1 ;;; calc-units.el --- unit conversion functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Colin Walters <walters@debian.org>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is distributed in the hope that it will be useful,
11 ;; but WITHOUT ANY WARRANTY. No author or distributor
12 ;; accepts responsibility to anyone for the consequences of using it
13 ;; or for whether it serves any particular purpose or works at all,
14 ;; unless he says so in writing. Refer to the GNU Emacs General Public
15 ;; License for full details.
17 ;; Everyone is granted permission to copy, modify and redistribute
18 ;; GNU Emacs, but only under the conditions described in the
19 ;; GNU Emacs General Public License. A copy of this license is
20 ;; supposed to have been given to you along with GNU Emacs so you
21 ;; can know your rights and responsibilities. It should be in a
22 ;; file named COPYING. Among other things, the copyright notice
23 ;; and this notice must be preserved on all copies.
29 ;; This file is autoloaded from calc-ext.el.
34 (defun calc-Need-calc-units () nil)
38 ;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
39 ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)
41 (defvar math-standard-units
44 ( in "2.54 cm" "Inch" )
47 ( mi "5280 ft" "Mile" )
48 ( au "1.495979e11 m" "Astronomical Unit" )
49 ( lyr "9460536207068016 m" "Light Year" )
50 ( pc "206264.80625 au" "Parsec" )
51 ( nmi "1852 m" "Nautical Mile" )
52 ( fath "6 ft" "Fathom" )
54 ( mil "in/1000" "Mil" )
55 ( point "in/72" "Point (1/72 inch)" )
56 ( tpt "in/72.27" "Point (TeX conventions)" )
57 ( Ang "1e-10 m" "Angstrom" )
58 ( mfi "mi+ft+in" "Miles + feet + inches" )
61 ( hect "10000 m^2" "*Hectare" )
62 ( acre "mi^2 / 640" "Acre" )
63 ( b "1e-28 m^2" "Barn" )
66 ( l "1e-3 m^3" "*Liter" )
67 ( L "1e-3 m^3" "Liter" )
68 ( gal "4 qt" "US Gallon" )
71 ( cup "8 ozfl" "Cup" )
72 ( ozfl "2 tbsp" "Fluid Ounce" )
73 ( floz "2 tbsp" "Fluid Ounce" )
74 ( tbsp "3 tsp" "Tablespoon" )
75 ( tsp "4.92892159375 ml" "Teaspoon" )
76 ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" )
77 ( galC "4.54609 l" "Canadian Gallon" )
78 ( galUK "4.546092 l" "UK Gallon" )
83 ( min "60 s" "Minute" )
84 ( hr "60 min" "Hour" )
87 ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" )
88 ( yr "365.25 day" "Year" )
92 ( mph "mi/hr" "*Miles per hour" )
93 ( kph "km/hr" "Kilometers per hour" )
94 ( knot "nmi/hr" "Knot" )
95 ( c "2.99792458e8 m/s" "Speed of light" )
98 ( ga "9.80665 m/s^2" "*\"g\" acceleration" )
102 ( lb "16 oz" "Pound (mass)" )
103 ( oz "28.349523125 g" "Ounce (mass)" )
104 ( ton "2000 lb" "Ton" )
105 ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
106 ( t "1000 kg" "Metric ton" )
107 ( tonUK "1016.0469088 kg" "UK ton" )
108 ( lbt "12 ozt" "Troy pound" )
109 ( ozt "31.103475 g" "Troy ounce" )
110 ( ct ".2 g" "Carat" )
111 ( amu "1.6605402e-24 g" "Unified atomic mass" )
114 ( N "m kg/s^2" "*Newton" )
115 ( dyn "1e-5 N" "Dyne" )
116 ( gf "ga g" "Gram (force)" )
117 ( lbf "4.44822161526 N" "Pound (force)" )
118 ( kip "1000 lbf" "Kilopound (force)" )
119 ( pdl "0.138255 N" "Poundal" )
123 ( erg "1e-7 J" "Erg" )
124 ( cal "4.1868 J" "International Table Calorie" )
125 ( Btu "1055.05585262 J" "International Table Btu" )
126 ( eV "ech V" "Electron volt" )
127 ( ev "eV" "Electron volt" )
128 ( therm "105506000 J" "EEC therm" )
129 ( invcm "h c/cm" "Energy in inverse centimeters" )
130 ( Kayser "invcm" "Kayser (inverse centimeter energy)" )
131 ( men "100/invcm" "Inverse energy in meters" )
132 ( Hzen "h Hz" "Energy in Hertz")
133 ( Ken "k K" "Energy in Kelvins")
134 ;; ( invcm "eV / 8065.47835185" "Energy in inverse centimeters" )
135 ;; ( Hzen "eV / 2.41796958004e14" "Energy in Hertz")
136 ;; ( Ken "eV / 11604.7967327" "Energy in Kelvins")
140 ( hp "745.7 W" "Horsepower" )
143 ( K nil "*Degree Kelvin" K )
144 ( dK "K" "Degree Kelvin" K )
145 ( degK "K" "Degree Kelvin" K )
146 ( dC "K" "Degree Celsius" C )
147 ( degC "K" "Degree Celsius" C )
148 ( dF "(5/9) K" "Degree Fahrenheit" F )
149 ( degF "(5/9) K" "Degree Fahrenheit" F )
152 ( Pa "N/m^2" "*Pascal" )
153 ( bar "1e5 Pa" "Bar" )
154 ( atm "101325 Pa" "Standard atmosphere" )
155 ( torr "atm/760" "Torr" )
156 ( mHg "1000 torr" "Meter of mercury" )
157 ( inHg "25.4 mmHg" "Inch of mercury" )
158 ( inH2O "248.84 Pa" "Inch of water" )
159 ( psi "6894.75729317 Pa" "Pound per square inch" )
162 ( P "0.1 Pa s" "*Poise" )
163 ( St "1e-4 m^2/s" "Stokes" )
167 ( C "A s" "Coulomb" )
168 ( Fdy "ech Nav" "Faraday" )
169 ( e "1.60217733e-19 C" "Elementary charge" )
170 ( ech "1.60217733e-19 C" "Elementary charge" )
174 ( S "A/V" "Siemens" )
177 ( T "Wb/m^2" "Tesla" )
178 ( G "1e-4 T" "Gauss" )
181 ;; Luminous intensity
182 ( cd nil "*Candela" )
183 ( sb "1e4 cd/m^2" "Stilb" )
184 ( lm "cd sr" "Lumen" )
185 ( lx "lm/m^2" "Lux" )
186 ( ph "1e4 lx" "Phot" )
187 ( fc "10.76 lx" "Footcandle" )
188 ( lam "1e4 lm/m^2" "Lambert" )
189 ( flam "1.07639104e-3 lam" "Footlambert" )
192 ( Bq "1/s" "*Becquerel" )
193 ( Ci "3.7e10 Bq" "Curie" )
195 ( Sv "Gy" "Sievert" )
196 ( R "2.58e-4 C/kg" "Roentgen" )
197 ( rd ".01 Gy" "Rad" )
200 ;; Amount of substance
204 ( rad nil "*Radian" )
205 ( circ "2 pi rad" "Full circle" )
206 ( rev "circ" "Full revolution" )
207 ( deg "circ/360" "Degree" )
208 ( arcmin "deg/60" "Arc minute" )
209 ( arcsec "arcmin/60" "Arc second" )
210 ( grad "circ/400" "Grade" )
211 ( rpm "rev/min" "Revolutions per minute" )
214 ( sr nil "*Steradian" )
216 ;; Other physical quantities (Physics Letters B239, 1 (1990))
217 ( h "6.6260755e-34 J s" "*Planck's constant" )
218 ( hbar "h / 2 pi" "Planck's constant" )
219 ( mu0 "4 pi 1e-7 H/m" "Permeability of vacuum" )
220 ( Grav "6.67259e-11 N m^2/kg^2" "Gravitational constant" )
221 ( Nav "6.0221367e23 / mol" "Avagadro's constant" )
222 ( me "0.51099906 MeV/c^2" "Electron rest mass" )
223 ( mp "1.007276470 amu" "Proton rest mass" )
224 ( mn "1.008664904 amu" "Neutron rest mass" )
225 ( mu "0.113428913 amu" "Muon rest mass" )
226 ( Ryd "1.0973731571e5 invcm" "Rydberg's constant" )
227 ( k "1.3806513e-23 J/K" "Boltzmann's constant" )
228 ( fsc "1 / 137.0359895" "Fine structure constant" )
229 ( muB "5.78838263e-11 MeV/T" "Bohr magneton" )
230 ( muN "3.15245166e-14 MeV/T" "Nuclear magneton" )
231 ( mue "1.001159652193 muB" "Electron magnetic moment" )
232 ( mup "2.792847386 muN" "Proton magnetic moment" )
233 ( R0 "Nav k" "Molar gas constant" )
234 ( V0 "22.413992 L/mol" "Standard volume of ideal gas" )))
237 (defvar math-additional-units nil
238 "*Additional units table for user-defined units.
239 Must be formatted like math-standard-units.
240 If this is changed, be sure to set math-units-table to nil to ensure
241 that the combined units table will be rebuilt.")
243 (defvar math-unit-prefixes
244 '( ( ?E (float 1 18) "Exa" )
245 ( ?P (float 1 15) "Peta" )
246 ( ?T (float 1 12) "Tera" )
247 ( ?G (float 1 9) "Giga" )
248 ( ?M (float 1 6) "Mega" )
249 ( ?k (float 1 3) "Kilo" )
250 ( ?K (float 1 3) "Kilo" )
251 ( ?h (float 1 2) "Hecto" )
252 ( ?H (float 1 2) "Hecto" )
253 ( ?D (float 1 1) "Deka" )
254 ( 0 (float 1 0) nil )
255 ( ?d (float 1 -1) "Deci" )
256 ( ?c (float 1 -2) "Centi" )
257 ( ?m (float 1 -3) "Milli" )
258 ( ?u (float 1 -6) "Micro" )
259 ( ?n (float 1 -9) "Nano" )
260 ( ?p (float 1 -12) "Pico" )
261 ( ?f (float 1 -15) "Femto" )
262 ( ?a (float 1 -18) "Atto" )))
264 (defvar math-standard-units-systems
266 ( si ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
267 ( mks ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
268 ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
270 (defvar math-units-table nil
271 "Internal units table derived from math-defined-units.
272 Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
274 (defvar math-units-table-buffer-valid nil)
278 (defun calc-base-units ()
281 (let ((calc-autorange-units nil))
282 (calc-enter-result 1 "bsun" (math-simplify-units
283 (math-to-standard-units (calc-top-n 1)
286 (defun calc-quick-units ()
289 (let* ((num (- last-command-char ?0))
290 (pos (if (= num 0) 10 num))
291 (units (calc-var-value 'var-Units))
292 (expr (calc-top-n 1)))
293 (unless (and (>= num 0) (<= num 9))
294 (errunless "Bad unit number"))
295 (unless (math-vectorp units)
296 (errunless "No \"quick units\" are defined"))
297 (unless (< pos (length units))
298 (errunless "Unit number %d not defined" pos))
299 (if (math-units-in-expr-p expr nil)
300 (calc-enter-result 1 (format "cun%d" num)
301 (math-convert-units expr (nth pos units)))
302 (calc-enter-result 1 (format "*un%d" num)
304 (math-mul expr (nth pos units))))))))
306 (defun calc-convert-units (&optional old-units new-units)
309 (let ((expr (calc-top-n 1))
312 (unless (math-units-in-expr-p expr t)
313 (let ((uold (or old-units
315 (setq uoldname (read-string "Old units: "))
316 (if (equal uoldname "")
320 (if (string-match "\\` */" uoldname)
321 (setq uoldname (concat "1" uoldname)))
322 (math-read-expr uoldname))))))
323 (when (eq (car-safe uold) 'error)
324 (error "Bad format in units expression: %s" (nth 1 uold)))
325 (setq expr (math-mul expr uold))))
327 (setq new-units (read-string (if uoldname
328 (concat "Old units: "
332 (when (string-match "\\` */" new-units)
333 (setq new-units (concat "1" new-units)))
334 (setq units (math-read-expr new-units))
335 (when (eq (car-safe units) 'error)
336 (error "Bad format in units expression: %s" (nth 2 units)))
337 (let ((unew (math-units-in-expr-p units t))
338 (std (and (eq (car-safe units) 'var)
339 (assq (nth 1 units) math-standard-units-systems))))
341 (calc-enter-result 1 "cvun" (math-simplify-units
342 (math-to-standard-units expr
345 (error "No units specified"))
346 (calc-enter-result 1 "cvun"
349 (and uoldname (not (equal uoldname "1"))))))))))
351 (defun calc-autorange-units (arg)
354 (calc-change-mode 'calc-autorange-units arg nil t)
355 (message (if calc-autorange-units
356 "Adjusting target unit prefix automatically"
357 "Using target units exactly"))))
359 (defun calc-convert-temperature (&optional old-units new-units)
362 (let ((expr (calc-top-n 1))
366 (setq uold (or old-units
367 (let ((units (math-single-units-in-expr-p expr)))
370 (list 'var (car units)
371 (intern (concat "var-"
374 (error "Not a pure temperature expression"))
376 (setq uoldname (read-string
377 "Old temperature units: ")))))))
378 (when (eq (car-safe uold) 'error)
379 (error "Bad format in units expression: %s" (nth 2 uold)))
380 (or (math-units-in-expr-p expr nil)
381 (setq expr (math-mul expr uold)))
382 (setq unew (or new-units
384 (read-string (if uoldname
385 (concat "Old temperature units: "
388 "New temperature units: ")))))
389 (when (eq (car-safe unew) 'error)
390 (error "Bad format in units expression: %s" (nth 2 unew)))
391 (calc-enter-result 1 "cvtm" (math-simplify-units
392 (math-convert-temperature expr uold unew
395 (defun calc-remove-units ()
398 (calc-enter-result 1 "rmun" (math-simplify-units
399 (math-remove-units (calc-top-n 1))))))
401 (defun calc-extract-units ()
404 (calc-enter-result 1 "rmun" (math-simplify-units
405 (math-extract-units (calc-top-n 1))))))
407 (defun calc-explain-units ()
410 (let ((num-units nil)
412 (calc-explain-units-rec (calc-top-n 1) 1)
413 (and den-units (string-match "^[^(].* .*[^)]$" den-units)
414 (setq den-units (concat "(" den-units ")")))
417 (message "%s per %s" num-units den-units)
418 (message "%s" num-units))
420 (message "1 per %s" den-units)
421 (message "No units in expression"))))))
423 (defun calc-explain-units-rec (expr pow)
424 (let ((u (math-check-unit-name expr))
426 (if (and u (not (math-zerop pow)))
427 (let ((name (or (nth 2 u) (symbol-name (car u)))))
428 (if (eq (aref name 0) ?\*)
429 (setq name (substring name 1)))
430 (if (string-match "[^a-zA-Z0-9']" name)
431 (if (string-match "^[a-zA-Z0-9' ()]*$" name)
432 (while (setq pos (string-match "[ ()]" name))
433 (setq name (concat (substring name 0 pos)
434 (if (eq (aref name pos) 32) "-" "")
435 (substring name (1+ pos)))))
436 (setq name (concat "(" name ")"))))
437 (or (eq (nth 1 expr) (car u))
438 (setq name (concat (nth 2 (assq (aref (symbol-name
441 (if (and (string-match "[^a-zA-Z0-9']" name)
442 (not (memq (car u) '(mHg gf))))
445 (cond ((or (math-equal-int pow 1)
446 (math-equal-int pow -1)))
447 ((or (math-equal-int pow 2)
448 (math-equal-int pow -2))
449 (if (equal (nth 4 u) '((m . 1)))
450 (setq name (concat "Square-" name))
451 (setq name (concat name "-squared"))))
452 ((or (math-equal-int pow 3)
453 (math-equal-int pow -3))
454 (if (equal (nth 4 u) '((m . 1)))
455 (setq name (concat "Cubic-" name))
456 (setq name (concat name "-cubed"))))
458 (setq name (concat name "^"
459 (math-format-number (math-abs pow))))))
461 (setq num-units (if num-units
462 (concat num-units " " name)
464 (setq den-units (if den-units
465 (concat den-units " " name)
467 (cond ((eq (car-safe expr) '*)
468 (calc-explain-units-rec (nth 1 expr) pow)
469 (calc-explain-units-rec (nth 2 expr) pow))
470 ((eq (car-safe expr) '/)
471 (calc-explain-units-rec (nth 1 expr) pow)
472 (calc-explain-units-rec (nth 2 expr) (- pow)))
473 ((memq (car-safe expr) '(neg + -))
474 (calc-explain-units-rec (nth 1 expr) pow))
475 ((and (eq (car-safe expr) '^)
476 (math-realp (nth 2 expr)))
477 (calc-explain-units-rec (nth 1 expr)
478 (math-mul pow (nth 2 expr))))))))
480 (defun calc-simplify-units ()
483 (calc-with-default-simplification
484 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
486 (defun calc-view-units-table (n)
488 (and n (setq math-units-table-buffer-valid nil))
489 (let ((win (get-buffer-window "*Units Table*")))
492 math-units-table-buffer-valid)
494 (bury-buffer (window-buffer win))
495 (let ((curwin (selected-window)))
497 (switch-to-buffer nil)
498 (select-window curwin)))
499 (math-build-units-table-buffer nil))))
501 (defun calc-enter-units-table (n)
503 (and n (setq math-units-table-buffer-valid nil))
504 (math-build-units-table-buffer t)
505 (message (substitute-command-keys "Type \\[calc] to return to the Calculator")))
507 (defun calc-define-unit (uname desc)
508 (interactive "SDefine unit name: \nsDescription: ")
510 (let ((form (calc-top-n 1))
511 (unit (assq uname math-additional-units)))
513 (setq math-additional-units
514 (cons (setq unit (list uname nil nil))
515 math-additional-units)
516 math-units-table nil))
517 (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
518 (eq (nth 1 form) uname)))
519 (not (math-equal-int form 1))
520 (math-format-flat-expr form 0)))
521 (setcar (cdr (cdr unit)) (and (not (equal desc ""))
523 (calc-invalidate-units-table))
525 (defun calc-undefine-unit (uname)
526 (interactive "SUndefine unit name: ")
528 (let ((unit (assq uname math-additional-units)))
530 (if (assq uname math-standard-units)
531 (error "\"%s\" is a predefined unit name" uname)
532 (error "Unit name \"%s\" not found" uname)))
533 (setq math-additional-units (delq unit math-additional-units)
534 math-units-table nil)))
535 (calc-invalidate-units-table))
537 (defun calc-invalidate-units-table ()
538 (setq math-units-table nil)
539 (let ((buf (get-buffer "*Units Table*")))
544 (goto-char (point-min))
545 (if (looking-at "Calculator Units Table")
546 (let ((buffer-read-only nil))
547 (insert "(Obsolete) "))))))))
549 (defun calc-get-unit-definition (uname)
550 (interactive "SGet definition for unit: ")
552 (math-build-units-table)
553 (let ((unit (assq uname math-units-table)))
555 (error "Unit name \"%s\" not found" uname))
556 (let ((msg (nth 2 unit)))
558 (if (string-match "^\\*" msg)
559 (setq msg (substring msg 1)))
560 (setq msg (symbol-name uname)))
563 (calc-enter-result 0 "ugdf" (nth 1 unit))
564 (message "Derived unit: %s" msg))
565 (calc-enter-result 0 "ugdf" (list 'var uname
568 (symbol-name uname)))))
569 (message "Base unit: %s" msg))))))
571 (defun calc-permanent-units ()
575 (set-buffer (find-file-noselect (substitute-in-file-name
576 calc-settings-file)))
577 (goto-char (point-min))
578 (if (and (search-forward ";;; Custom units stored by Calc" nil t)
582 (search-forward "\n;;; End of custom units" nil t)))
586 (delete-region pos (point)))
587 (goto-char (point-max))
590 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
591 (if math-additional-units
593 (insert "(setq math-additional-units '(\n")
594 (let ((list math-additional-units))
596 (insert " (" (symbol-name (car (car list))) " "
597 (if (nth 1 (car list))
598 (if (stringp (nth 1 (car list)))
599 (prin1-to-string (nth 1 (car list)))
600 (prin1-to-string (math-format-flat-expr
601 (nth 1 (car list)) 0)))
604 (prin1-to-string (nth 2 (car list)))
606 (setq list (cdr list))))
608 (insert ";;; (no custom units defined)\n"))
609 (insert ";;; End of custom units\n")
614 (defun math-build-units-table ()
616 (let* ((combined-units (append math-additional-units
617 math-standard-units))
618 (unit-list (mapcar 'car combined-units))
620 (message "Building units table...")
621 (setq math-units-table-buffer-valid nil)
622 (setq tab (mapcar (function
626 (if (stringp (nth 1 x))
627 (let ((exp (math-read-plain-expr
629 (if (eq (car-safe exp) 'error)
630 (error "Format error in definition of %s in units table: %s"
637 (list (cons (car x) 1))))))
639 (let ((math-units-table tab))
640 (mapcar 'math-find-base-units tab))
641 (message "Building units table...done")
642 (setq math-units-table tab))))
644 (defun math-find-base-units (entry)
645 (if (eq (nth 4 entry) 'boom)
646 (error "Circular definition involving unit %s" (car entry)))
649 (setcar (nthcdr 4 entry) 'boom)
650 (math-find-base-units-rec (nth 1 entry) 1)
652 (error "Dimensionless definition for unit %s" (car entry)))
653 (while (eq (cdr (car base)) 0)
654 (setq base (cdr base)))
657 (if (eq (cdr (car (cdr b))) 0)
658 (setcdr b (cdr (cdr b)))
660 (setq base (sort base 'math-compare-unit-names))
661 (setcar (nthcdr 4 entry) base)
664 (defun math-compare-unit-names (a b)
665 (memq (car b) (cdr (memq (car a) unit-list))))
667 (defun math-find-base-units-rec (expr pow)
668 (let ((u (math-check-unit-name expr)))
670 (let ((ulist (math-find-base-units u)))
672 (let ((p (* (cdr (car ulist)) pow))
673 (old (assq (car (car ulist)) base)))
675 (setcdr old (+ (cdr old) p))
676 (setq base (cons (cons (car (car ulist)) p) base))))
677 (setq ulist (cdr ulist)))))
678 ((math-scalarp expr))
679 ((and (eq (car expr) '^)
680 (integerp (nth 2 expr)))
681 (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
683 (math-find-base-units-rec (nth 1 expr) pow)
684 (math-find-base-units-rec (nth 2 expr) pow))
686 (math-find-base-units-rec (nth 1 expr) pow)
687 (math-find-base-units-rec (nth 2 expr) (- pow)))
688 ((eq (car expr) 'neg)
689 (math-find-base-units-rec (nth 1 expr) pow))
691 (math-find-base-units-rec (nth 1 expr) pow))
692 ((eq (car expr) 'var)
693 (or (eq (nth 1 expr) 'pi)
694 (error "Unknown name %s in defining expression for unit %s"
695 (nth 1 expr) (car entry))))
696 (t (error "Malformed defining expression for unit %s" (car entry))))))
699 (defun math-units-in-expr-p (expr sub-exprs)
701 (if (eq (car expr) 'var)
702 (math-check-unit-name expr)
704 (memq (car expr) '(* / ^)))
705 (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
706 (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
708 (defun math-only-units-in-expr-p (expr)
710 (if (eq (car expr) 'var)
711 (math-check-unit-name expr)
712 (if (memq (car expr) '(* /))
713 (and (math-only-units-in-expr-p (nth 1 expr))
714 (math-only-units-in-expr-p (nth 2 expr)))
715 (and (eq (car expr) '^)
716 (and (math-only-units-in-expr-p (nth 1 expr))
717 (math-realp (nth 2 expr))))))))
719 (defun math-single-units-in-expr-p (expr)
720 (cond ((math-scalarp expr) nil)
721 ((eq (car expr) 'var)
722 (math-check-unit-name expr))
724 (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
725 (u2 (math-single-units-in-expr-p (nth 2 expr))))
726 (or (and u1 u2 'wrong)
730 (if (math-units-in-expr-p (nth 2 expr) nil)
732 (math-single-units-in-expr-p (nth 1 expr))))
735 (defun math-check-unit-name (v)
736 (and (eq (car-safe v) 'var)
737 (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
738 (let ((name (symbol-name (nth 1 v))))
739 (and (> (length name) 1)
740 (assq (aref name 0) math-unit-prefixes)
741 (or (assq (intern (substring name 1)) math-units-table)
742 (and (eq (aref name 0) ?M)
744 (eq (aref name 1) ?e)
745 (eq (aref name 2) ?g)
746 (assq (intern (substring name 3))
747 math-units-table))))))))
750 (defun math-to-standard-units (expr which-standard)
751 (math-to-standard-rec expr))
753 (defun math-to-standard-rec (expr)
754 (if (eq (car-safe expr) 'var)
755 (let ((u (math-check-unit-name expr))
760 (setq expr (math-to-standard-rec (nth 1 u)))
761 (let ((st (assq (car u) which-standard)))
763 (setq expr (nth 1 st))
764 (setq expr (list 'var (car u)
765 (intern (concat "var-"
771 (nth 1 (assq (aref (symbol-name base) 0)
778 (if (Math-primp expr)
781 (mapcar 'math-to-standard-rec (cdr expr))))))
783 (defun math-apply-units (expr units ulist &optional pure)
787 (setq expr (math-simplify-units expr))
788 (or (math-numberp expr)
789 (error "Incompatible units"))
791 (setq value (math-div expr (nth 1 (car ulist)))
792 value (math-floor (let ((calc-internal-prec
793 (1- calc-internal-prec)))
794 (math-normalize value)))
795 new (math-add new (math-mul value (car (car ulist))))
796 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
798 (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
800 (math-simplify-units (if pure
802 (list '* expr units)))))
804 (defvar math-decompose-units-cache nil)
805 (defun math-decompose-units (units)
806 (let ((u (math-check-unit-name units)))
807 (and u (eq (car-safe (nth 1 u)) '+)
808 (setq units (nth 1 u))))
809 (setq units (calcFunc-expand units))
810 (and (eq (car-safe units) '+)
811 (let ((entry (list units calc-internal-prec calc-prefer-frac)))
812 (or (equal entry (car math-decompose-units-cache))
816 (while (eq (car-safe utemp) '+)
817 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
819 utemp (nth 1 utemp)))
820 (setq ulist (cons (math-decompose-unit-part utemp) ulist)
822 (while (setq utemp (cdr utemp))
823 (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
824 (error "Inconsistent units in sum")))
825 (setq math-decompose-units-cache
830 (not (Math-lessp (nth 1 x)
832 (cdr math-decompose-units-cache))))
834 (defun math-decompose-unit-part (unit)
836 (math-is-multiple (math-simplify-units (math-to-standard-units
840 (defun math-find-compatible-unit (expr unit)
841 (let ((u (math-check-unit-name unit)))
843 (math-find-compatible-unit-rec expr 1))))
845 (defun math-find-compatible-unit-rec (expr pow)
846 (cond ((eq (car-safe expr) '*)
847 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
848 (math-find-compatible-unit-rec (nth 2 expr) pow)))
849 ((eq (car-safe expr) '/)
850 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
851 (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
852 ((and (eq (car-safe expr) '^)
853 (integerp (nth 2 expr)))
854 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
856 (let ((u2 (math-check-unit-name expr)))
857 (if (equal (nth 4 u) (nth 4 u2))
860 (defun math-convert-units (expr new-units &optional pure)
861 (math-with-extra-prec 2
862 (let ((compat (and (not pure) (math-find-compatible-unit expr new-units)))
864 (math-combining-units nil))
867 (math-mul (math-mul (math-simplify-units
868 (math-div expr (math-pow (car compat)
870 (math-pow new-units (cdr compat)))
872 (math-to-standard-units
873 (math-pow (math-div (car compat) new-units)
876 (when (setq unit-list (math-decompose-units new-units))
877 (setq new-units (nth 2 (car unit-list))))
878 (when (eq (car-safe expr) '+)
879 (setq expr (math-simplify-units expr)))
880 (if (math-units-in-expr-p expr t)
881 (math-convert-units-rec expr)
882 (math-apply-units (math-to-standard-units
883 (list '/ expr new-units) nil)
884 new-units unit-list pure))))))
886 (defun math-convert-units-rec (expr)
887 (if (math-units-in-expr-p expr nil)
888 (math-apply-units (math-to-standard-units (list '/ expr new-units) nil)
889 new-units unit-list pure)
890 (if (Math-primp expr)
893 (mapcar 'math-convert-units-rec (cdr expr))))))
895 (defun math-convert-temperature (expr old new &optional pure)
896 (let* ((units (math-single-units-in-expr-p expr))
899 (equal (nth 1 old) (car units)))
900 (math-check-unit-name old)
901 (error "Inconsistent temperature units"))
903 (unew (math-check-unit-name new)))
904 (unless (and (consp unew) (nth 3 unew))
905 (error "Not a valid temperature unit"))
906 (unless (and (consp uold) (nth 3 uold))
907 (error "Not a pure temperature expression"))
908 (let ((v (car uold)))
909 (setq expr (list '/ expr (list 'var v
910 (intern (concat "var-"
911 (symbol-name v)))))))
912 (or (eq (nth 3 uold) (nth 3 unew))
913 (cond ((eq (nth 3 uold) 'K)
914 (setq expr (list '- expr '(float 27315 -2)))
915 (if (eq (nth 3 unew) 'F)
916 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))))
917 ((eq (nth 3 uold) 'C)
918 (if (eq (nth 3 unew) 'F)
919 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))
920 (setq expr (list '+ expr '(float 27315 -2)))))
922 (setq expr (list '* (list '- expr 32) '(frac 5 9)))
923 (if (eq (nth 3 unew) 'K)
924 (setq expr (list '+ expr '(float 27315 -2)))))))
927 (list '* expr new))))
931 (defun math-simplify-units (a)
932 (let ((math-simplifying-units t)
933 (calc-matrix-mode 'scalar))
935 (defalias 'calcFunc-usimplify 'math-simplify-units)
937 (math-defsimplify (+ -)
938 (and math-simplifying-units
939 (math-units-in-expr-p (nth 1 expr) nil)
940 (let* ((units (math-extract-units (nth 1 expr)))
941 (ratio (math-simplify (math-to-standard-units
942 (list '/ (nth 2 expr) units) nil))))
943 (if (math-units-in-expr-p ratio nil)
945 (calc-record-why "*Inconsistent units" expr)
947 (list '* (math-add (math-remove-units (nth 1 expr))
948 (if (eq (car expr) '-) (math-neg ratio) ratio))
952 (math-simplify-units-prod))
954 (defun math-simplify-units-prod ()
955 (and math-simplifying-units
957 (Math-realp (nth 1 expr))
958 (let* ((num (math-float (nth 1 expr)))
959 (xpon (calcFunc-xpon num))
960 (unitp (cdr (cdr expr)))
962 (pow (if (eq (car expr) '*) 1 -1))
964 (and (eq (car-safe unit) '*)
965 (setq unitp (cdr unit)
967 (and (eq (car-safe unit) '^)
968 (integerp (nth 2 unit))
969 (setq pow (* pow (nth 2 unit))
972 (and (setq u (math-check-unit-name unit))
975 (>= xpon (if (eq (car u) 'm) 1 3)))
978 (reverse math-unit-prefixes)
982 (or (eq (car u) (nth 1 unit))
987 math-unit-prefixes))))))
988 (setq xpon (+ xpon uxpon))
990 (or (memq (car (car p)) '(?d ?D ?h ?H))
991 (and (eq (car (car p)) ?c)
992 (not (eq (car u) 'm)))
993 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
996 (setq pname (math-build-var-name
997 (if (eq (car (car p)) 0)
999 (concat (char-to-string
1003 (and (/= (car (car p)) 0)
1005 math-units-table)))))
1009 (or (not (eq p pref))
1010 (< xpon (+ pxpon (* (math-abs pow) 3))))
1013 (let ((calc-prefer-frac nil))
1014 (calcFunc-scf (nth 1 expr)
1016 (setcar unitp pname)
1020 (and math-simplifying-units
1021 (let ((np (cdr expr))
1022 (try-cancel-units 0)
1024 (setq n (if (eq (car-safe (nth 2 expr)) '*)
1027 (if (math-realp (car n))
1029 (setcar (cdr expr) (math-mul (nth 1 expr)
1030 (let ((calc-prefer-frac nil))
1031 (math-div 1 (car n)))))
1033 (while (eq (car-safe (setq n (car np))) '*)
1034 (math-simplify-units-divisor (cdr n) (cdr (cdr expr)))
1035 (setq np (cdr (cdr n))))
1036 (math-simplify-units-divisor np (cdr (cdr expr)))
1037 (if (eq try-cancel-units 0)
1038 (let* ((math-simplifying-units nil)
1039 (base (math-simplify (math-to-standard-units expr nil))))
1040 (if (Math-numberp base)
1042 (if (eq (car-safe expr) '/)
1043 (math-simplify-units-prod))
1046 (defun math-simplify-units-divisor (np dp)
1049 (while (eq (car-safe (setq d (car dp))) '*)
1050 (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1051 (setcar np (setq n temp))
1053 (setq dp (cdr (cdr d))))
1054 (when (setq temp (math-simplify-units-quotient n d))
1055 (setcar np (setq n temp))
1058 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1059 (defun math-simplify-units-quotient (n d)
1062 (when (and (eq (car-safe n) '^)
1063 (integerp (nth 2 n)))
1064 (setq pow1 (nth 2 n) n (nth 1 n)))
1065 (when (and (eq (car-safe d) '^)
1066 (integerp (nth 2 d)))
1067 (setq pow2 (nth 2 d) d (nth 1 d)))
1068 (let ((un (math-check-unit-name n))
1069 (ud (math-check-unit-name d)))
1071 (if (and (equal (nth 4 un) (nth 4 ud))
1073 (math-to-standard-units (list '/ n d) nil)
1080 (and (eq (car (car un)) (car (car ud1)))
1081 (setq try-cancel-units
1083 (- (* (cdr (car un)) pow1)
1084 (* (cdr (car ud)) pow2)))))
1085 (setq ud1 (cdr ud1)))
1090 (and math-simplifying-units
1091 (math-realp (nth 2 expr))
1092 (if (memq (car-safe (nth 1 expr)) '(* /))
1093 (list (car (nth 1 expr))
1094 (list '^ (nth 1 (nth 1 expr)) (nth 2 expr))
1095 (list '^ (nth 2 (nth 1 expr)) (nth 2 expr)))
1096 (math-simplify-units-pow (nth 1 expr) (nth 2 expr)))))
1098 (math-defsimplify calcFunc-sqrt
1099 (and math-simplifying-units
1100 (if (memq (car-safe (nth 1 expr)) '(* /))
1101 (list (car (nth 1 expr))
1102 (list 'calcFunc-sqrt (nth 1 (nth 1 expr)))
1103 (list 'calcFunc-sqrt (nth 2 (nth 1 expr))))
1104 (math-simplify-units-pow (nth 1 expr) '(frac 1 2)))))
1106 (math-defsimplify (calcFunc-floor
1116 (and math-simplifying-units
1118 (if (math-only-units-in-expr-p (nth 1 expr))
1120 (if (and (memq (car-safe (nth 1 expr)) '(* /))
1121 (or (math-only-units-in-expr-p
1122 (nth 1 (nth 1 expr)))
1123 (math-only-units-in-expr-p
1124 (nth 2 (nth 1 expr)))))
1125 (list (car (nth 1 expr))
1127 (cons (nth 1 (nth 1 expr))
1130 (cons (nth 2 (nth 1 expr))
1131 (cdr (cdr expr)))))))))
1133 (defun math-simplify-units-pow (a pow)
1134 (if (and (eq (car-safe a) '^)
1135 (math-check-unit-name (nth 1 a))
1136 (math-realp (nth 2 a)))
1137 (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1138 (let* ((u (math-check-unit-name a))
1139 (pf (math-to-simple-fraction pow))
1140 (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1142 (math-units-are-multiple u d)
1143 (list '^ (math-to-standard-units a nil) pow)))))
1146 (defun math-units-are-multiple (u n)
1148 (while (and u (= (% (cdr (car u)) n) 0))
1152 (math-defsimplify calcFunc-sin
1153 (and math-simplifying-units
1154 (math-units-in-expr-p (nth 1 expr) nil)
1155 (let ((rad (math-simplify-units
1157 (math-to-standard-units (nth 1 expr) nil))))
1158 (calc-angle-mode 'rad))
1159 (and (eq (car-safe rad) '*)
1160 (math-realp (nth 1 rad))
1161 (eq (car-safe (nth 2 rad)) 'var)
1162 (eq (nth 1 (nth 2 rad)) 'rad)
1163 (list 'calcFunc-sin (nth 1 rad))))))
1165 (math-defsimplify calcFunc-cos
1166 (and math-simplifying-units
1167 (math-units-in-expr-p (nth 1 expr) nil)
1168 (let ((rad (math-simplify-units
1170 (math-to-standard-units (nth 1 expr) nil))))
1171 (calc-angle-mode 'rad))
1172 (and (eq (car-safe rad) '*)
1173 (math-realp (nth 1 rad))
1174 (eq (car-safe (nth 2 rad)) 'var)
1175 (eq (nth 1 (nth 2 rad)) 'rad)
1176 (list 'calcFunc-cos (nth 1 rad))))))
1178 (math-defsimplify calcFunc-tan
1179 (and math-simplifying-units
1180 (math-units-in-expr-p (nth 1 expr) nil)
1181 (let ((rad (math-simplify-units
1183 (math-to-standard-units (nth 1 expr) nil))))
1184 (calc-angle-mode 'rad))
1185 (and (eq (car-safe rad) '*)
1186 (math-realp (nth 1 rad))
1187 (eq (car-safe (nth 2 rad)) 'var)
1188 (eq (nth 1 (nth 2 rad)) 'rad)
1189 (list 'calcFunc-tan (nth 1 rad))))))
1192 (defun math-remove-units (expr)
1193 (if (math-check-unit-name expr)
1195 (if (Math-primp expr)
1198 (mapcar 'math-remove-units (cdr expr))))))
1200 (defun math-extract-units (expr)
1201 (if (memq (car-safe expr) '(* /))
1203 (mapcar 'math-extract-units (cdr expr)))
1204 (if (math-check-unit-name expr) expr 1)))
1206 (defun math-build-units-table-buffer (enter-buffer)
1207 (if (not (and math-units-table math-units-table-buffer-valid
1208 (get-buffer "*Units Table*")))
1209 (let ((buf (get-buffer-create "*Units Table*"))
1210 (uptr (math-build-units-table))
1211 (calc-language (if (eq calc-language 'big) nil calc-language))
1212 (calc-float-format '(float 0))
1213 (calc-group-digits nil)
1214 (calc-number-radix 10)
1215 (calc-point-char ".")
1219 (message "Formatting units table...")
1221 (setq buffer-read-only nil)
1223 (insert "Calculator Units Table:\n\n")
1224 (insert "Unit Type Definition Description\n\n")
1228 (when (eq (car u) 'm)
1230 (setq shadowed (and std (assq (car u) math-additional-units)))
1233 (eq (aref name 0) ?\*))
1234 (unless (eq uptr math-units-table)
1236 (setq name (substring name 1)))
1238 (and shadowed (insert "("))
1239 (insert (symbol-name (car u)))
1240 (and shadowed (insert ")"))
1244 (insert (symbol-name (nth 3 u))))
1250 (and shadowed (insert "("))
1252 (insert (math-format-value (nth 1 u) 80))
1253 (insert (symbol-name (car u))))
1254 (and shadowed (insert ")"))
1260 (insert " (redefined above)")
1262 (insert " (base unit)")))
1264 (setq uptr (cdr uptr)))
1265 (insert "\n\nUnit Prefix Table:\n\n")
1266 (setq uptr math-unit-prefixes)
1269 (insert " " (char-to-string (car u)))
1270 (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1271 (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1274 (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1276 (insert " " (nth 2 u) "\n")
1277 (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1279 (setq buffer-read-only t)
1280 (message "Formatting units table...done"))
1281 (setq math-units-table-buffer-valid t)
1282 (let ((oldbuf (current-buffer)))
1284 (goto-char (point-min))
1285 (set-buffer oldbuf))
1288 (display-buffer buf)))
1290 (pop-to-buffer (get-buffer "*Units Table*"))
1291 (display-buffer (get-buffer "*Units Table*")))))
1293 ;;; calc-units.el ends here