 0) math-unit-prefixes)
779 (or (assq (intern (substring name 1)) math-units-table)
780 (and (eq (aref name 0) ?M)
781 (> (length name) 3)
782 (eq (aref name 1) ?e)
783 (eq (aref name 2) ?g)
784 (assq (intern (substring name 3))
785 math-units-table))))))))
786
787 ;; The variable math-which-standard is local to math-to-standard-units,
788 ;; but is used by math-to-standard-rec, which is called by
789 ;; math-to-standard-units.
790 (defvar math-which-standard)
791
792 (defun math-to-standard-units (expr math-which-standard)
793 (math-to-standard-rec expr))
794
795 (defun math-to-standard-rec (expr)
796 (if (eq (car-safe expr) 'var)
797 (let ((u (math-check-unit-name expr))
798 (base (nth 1 expr)))
799 (if u
800 (progn
801 (if (nth 1 u)
802 (setq expr (math-to-standard-rec (nth 1 u)))
803 (let ((st (assq (car u) math-which-standard)))
804 (if st
805 (setq expr (nth 1 st))
806 (setq expr (list 'var (car u)
807 (intern (concat "var-"
808 (symbol-name
809 (car u)))))))))
810 (or (null u)
811 (eq base (car u))
812 (setq expr (list '*
813 (nth 1 (assq (aref (symbol-name base) 0)
814 math-unit-prefixes))
815 expr)))
816 expr)
817 (if (eq base 'pi)
818 (math-pi)
819 expr)))
820 (if (Math-primp expr)
821 expr
822 (cons (car expr)
823 (mapcar 'math-to-standard-rec (cdr expr))))))
824
825 (defun math-apply-units (expr units ulist &optional pure)
826 (setq expr (math-simplify-units expr))
827 (if ulist
828 (let ((new 0)
829 value)
830 (or (math-numberp expr)
831 (error "Incompatible units"))
832 (while (cdr ulist)
833 (setq value (math-div expr (nth 1 (car ulist)))
834 value (math-floor (let ((calc-internal-prec
835 (1- calc-internal-prec)))
836 (math-normalize value)))
837 new (math-add new (math-mul value (car (car ulist))))
838 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
839 ulist (cdr ulist)))
840 (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
841 (car (car ulist)))))
842 (if pure
843 expr
844 (math-simplify-units (list '* expr units)))))
845
846 (defvar math-decompose-units-cache nil)
847 (defun math-decompose-units (units)
848 (let ((u (math-check-unit-name units)))
849 (and u (eq (car-safe (nth 1 u)) '+)
850 (setq units (nth 1 u))))
851 (setq units (calcFunc-expand units))
852 (and (eq (car-safe units) '+)
853 (let ((entry (list units calc-internal-prec calc-prefer-frac)))
854 (or (equal entry (car math-decompose-units-cache))
855 (let ((ulist nil)
856 (utemp units)
857 qty unit)
858 (while (eq (car-safe utemp) '+)
859 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
860 ulist)
861 utemp (nth 1 utemp)))
862 (setq ulist (cons (math-decompose-unit-part utemp) ulist)
863 utemp ulist)
864 (while (setq utemp (cdr utemp))
865 (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
866 (error "Inconsistent units in sum")))
867 (setq math-decompose-units-cache
868 (cons entry
869 (sort ulist
870 (function
871 (lambda (x y)
872 (not (Math-lessp (nth 1 x)
873 (nth 1 y))))))))))
874 (cdr math-decompose-units-cache))))
875
876 (defun math-decompose-unit-part (unit)
877 (cons unit
878 (math-is-multiple (math-simplify-units (math-to-standard-units
879 unit nil))
880 t)))
881
882 ;; The variable math-fcu-u is local to math-find-compatible-unit,
883 ;; but is used by math-find-compatible-rec which is called by
884 ;; math-find-compatible-unit.
885 (defvar math-fcu-u)
886
887 (defun math-find-compatible-unit (expr unit)
888 (let ((math-fcu-u (math-check-unit-name unit)))
889 (if math-fcu-u
890 (math-find-compatible-unit-rec expr 1))))
891
892 (defun math-find-compatible-unit-rec (expr pow)
893 (cond ((eq (car-safe expr) '*)
894 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
895 (math-find-compatible-unit-rec (nth 2 expr) pow)))
896 ((eq (car-safe expr) '/)
897 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
898 (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
899 ((and (eq (car-safe expr) '^)
900 (integerp (nth 2 expr)))
901 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
902 (t
903 (let ((u2 (math-check-unit-name expr)))
904 (if (equal (nth 4 math-fcu-u) (nth 4 u2))
905 (cons expr pow))))))
906
907 ;; The variables math-cu-new-units and math-cu-pure are local to
908 ;; math-convert-units, but are used by math-convert-units-rec,
909 ;; which is called by math-convert-units.
910 (defvar math-cu-new-units)
911 (defvar math-cu-pure)
912
913 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
914 (if (eq (car-safe math-cu-new-units) 'var)
915 (let ((unew (assq (nth 1 math-cu-new-units)
916 (math-build-units-table))))
917 (if (eq (car-safe (nth 1 unew)) '+)
918 (setq math-cu-new-units (nth 1 unew)))))
919 (math-with-extra-prec 2
920 (let ((compat (and (not math-cu-pure)
921 (math-find-compatible-unit expr math-cu-new-units)))
922 (math-cu-unit-list nil)
923 (math-combining-units nil))
924 (if compat
925 (math-simplify-units
926 (math-mul (math-mul (math-simplify-units
927 (math-div expr (math-pow (car compat)
928 (cdr compat))))
929 (math-pow math-cu-new-units (cdr compat)))
930 (math-simplify-units
931 (math-to-standard-units
932 (math-pow (math-div (car compat) math-cu-new-units)
933 (cdr compat))
934 nil))))
935 (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
936 (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
937 (when (eq (car-safe expr) '+)
938 (setq expr (math-simplify-units expr)))
939 (if (math-units-in-expr-p expr t)
940 (math-convert-units-rec expr)
941 (math-apply-units (math-to-standard-units
942 (list '/ expr math-cu-new-units) nil)
943 math-cu-new-units math-cu-unit-list math-cu-pure))))))
944
945 (defun math-convert-units-rec (expr)
946 (if (math-units-in-expr-p expr nil)
947 (math-apply-units (math-to-standard-units
948 (list '/ expr math-cu-new-units) nil)
949 math-cu-new-units math-cu-unit-list math-cu-pure)
950 (if (Math-primp expr)
951 expr
952 (cons (car expr)
953 (mapcar 'math-convert-units-rec (cdr expr))))))
954
955 (defun math-convert-temperature (expr old new &optional pure)
956 (let* ((units (math-single-units-in-expr-p expr))
957 (uold (if old
958 (if (or (null units)
959 (equal (nth 1 old) (car units)))
960 (math-check-unit-name old)
961 (error "Inconsistent temperature units"))
962 units))
963 (unew (math-check-unit-name new)))
964 (unless (and (consp unew) (nth 3 unew))
965 (error "Not a valid temperature unit"))
966 (unless (and (consp uold) (nth 3 uold))
967 (error "Not a pure temperature expression"))
968 (let ((v (car uold)))
969 (setq expr (list '/ expr (list 'var v
970 (intern (concat "var-"
971 (symbol-name v)))))))
972 (or (eq (nth 3 uold) (nth 3 unew))
973 (cond ((eq (nth 3 uold) 'K)
974 (setq expr (list '- expr '(float 27315 -2)))
975 (if (eq (nth 3 unew) 'F)
976 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))))
977 ((eq (nth 3 uold) 'C)
978 (if (eq (nth 3 unew) 'F)
979 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))
980 (setq expr (list '+ expr '(float 27315 -2)))))
981 (t
982 (setq expr (list '* (list '- expr 32) '(frac 5 9)))
983 (if (eq (nth 3 unew) 'K)
984 (setq expr (list '+ expr '(float 27315 -2)))))))
985 (if pure
986 expr
987 (list '* expr new))))
988
989
990
991 (defun math-simplify-units (a)
992 (let ((math-simplifying-units t)
993 (calc-matrix-mode 'scalar))
994 (math-simplify a)))
995 (defalias 'calcFunc-usimplify 'math-simplify-units)
996
997 ;; The function created by math-defsimplify uses the variable
998 ;; math-simplify-expr, and so is used by functions in math-defsimplify
999 (defvar math-simplify-expr)
1000
1001 (math-defsimplify (+ -)
1002 (and math-simplifying-units
1003 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1004 (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1005 (ratio (math-simplify (math-to-standard-units
1006 (list '/ (nth 2 math-simplify-expr) units) nil))))
1007 (if (math-units-in-expr-p ratio nil)
1008 (progn
1009 (calc-record-why "*Inconsistent units" math-simplify-expr)
1010 math-simplify-expr)
1011 (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1012 (if (eq (car math-simplify-expr) '-)
1013 (math-neg ratio) ratio))
1014 units)))))
1015
1016 (math-defsimplify *
1017 (math-simplify-units-prod))
1018
1019 (defun math-simplify-units-prod ()
1020 (and math-simplifying-units
1021 calc-autorange-units
1022 (Math-realp (nth 1 math-simplify-expr))
1023 (let* ((num (math-float (nth 1 math-simplify-expr)))
1024 (xpon (calcFunc-xpon num))
1025 (unitp (cdr (cdr math-simplify-expr)))
1026 (unit (car unitp))
1027 (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1028 u)
1029 (and (eq (car-safe unit) '*)
1030 (setq unitp (cdr unit)
1031 unit (car unitp)))
1032 (and (eq (car-safe unit) '^)
1033 (integerp (nth 2 unit))
1034 (setq pow (* pow (nth 2 unit))
1035 unitp (cdr unit)
1036 unit (car unitp)))
1037 (and (setq u (math-check-unit-name unit))
1038 (integerp xpon)
1039 (or (< xpon 0)
1040 (>= xpon (if (eq (car u) 'm) 1 3)))
1041 (let* ((uxpon 0)
1042 (pref (if (< pow 0)
1043 (reverse math-unit-prefixes)
1044 math-unit-prefixes))
1045 (p pref)
1046 pxpon pname)
1047 (or (eq (car u) (nth 1 unit))
1048 (setq uxpon (* pow
1049 (nth 2 (nth 1 (assq
1050 (aref (symbol-name
1051 (nth 1 unit)) 0)
1052 math-unit-prefixes))))))
1053 (setq xpon (+ xpon uxpon))
1054 (while (and p
1055 (or (memq (car (car p)) '(?d ?D ?h ?H))
1056 (and (eq (car (car p)) ?c)
1057 (not (eq (car u) 'm)))
1058 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1059 pow)))
1060 (progn
1061 (setq pname (math-build-var-name
1062 (if (eq (car (car p)) 0)
1063 (car u)
1064 (concat (char-to-string
1065 (car (car p)))
1066 (symbol-name
1067 (car u))))))
1068 (and (/= (car (car p)) 0)
1069 (assq (nth 1 pname)
1070 math-units-table)))))
1071 (setq p (cdr p)))
1072 (and p
1073 (/= pxpon uxpon)
1074 (or (not (eq p pref))
1075 (< xpon (+ pxpon (* (math-abs pow) 3))))
1076 (progn
1077 (setcar (cdr math-simplify-expr)
1078 (let ((calc-prefer-frac nil))
1079 (calcFunc-scf (nth 1 math-simplify-expr)
1080 (- uxpon pxpon))))
1081 (setcar unitp pname)
1082 math-simplify-expr)))))))
1083
1084 (defvar math-try-cancel-units)
1085
1086 (math-defsimplify /
1087 (and math-simplifying-units
1088 (let ((np (cdr math-simplify-expr))
1089 (math-try-cancel-units 0)
1090 n nn)
1091 (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1092 (cdr (nth 2 math-simplify-expr))
1093 (nthcdr 2 math-simplify-expr)))
1094 (if (math-realp (car n))
1095 (progn
1096 (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1097 (let ((calc-prefer-frac nil))
1098 (math-div 1 (car n)))))
1099 (setcar n 1)))
1100 (while (eq (car-safe (setq n (car np))) '*)
1101 (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1102 (setq np (cdr (cdr n))))
1103 (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1104 (if (eq math-try-cancel-units 0)
1105 (let* ((math-simplifying-units nil)
1106 (base (math-simplify
1107 (math-to-standard-units math-simplify-expr nil))))
1108 (if (Math-numberp base)
1109 (setq math-simplify-expr base))))
1110 (if (eq (car-safe math-simplify-expr) '/)
1111 (math-simplify-units-prod))
1112 math-simplify-expr)))
1113
1114 (defun math-simplify-units-divisor (np dp)
1115 (let ((n (car np))
1116 d dd temp)
1117 (while (eq (car-safe (setq d (car dp))) '*)
1118 (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1119 (setcar np (setq n temp))
1120 (setcar (cdr d) 1))
1121 (setq dp (cdr (cdr d))))
1122 (when (setq temp (math-simplify-units-quotient n d))
1123 (setcar np (setq n temp))
1124 (setcar dp 1))))
1125
1126 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1127 (defun math-simplify-units-quotient (n d)
1128 (let ((pow1 1)
1129 (pow2 1))
1130 (when (and (eq (car-safe n) '^)
1131 (integerp (nth 2 n)))
1132 (setq pow1 (nth 2 n) n (nth 1 n)))
1133 (when (and (eq (car-safe d) '^)
1134 (integerp (nth 2 d)))
1135 (setq pow2 (nth 2 d) d (nth 1 d)))
1136 (let ((un (math-check-unit-name n))
1137 (ud (math-check-unit-name d)))
1138 (and un ud
1139 (if (and (equal (nth 4 un) (nth 4 ud))
1140 (eq pow1 pow2))
1141 (math-to-standard-units (list '/ n d) nil)
1142 (let (ud1)
1143 (setq un (nth 4 un)
1144 ud (nth 4 ud))
1145 (while un
1146 (setq ud1 ud)
1147 (while ud1
1148 (and (eq (car (car un)) (car (car ud1)))
1149 (setq math-try-cancel-units
1150 (+ math-try-cancel-units
1151 (- (* (cdr (car un)) pow1)
1152 (* (cdr (car ud)) pow2)))))
1153 (setq ud1 (cdr ud1)))
1154 (setq un (cdr un)))
1155 nil))))))
1156
1157 (math-defsimplify ^
1158 (and math-simplifying-units
1159 (math-realp (nth 2 math-simplify-expr))
1160 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1161 (list (car (nth 1 math-simplify-expr))
1162 (list '^ (nth 1 (nth 1 math-simplify-expr))
1163 (nth 2 math-simplify-expr))
1164 (list '^ (nth 2 (nth 1 math-simplify-expr))
1165 (nth 2 math-simplify-expr)))
1166 (math-simplify-units-pow (nth 1 math-simplify-expr)
1167 (nth 2 math-simplify-expr)))))
1168
1169 (math-defsimplify calcFunc-sqrt
1170 (and math-simplifying-units
1171 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1172 (list (car (nth 1 math-simplify-expr))
1173 (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1174 (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1175 (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1176
1177 (math-defsimplify (calcFunc-floor
1178 calcFunc-ceil
1179 calcFunc-round
1180 calcFunc-rounde
1181 calcFunc-roundu
1182 calcFunc-trunc
1183 calcFunc-float
1184 calcFunc-frac
1185 calcFunc-abs
1186 calcFunc-clean)
1187 (and math-simplifying-units
1188 (= (length math-simplify-expr) 2)
1189 (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1190 (nth 1 math-simplify-expr)
1191 (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1192 (or (math-only-units-in-expr-p
1193 (nth 1 (nth 1 math-simplify-expr)))
1194 (math-only-units-in-expr-p
1195 (nth 2 (nth 1 math-simplify-expr)))))
1196 (list (car (nth 1 math-simplify-expr))
1197 (cons (car math-simplify-expr)
1198 (cons (nth 1 (nth 1 math-simplify-expr))
1199 (cdr (cdr math-simplify-expr))))
1200 (cons (car math-simplify-expr)
1201 (cons (nth 2 (nth 1 math-simplify-expr))
1202 (cdr (cdr math-simplify-expr)))))))))
1203
1204 (defun math-simplify-units-pow (a pow)
1205 (if (and (eq (car-safe a) '^)
1206 (math-check-unit-name (nth 1 a))
1207 (math-realp (nth 2 a)))
1208 (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1209 (let* ((u (math-check-unit-name a))
1210 (pf (math-to-simple-fraction pow))
1211 (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1212 (and u d
1213 (math-units-are-multiple u d)
1214 (list '^ (math-to-standard-units a nil) pow)))))
1215
1216
1217 (defun math-units-are-multiple (u n)
1218 (setq u (nth 4 u))
1219 (while (and u (= (% (cdr (car u)) n) 0))
1220 (setq u (cdr u)))
1221 (null u))
1222
1223 (math-defsimplify calcFunc-sin
1224 (and math-simplifying-units
1225 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1226 (let ((rad (math-simplify-units
1227 (math-evaluate-expr
1228 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1229 (calc-angle-mode 'rad))
1230 (and (eq (car-safe rad) '*)
1231 (math-realp (nth 1 rad))
1232 (eq (car-safe (nth 2 rad)) 'var)
1233 (eq (nth 1 (nth 2 rad)) 'rad)
1234 (list 'calcFunc-sin (nth 1 rad))))))
1235
1236 (math-defsimplify calcFunc-cos
1237 (and math-simplifying-units
1238 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1239 (let ((rad (math-simplify-units
1240 (math-evaluate-expr
1241 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1242 (calc-angle-mode 'rad))
1243 (and (eq (car-safe rad) '*)
1244 (math-realp (nth 1 rad))
1245 (eq (car-safe (nth 2 rad)) 'var)
1246 (eq (nth 1 (nth 2 rad)) 'rad)
1247 (list 'calcFunc-cos (nth 1 rad))))))
1248
1249 (math-defsimplify calcFunc-tan
1250 (and math-simplifying-units
1251 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1252 (let ((rad (math-simplify-units
1253 (math-evaluate-expr
1254 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1255 (calc-angle-mode 'rad))
1256 (and (eq (car-safe rad) '*)
1257 (math-realp (nth 1 rad))
1258 (eq (car-safe (nth 2 rad)) 'var)
1259 (eq (nth 1 (nth 2 rad)) 'rad)
1260 (list 'calcFunc-tan (nth 1 rad))))))
1261
1262 (math-defsimplify calcFunc-sec
1263 (and math-simplifying-units
1264 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1265 (let ((rad (math-simplify-units
1266 (math-evaluate-expr
1267 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1268 (calc-angle-mode 'rad))
1269 (and (eq (car-safe rad) '*)
1270 (math-realp (nth 1 rad))
1271 (eq (car-safe (nth 2 rad)) 'var)
1272 (eq (nth 1 (nth 2 rad)) 'rad)
1273 (list 'calcFunc-sec (nth 1 rad))))))
1274
1275 (math-defsimplify calcFunc-csc
1276 (and math-simplifying-units
1277 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1278 (let ((rad (math-simplify-units
1279 (math-evaluate-expr
1280 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1281 (calc-angle-mode 'rad))
1282 (and (eq (car-safe rad) '*)
1283 (math-realp (nth 1 rad))
1284 (eq (car-safe (nth 2 rad)) 'var)
1285 (eq (nth 1 (nth 2 rad)) 'rad)
1286 (list 'calcFunc-csc (nth 1 rad))))))
1287
1288 (math-defsimplify calcFunc-cot
1289 (and math-simplifying-units
1290 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1291 (let ((rad (math-simplify-units
1292 (math-evaluate-expr
1293 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1294 (calc-angle-mode 'rad))
1295 (and (eq (car-safe rad) '*)
1296 (math-realp (nth 1 rad))
1297 (eq (car-safe (nth 2 rad)) 'var)
1298 (eq (nth 1 (nth 2 rad)) 'rad)
1299 (list 'calcFunc-cot (nth 1 rad))))))
1300
1301
1302 (defun math-remove-units (expr)
1303 (if (math-check-unit-name expr)
1304 1
1305 (if (Math-primp expr)
1306 expr
1307 (cons (car expr)
1308 (mapcar 'math-remove-units (cdr expr))))))
1309
1310 (defun math-extract-units (expr)
1311 (if (memq (car-safe expr) '(* /))
1312 (cons (car expr)
1313 (mapcar 'math-extract-units (cdr expr)))
1314 (if (math-check-unit-name expr) expr 1)))
1315
1316 (defun math-build-units-table-buffer (enter-buffer)
1317 (if (not (and math-units-table math-units-table-buffer-valid
1318 (get-buffer "*Units Table*")))
1319 (let ((buf (get-buffer-create "*Units Table*"))
1320 (uptr (math-build-units-table))
1321 (calc-language (if (eq calc-language 'big) nil calc-language))
1322 (calc-float-format '(float 0))
1323 (calc-group-digits nil)
1324 (calc-number-radix 10)
1325 (calc-point-char ".")
1326 (std nil)
1327 u name shadowed)
1328 (save-excursion
1329 (message "Formatting units table...")
1330 (set-buffer buf)
1331 (let ((inhibit-read-only t))
1332 (erase-buffer)
1333 (insert "Calculator Units Table:\n\n")
1334 (insert "Unit Type Definition Description\n\n")
1335 (while uptr
1336 (setq u (car uptr)
1337 name (nth 2 u))
1338 (when (eq (car u) 'm)
1339 (setq std t))
1340 (setq shadowed (and std (assq (car u) math-additional-units)))
1341 (when (and name
1342 (> (length name) 1)
1343 (eq (aref name 0) ?\*))
1344 (unless (eq uptr math-units-table)
1345 (insert "\n"))
1346 (setq name (substring name 1)))
1347 (insert " ")
1348 (and shadowed (insert "("))
1349 (insert (symbol-name (car u)))
1350 (and shadowed (insert ")"))
1351 (if (nth 3 u)
1352 (progn
1353 (indent-to 10)
1354 (insert (symbol-name (nth 3 u))))
1355 (or std
1356 (progn
1357 (indent-to 10)
1358 (insert "U"))))
1359 (indent-to 14)
1360 (and shadowed (insert "("))
1361 (if (nth 1 u)
1362 (insert (math-format-value (nth 1 u) 80))
1363 (insert (symbol-name (car u))))
1364 (and shadowed (insert ")"))
1365 (indent-to 41)
1366 (insert " ")
1367 (when name
1368 (insert name))
1369 (if shadowed
1370 (insert " (redefined above)")
1371 (unless (nth 1 u)
1372 (insert " (base unit)")))
1373 (insert "\n")
1374 (setq uptr (cdr uptr)))
1375 (insert "\n\nUnit Prefix Table:\n\n")
1376 (setq uptr math-unit-prefixes)
1377 (while uptr
1378 (setq u (car uptr))
1379 (insert " " (char-to-string (car u)))
1380 (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1381 (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1382 " ")
1383 (insert " "))
1384 (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1385 (indent-to 15)
1386 (insert " " (nth 2 u) "\n")
1387 (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1388 (insert "\n"))
1389 (view-mode)
1390 (message "Formatting units table...done"))
1391 (setq math-units-table-buffer-valid t)
1392 (let ((oldbuf (current-buffer)))
1393 (set-buffer buf)
1394 (goto-char (point-min))
1395 (set-buffer oldbuf))
1396 (if enter-buffer
1397 (pop-to-buffer buf)
1398 (display-buffer buf)))
1399 (if enter-buffer
1400 (pop-to-buffer (get-buffer "*Units Table*"))
1401 (display-buffer (get-buffer "*Units Table*")))))
1402
1403 (provide 'calc-units)
1404
1405 ;; Local Variables:
1406 ;; coding: iso-latin-1
1407 ;; End:
1408
1409 ;;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
1410 ;;; calc-units.el ends here
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