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 ;; Maintainers: D. Goel <deego@gnufans.org>
7 ;; Colin Walters <walters@debian.org>
9 ;; This file is part of GNU Emacs.
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.
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.
30 ;; This file is autoloaded from calc-ext.el.
35 (defun calc-Need-calc-units () nil)
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
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 ;;; - http://physics.nist.gov/cuu/Constants/index.html
48 (defvar math-standard-units
51 ( in "2.54 cm" "Inch" )
54 ( mi "5280 ft" "Mile" )
55 ( au "149597870691 m" "Astronomical Unit" ) ;; NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
56 ( lyr "9460536207068016 m" "Light Year" )
57 ( pc "206264.80625 au" "Parsec" )
58 ( nmi "1852 m" "Nautical Mile" )
59 ( fath "6 ft" "Fathom" )
61 ( mil "in/1000" "Mil" )
62 ( point "in/72" "Point (1/72 inch)" )
63 ( tpt "in/72.27" "Point (TeX conventions)" )
64 ( Ang "1e-10 m" "Angstrom" )
65 ( mfi "mi+ft+in" "Miles + feet + inches" )
68 ( hect "10000 m^2" "*Hectare" )
69 ( acre "mi^2 / 640" "Acre" )
70 ( b "1e-28 m^2" "Barn" )
73 ( l "1e-3 m^3" "*Liter" )
74 ( L "1e-3 m^3" "Liter" )
75 ( gal "4 qt" "US Gallon" )
78 ( cup "8 ozfl" "Cup" )
79 ( ozfl "2 tbsp" "Fluid Ounce" )
80 ( floz "2 tbsp" "Fluid Ounce" )
81 ( tbsp "3 tsp" "Tablespoon" )
82 ( tsp "4.92892159375 ml" "Teaspoon" )
83 ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" )
84 ( galC "4.54609 l" "Canadian Gallon" )
85 ( galUK "4.546092 l" "UK Gallon" )
90 ( min "60 s" "Minute" )
91 ( hr "60 min" "Hour" )
94 ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" )
95 ( yr "365.25 day" "Year" )
99 ( mph "mi/hr" "*Miles per hour" )
100 ( kph "km/hr" "Kilometers per hour" )
101 ( knot "nmi/hr" "Knot" )
102 ( c "2.99792458e8 m/s" "Speed of light" )
105 ( ga "9.80665 m/s^2" "*\"g\" acceleration" )
109 ( lb "16 oz" "Pound (mass)" )
110 ( oz "28.349523125 g" "Ounce (mass)" )
111 ( ton "2000 lb" "Ton" )
112 ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
113 ( t "1000 kg" "Metric ton" )
114 ( tonUK "1016.0469088 kg" "UK ton" )
115 ( lbt "12 ozt" "Troy pound" )
116 ( ozt "31.103475 g" "Troy ounce" )
117 ( ct ".2 g" "Carat" )
118 ( amu "1.66053873e-27 kg" "Unified atomic mass" ) ;; CODATA 1998
121 ( N "m kg/s^2" "*Newton" )
122 ( dyn "1e-5 N" "Dyne" )
123 ( gf "ga g" "Gram (force)" )
124 ( lbf "4.44822161526 N" "Pound (force)" )
125 ( kip "1000 lbf" "Kilopound (force)" )
126 ( pdl "0.138255 N" "Poundal" )
130 ( erg "1e-7 J" "Erg" )
131 ( cal "4.1868 J" "International Table Calorie" )
132 ( Btu "1055.05585262 J" "International Table Btu" )
133 ( eV "ech V" "Electron volt" )
134 ( ev "eV" "Electron volt" )
135 ( therm "105506000 J" "EEC therm" )
136 ( invcm "h c/cm" "Energy in inverse centimeters" )
137 ( Kayser "invcm" "Kayser (inverse centimeter energy)" )
138 ( men "100/invcm" "Inverse energy in meters" )
139 ( Hzen "h Hz" "Energy in Hertz")
140 ( Ken "k K" "Energy in Kelvins")
141 ( Wh "W h" "Watt hour")
142 ( Ws "W s" "Watt second")
146 ( hp "745.7 W" "Horsepower" )
149 ( K nil "*Degree Kelvin" K )
150 ( dK "K" "Degree Kelvin" K )
151 ( degK "K" "Degree Kelvin" K )
152 ( dC "K" "Degree Celsius" C )
153 ( degC "K" "Degree Celsius" C )
154 ( dF "(5/9) K" "Degree Fahrenheit" F )
155 ( degF "(5/9) K" "Degree Fahrenheit" F )
158 ( Pa "N/m^2" "*Pascal" )
159 ( bar "1e5 Pa" "Bar" )
160 ( atm "101325 Pa" "Standard atmosphere" )
161 ( torr " 1.333224e2 Pa" "Torr" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
162 ( mHg "1000 torr" "Meter of mercury" )
163 ( inHg "25.4 mmHg" "Inch of mercury" )
164 ( inH2O "2.490889e2 Pa" "Inch of water" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
165 ( psi "6894.75729317 Pa" "Pound per square inch" )
168 ( P "0.1 Pa s" "*Poise" )
169 ( St "1e-4 m^2/s" "Stokes" )
173 ( C "A s" "Coulomb" )
174 ( Fdy "ech Nav" "Faraday" )
175 ( e "1.602176462e-19 C" "Elementary charge" ) ;; CODATA 1998
176 ( ech "1.602176462e-19 C" "Elementary charge" ) ;; CODATA 1998
180 ( S "A/V" "Siemens" )
183 ( T "Wb/m^2" "Tesla" )
184 ( G "1e-4 T" "Gauss" )
187 ;; Luminous intensity
188 ( cd nil "*Candela" )
189 ( sb "1e4 cd/m^2" "Stilb" )
190 ( lm "cd sr" "Lumen" )
191 ( lx "lm/m^2" "Lux" )
192 ( ph "1e4 lx" "Phot" )
193 ( fc "10.76391 lx" "Footcandle" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
194 ( lam "1e4 lm/m^2" "Lambert" )
195 ( flam "3.426259 cd/m^2" "Footlambert" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
198 ( Bq "1/s" "*Becquerel" )
199 ( Ci "3.7e10 Bq" "Curie" )
201 ( Sv "Gy" "Sievert" )
202 ( R "2.58e-4 C/kg" "Roentgen" )
203 ( rd ".01 Gy" "Rad" )
206 ;; Amount of substance
210 ( rad nil "*Radian" )
211 ( circ "2 pi rad" "Full circle" )
212 ( rev "circ" "Full revolution" )
213 ( deg "circ/360" "Degree" )
214 ( arcmin "deg/60" "Arc minute" )
215 ( arcsec "arcmin/60" "Arc second" )
216 ( grad "circ/400" "Grade" )
217 ( rpm "rev/min" "Revolutions per minute" )
220 ( sr nil "*Steradian" )
222 ;; Other physical quantities (CODATA 1998)
223 ( h "6.62606876e-34 J s" "*Planck's constant" )
224 ( hbar "h / 2 pi" "Planck's constant" )
225 ( mu0 "4 pi 1e-7 H/m" "Permeability of vacuum" )
226 ( Grav "6.673e-11 m^3/kg^1/s^2" "Gravitational constant" )
227 ( Nav "6.02214199e23 / mol" "Avagadro's constant" )
228 ( me "9.10938188e-31 kg" "Electron rest mass" )
229 ( mp "1.67262158e-27 kg" "Proton rest mass" )
230 ( mn "1.67492716e-27 kg" "Neutron rest mass" )
231 ( mu "1.88353109e-28 kg" "Muon rest mass" )
232 ( Ryd "10973731.568549 /m" "Rydberg's constant" )
233 ( k "1.3806503e-23 J/K" "Boltzmann's constant" )
234 ( fsc "7.297352533e-3" "Fine structure constant" )
235 ( muB "927.400899e-26 J/T" "Bohr magneton" )
236 ( muN "5.05078317e-27 J/T" "Nuclear magneton" )
237 ( mue "-928.476362e-26 J/T" "Electron magnetic moment" )
238 ( mup "1.410606633e-26 J/T" "Proton magnetic moment" )
239 ( R0 "8.314472 J/mol/K" "Molar gas constant" )
240 ( V0 "22.710981e-3 m^3/mol" "Standard volume of ideal gas" )))
243 (defvar math-additional-units nil
244 "*Additional units table for user-defined units.
245 Must be formatted like math-standard-units.
246 If this is changed, be sure to set math-units-table to nil to ensure
247 that the combined units table will be rebuilt.")
249 (defvar math-unit-prefixes
250 '( ( ?E (float 1 18) "Exa" )
251 ( ?P (float 1 15) "Peta" )
252 ( ?T (float 1 12) "Tera" )
253 ( ?G (float 1 9) "Giga" )
254 ( ?M (float 1 6) "Mega" )
255 ( ?k (float 1 3) "Kilo" )
256 ( ?K (float 1 3) "Kilo" )
257 ( ?h (float 1 2) "Hecto" )
258 ( ?H (float 1 2) "Hecto" )
259 ( ?D (float 1 1) "Deka" )
260 ( 0 (float 1 0) nil )
261 ( ?d (float 1 -1) "Deci" )
262 ( ?c (float 1 -2) "Centi" )
263 ( ?m (float 1 -3) "Milli" )
264 ( ?u (float 1 -6) "Micro" )
265 ( ?n (float 1 -9) "Nano" )
266 ( ?p (float 1 -12) "Pico" )
267 ( ?f (float 1 -15) "Femto" )
268 ( ?a (float 1 -18) "Atto" )))
270 (defvar math-standard-units-systems
272 ( si ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
273 ( mks ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) )
274 ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
276 (defvar math-units-table nil
277 "Internal units table derived from math-defined-units.
278 Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
280 (defvar math-units-table-buffer-valid nil)
284 (defun calc-base-units ()
287 (let ((calc-autorange-units nil))
288 (calc-enter-result 1 "bsun" (math-simplify-units
289 (math-to-standard-units (calc-top-n 1)
292 (defun calc-quick-units ()
295 (let* ((num (- last-command-char ?0))
296 (pos (if (= num 0) 10 num))
297 (units (calc-var-value 'var-Units))
298 (expr (calc-top-n 1)))
299 (unless (and (>= num 0) (<= num 9))
300 (errunless "Bad unit number"))
301 (unless (math-vectorp units)
302 (errunless "No \"quick units\" are defined"))
303 (unless (< pos (length units))
304 (errunless "Unit number %d not defined" pos))
305 (if (math-units-in-expr-p expr nil)
306 (calc-enter-result 1 (format "cun%d" num)
307 (math-convert-units expr (nth pos units)))
308 (calc-enter-result 1 (format "*un%d" num)
310 (math-mul expr (nth pos units))))))))
312 (defun calc-convert-units (&optional old-units new-units)
315 (let ((expr (calc-top-n 1))
318 (unless (math-units-in-expr-p expr t)
319 (let ((uold (or old-units
321 (setq uoldname (read-string "Old units: "))
322 (if (equal uoldname "")
326 (if (string-match "\\` */" uoldname)
327 (setq uoldname (concat "1" uoldname)))
328 (math-read-expr uoldname))))))
329 (when (eq (car-safe uold) 'error)
330 (error "Bad format in units expression: %s" (nth 1 uold)))
331 (setq expr (math-mul expr uold))))
333 (setq new-units (read-string (if uoldname
334 (concat "Old units: "
338 (when (string-match "\\` */" new-units)
339 (setq new-units (concat "1" new-units)))
340 (setq units (math-read-expr new-units))
341 (when (eq (car-safe units) 'error)
342 (error "Bad format in units expression: %s" (nth 2 units)))
343 (let ((unew (math-units-in-expr-p units t))
344 (std (and (eq (car-safe units) 'var)
345 (assq (nth 1 units) math-standard-units-systems))))
347 (calc-enter-result 1 "cvun" (math-simplify-units
348 (math-to-standard-units expr
351 (error "No units specified"))
352 (calc-enter-result 1 "cvun"
355 (and uoldname (not (equal uoldname "1"))))))))))
357 (defun calc-autorange-units (arg)
360 (calc-change-mode 'calc-autorange-units arg nil t)
361 (message (if calc-autorange-units
362 "Adjusting target unit prefix automatically"
363 "Using target units exactly"))))
365 (defun calc-convert-temperature (&optional old-units new-units)
368 (let ((expr (calc-top-n 1))
372 (setq uold (or old-units
373 (let ((units (math-single-units-in-expr-p expr)))
376 (list 'var (car units)
377 (intern (concat "var-"
380 (error "Not a pure temperature expression"))
382 (setq uoldname (read-string
383 "Old temperature units: ")))))))
384 (when (eq (car-safe uold) 'error)
385 (error "Bad format in units expression: %s" (nth 2 uold)))
386 (or (math-units-in-expr-p expr nil)
387 (setq expr (math-mul expr uold)))
388 (setq unew (or new-units
390 (read-string (if uoldname
391 (concat "Old temperature units: "
394 "New temperature units: ")))))
395 (when (eq (car-safe unew) 'error)
396 (error "Bad format in units expression: %s" (nth 2 unew)))
397 (calc-enter-result 1 "cvtm" (math-simplify-units
398 (math-convert-temperature expr uold unew
401 (defun calc-remove-units ()
404 (calc-enter-result 1 "rmun" (math-simplify-units
405 (math-remove-units (calc-top-n 1))))))
407 (defun calc-extract-units ()
410 (calc-enter-result 1 "rmun" (math-simplify-units
411 (math-extract-units (calc-top-n 1))))))
413 (defun calc-explain-units ()
416 (let ((num-units nil)
418 (calc-explain-units-rec (calc-top-n 1) 1)
419 (and den-units (string-match "^[^(].* .*[^)]$" den-units)
420 (setq den-units (concat "(" den-units ")")))
423 (message "%s per %s" num-units den-units)
424 (message "%s" num-units))
426 (message "1 per %s" den-units)
427 (message "No units in expression"))))))
429 (defun calc-explain-units-rec (expr pow)
430 (let ((u (math-check-unit-name expr))
432 (if (and u (not (math-zerop pow)))
433 (let ((name (or (nth 2 u) (symbol-name (car u)))))
434 (if (eq (aref name 0) ?\*)
435 (setq name (substring name 1)))
436 (if (string-match "[^a-zA-Z0-9']" name)
437 (if (string-match "^[a-zA-Z0-9' ()]*$" name)
438 (while (setq pos (string-match "[ ()]" name))
439 (setq name (concat (substring name 0 pos)
440 (if (eq (aref name pos) 32) "-" "")
441 (substring name (1+ pos)))))
442 (setq name (concat "(" name ")"))))
443 (or (eq (nth 1 expr) (car u))
444 (setq name (concat (nth 2 (assq (aref (symbol-name
447 (if (and (string-match "[^a-zA-Z0-9']" name)
448 (not (memq (car u) '(mHg gf))))
451 (cond ((or (math-equal-int pow 1)
452 (math-equal-int pow -1)))
453 ((or (math-equal-int pow 2)
454 (math-equal-int pow -2))
455 (if (equal (nth 4 u) '((m . 1)))
456 (setq name (concat "Square-" name))
457 (setq name (concat name "-squared"))))
458 ((or (math-equal-int pow 3)
459 (math-equal-int pow -3))
460 (if (equal (nth 4 u) '((m . 1)))
461 (setq name (concat "Cubic-" name))
462 (setq name (concat name "-cubed"))))
464 (setq name (concat name "^"
465 (math-format-number (math-abs pow))))))
467 (setq num-units (if num-units
468 (concat num-units " " name)
470 (setq den-units (if den-units
471 (concat den-units " " name)
473 (cond ((eq (car-safe expr) '*)
474 (calc-explain-units-rec (nth 1 expr) pow)
475 (calc-explain-units-rec (nth 2 expr) pow))
476 ((eq (car-safe expr) '/)
477 (calc-explain-units-rec (nth 1 expr) pow)
478 (calc-explain-units-rec (nth 2 expr) (- pow)))
479 ((memq (car-safe expr) '(neg + -))
480 (calc-explain-units-rec (nth 1 expr) pow))
481 ((and (eq (car-safe expr) '^)
482 (math-realp (nth 2 expr)))
483 (calc-explain-units-rec (nth 1 expr)
484 (math-mul pow (nth 2 expr))))))))
486 (defun calc-simplify-units ()
489 (calc-with-default-simplification
490 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
492 (defun calc-view-units-table (n)
494 (and n (setq math-units-table-buffer-valid nil))
495 (let ((win (get-buffer-window "*Units Table*")))
498 math-units-table-buffer-valid)
500 (bury-buffer (window-buffer win))
501 (let ((curwin (selected-window)))
503 (switch-to-buffer nil)
504 (select-window curwin)))
505 (math-build-units-table-buffer nil))))
507 (defun calc-enter-units-table (n)
509 (and n (setq math-units-table-buffer-valid nil))
510 (math-build-units-table-buffer t)
511 (message (substitute-command-keys "Type \\[calc] to return to the Calculator")))
513 (defun calc-define-unit (uname desc)
514 (interactive "SDefine unit name: \nsDescription: ")
516 (let ((form (calc-top-n 1))
517 (unit (assq uname math-additional-units)))
519 (setq math-additional-units
520 (cons (setq unit (list uname nil nil))
521 math-additional-units)
522 math-units-table nil))
523 (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
524 (eq (nth 1 form) uname)))
525 (not (math-equal-int form 1))
526 (math-format-flat-expr form 0)))
527 (setcar (cdr (cdr unit)) (and (not (equal desc ""))
529 (calc-invalidate-units-table))
531 (defun calc-undefine-unit (uname)
532 (interactive "SUndefine unit name: ")
534 (let ((unit (assq uname math-additional-units)))
536 (if (assq uname math-standard-units)
537 (error "\"%s\" is a predefined unit name" uname)
538 (error "Unit name \"%s\" not found" uname)))
539 (setq math-additional-units (delq unit math-additional-units)
540 math-units-table nil)))
541 (calc-invalidate-units-table))
543 (defun calc-invalidate-units-table ()
544 (setq math-units-table nil)
545 (let ((buf (get-buffer "*Units Table*")))
550 (goto-char (point-min))
551 (if (looking-at "Calculator Units Table")
552 (let ((buffer-read-only nil))
553 (insert "(Obsolete) "))))))))
555 (defun calc-get-unit-definition (uname)
556 (interactive "SGet definition for unit: ")
558 (math-build-units-table)
559 (let ((unit (assq uname math-units-table)))
561 (error "Unit name \"%s\" not found" uname))
562 (let ((msg (nth 2 unit)))
564 (if (string-match "^\\*" msg)
565 (setq msg (substring msg 1)))
566 (setq msg (symbol-name uname)))
569 (calc-enter-result 0 "ugdf" (nth 1 unit))
570 (message "Derived unit: %s" msg))
571 (calc-enter-result 0 "ugdf" (list 'var uname
574 (symbol-name uname)))))
575 (message "Base unit: %s" msg))))))
577 (defun calc-permanent-units ()
581 (set-buffer (find-file-noselect (substitute-in-file-name
582 calc-settings-file)))
583 (goto-char (point-min))
584 (if (and (search-forward ";;; Custom units stored by Calc" nil t)
588 (search-forward "\n;;; End of custom units" nil t)))
592 (delete-region pos (point)))
593 (goto-char (point-max))
596 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
597 (if math-additional-units
599 (insert "(setq math-additional-units '(\n")
600 (let ((list math-additional-units))
602 (insert " (" (symbol-name (car (car list))) " "
603 (if (nth 1 (car list))
604 (if (stringp (nth 1 (car list)))
605 (prin1-to-string (nth 1 (car list)))
606 (prin1-to-string (math-format-flat-expr
607 (nth 1 (car list)) 0)))
610 (prin1-to-string (nth 2 (car list)))
612 (setq list (cdr list))))
614 (insert ";;; (no custom units defined)\n"))
615 (insert ";;; End of custom units\n")
620 (defun math-build-units-table ()
622 (let* ((combined-units (append math-additional-units
623 math-standard-units))
624 (unit-list (mapcar 'car combined-units))
626 (message "Building units table...")
627 (setq math-units-table-buffer-valid nil)
628 (setq tab (mapcar (function
632 (if (stringp (nth 1 x))
633 (let ((exp (math-read-plain-expr
635 (if (eq (car-safe exp) 'error)
636 (error "Format error in definition of %s in units table: %s"
643 (list (cons (car x) 1))))))
645 (let ((math-units-table tab))
646 (mapcar 'math-find-base-units tab))
647 (message "Building units table...done")
648 (setq math-units-table tab))))
650 (defun math-find-base-units (entry)
651 (if (eq (nth 4 entry) 'boom)
652 (error "Circular definition involving unit %s" (car entry)))
655 (setcar (nthcdr 4 entry) 'boom)
656 (math-find-base-units-rec (nth 1 entry) 1)
658 (error "Dimensionless definition for unit %s" (car entry)))
659 (while (eq (cdr (car base)) 0)
660 (setq base (cdr base)))
663 (if (eq (cdr (car (cdr b))) 0)
664 (setcdr b (cdr (cdr b)))
666 (setq base (sort base 'math-compare-unit-names))
667 (setcar (nthcdr 4 entry) base)
670 (defun math-compare-unit-names (a b)
671 (memq (car b) (cdr (memq (car a) unit-list))))
673 (defun math-find-base-units-rec (expr pow)
674 (let ((u (math-check-unit-name expr)))
676 (let ((ulist (math-find-base-units u)))
678 (let ((p (* (cdr (car ulist)) pow))
679 (old (assq (car (car ulist)) base)))
681 (setcdr old (+ (cdr old) p))
682 (setq base (cons (cons (car (car ulist)) p) base))))
683 (setq ulist (cdr ulist)))))
684 ((math-scalarp expr))
685 ((and (eq (car expr) '^)
686 (integerp (nth 2 expr)))
687 (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
689 (math-find-base-units-rec (nth 1 expr) pow)
690 (math-find-base-units-rec (nth 2 expr) pow))
692 (math-find-base-units-rec (nth 1 expr) pow)
693 (math-find-base-units-rec (nth 2 expr) (- pow)))
694 ((eq (car expr) 'neg)
695 (math-find-base-units-rec (nth 1 expr) pow))
697 (math-find-base-units-rec (nth 1 expr) pow))
698 ((eq (car expr) 'var)
699 (or (eq (nth 1 expr) 'pi)
700 (error "Unknown name %s in defining expression for unit %s"
701 (nth 1 expr) (car entry))))
702 (t (error "Malformed defining expression for unit %s" (car entry))))))
705 (defun math-units-in-expr-p (expr sub-exprs)
707 (if (eq (car expr) 'var)
708 (math-check-unit-name expr)
710 (memq (car expr) '(* / ^)))
711 (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
712 (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
714 (defun math-only-units-in-expr-p (expr)
716 (if (eq (car expr) 'var)
717 (math-check-unit-name expr)
718 (if (memq (car expr) '(* /))
719 (and (math-only-units-in-expr-p (nth 1 expr))
720 (math-only-units-in-expr-p (nth 2 expr)))
721 (and (eq (car expr) '^)
722 (and (math-only-units-in-expr-p (nth 1 expr))
723 (math-realp (nth 2 expr))))))))
725 (defun math-single-units-in-expr-p (expr)
726 (cond ((math-scalarp expr) nil)
727 ((eq (car expr) 'var)
728 (math-check-unit-name expr))
730 (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
731 (u2 (math-single-units-in-expr-p (nth 2 expr))))
732 (or (and u1 u2 'wrong)
736 (if (math-units-in-expr-p (nth 2 expr) nil)
738 (math-single-units-in-expr-p (nth 1 expr))))
741 (defun math-check-unit-name (v)
742 (and (eq (car-safe v) 'var)
743 (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
744 (let ((name (symbol-name (nth 1 v))))
745 (and (> (length name) 1)
746 (assq (aref name 0) math-unit-prefixes)
747 (or (assq (intern (substring name 1)) math-units-table)
748 (and (eq (aref name 0) ?M)
750 (eq (aref name 1) ?e)
751 (eq (aref name 2) ?g)
752 (assq (intern (substring name 3))
753 math-units-table))))))))
756 (defun math-to-standard-units (expr which-standard)
757 (math-to-standard-rec expr))
759 (defun math-to-standard-rec (expr)
760 (if (eq (car-safe expr) 'var)
761 (let ((u (math-check-unit-name expr))
766 (setq expr (math-to-standard-rec (nth 1 u)))
767 (let ((st (assq (car u) which-standard)))
769 (setq expr (nth 1 st))
770 (setq expr (list 'var (car u)
771 (intern (concat "var-"
777 (nth 1 (assq (aref (symbol-name base) 0)
784 (if (Math-primp expr)
787 (mapcar 'math-to-standard-rec (cdr expr))))))
789 (defun math-apply-units (expr units ulist &optional pure)
793 (setq expr (math-simplify-units expr))
794 (or (math-numberp expr)
795 (error "Incompatible units"))
797 (setq value (math-div expr (nth 1 (car ulist)))
798 value (math-floor (let ((calc-internal-prec
799 (1- calc-internal-prec)))
800 (math-normalize value)))
801 new (math-add new (math-mul value (car (car ulist))))
802 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
804 (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
806 (math-simplify-units (if pure
808 (list '* expr units)))))
810 (defvar math-decompose-units-cache nil)
811 (defun math-decompose-units (units)
812 (let ((u (math-check-unit-name units)))
813 (and u (eq (car-safe (nth 1 u)) '+)
814 (setq units (nth 1 u))))
815 (setq units (calcFunc-expand units))
816 (and (eq (car-safe units) '+)
817 (let ((entry (list units calc-internal-prec calc-prefer-frac)))
818 (or (equal entry (car math-decompose-units-cache))
822 (while (eq (car-safe utemp) '+)
823 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
825 utemp (nth 1 utemp)))
826 (setq ulist (cons (math-decompose-unit-part utemp) ulist)
828 (while (setq utemp (cdr utemp))
829 (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
830 (error "Inconsistent units in sum")))
831 (setq math-decompose-units-cache
836 (not (Math-lessp (nth 1 x)
838 (cdr math-decompose-units-cache))))
840 (defun math-decompose-unit-part (unit)
842 (math-is-multiple (math-simplify-units (math-to-standard-units
846 (defun math-find-compatible-unit (expr unit)
847 (let ((u (math-check-unit-name unit)))
849 (math-find-compatible-unit-rec expr 1))))
851 (defun math-find-compatible-unit-rec (expr pow)
852 (cond ((eq (car-safe expr) '*)
853 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
854 (math-find-compatible-unit-rec (nth 2 expr) pow)))
855 ((eq (car-safe expr) '/)
856 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
857 (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
858 ((and (eq (car-safe expr) '^)
859 (integerp (nth 2 expr)))
860 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
862 (let ((u2 (math-check-unit-name expr)))
863 (if (equal (nth 4 u) (nth 4 u2))
866 (defun math-convert-units (expr new-units &optional pure)
867 (math-with-extra-prec 2
868 (let ((compat (and (not pure) (math-find-compatible-unit expr new-units)))
870 (math-combining-units nil))
873 (math-mul (math-mul (math-simplify-units
874 (math-div expr (math-pow (car compat)
876 (math-pow new-units (cdr compat)))
878 (math-to-standard-units
879 (math-pow (math-div (car compat) new-units)
882 (when (setq unit-list (math-decompose-units new-units))
883 (setq new-units (nth 2 (car unit-list))))
884 (when (eq (car-safe expr) '+)
885 (setq expr (math-simplify-units expr)))
886 (if (math-units-in-expr-p expr t)
887 (math-convert-units-rec expr)
888 (math-apply-units (math-to-standard-units
889 (list '/ expr new-units) nil)
890 new-units unit-list pure))))))
892 (defun math-convert-units-rec (expr)
893 (if (math-units-in-expr-p expr nil)
894 (math-apply-units (math-to-standard-units (list '/ expr new-units) nil)
895 new-units unit-list pure)
896 (if (Math-primp expr)
899 (mapcar 'math-convert-units-rec (cdr expr))))))
901 (defun math-convert-temperature (expr old new &optional pure)
902 (let* ((units (math-single-units-in-expr-p expr))
905 (equal (nth 1 old) (car units)))
906 (math-check-unit-name old)
907 (error "Inconsistent temperature units"))
909 (unew (math-check-unit-name new)))
910 (unless (and (consp unew) (nth 3 unew))
911 (error "Not a valid temperature unit"))
912 (unless (and (consp uold) (nth 3 uold))
913 (error "Not a pure temperature expression"))
914 (let ((v (car uold)))
915 (setq expr (list '/ expr (list 'var v
916 (intern (concat "var-"
917 (symbol-name v)))))))
918 (or (eq (nth 3 uold) (nth 3 unew))
919 (cond ((eq (nth 3 uold) 'K)
920 (setq expr (list '- expr '(float 27315 -2)))
921 (if (eq (nth 3 unew) 'F)
922 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))))
923 ((eq (nth 3 uold) 'C)
924 (if (eq (nth 3 unew) 'F)
925 (setq expr (list '+ (list '* expr '(frac 9 5)) 32))
926 (setq expr (list '+ expr '(float 27315 -2)))))
928 (setq expr (list '* (list '- expr 32) '(frac 5 9)))
929 (if (eq (nth 3 unew) 'K)
930 (setq expr (list '+ expr '(float 27315 -2)))))))
933 (list '* expr new))))
937 (defun math-simplify-units (a)
938 (let ((math-simplifying-units t)
939 (calc-matrix-mode 'scalar))
941 (defalias 'calcFunc-usimplify 'math-simplify-units)
943 (math-defsimplify (+ -)
944 (and math-simplifying-units
945 (math-units-in-expr-p (nth 1 expr) nil)
946 (let* ((units (math-extract-units (nth 1 expr)))
947 (ratio (math-simplify (math-to-standard-units
948 (list '/ (nth 2 expr) units) nil))))
949 (if (math-units-in-expr-p ratio nil)
951 (calc-record-why "*Inconsistent units" expr)
953 (list '* (math-add (math-remove-units (nth 1 expr))
954 (if (eq (car expr) '-) (math-neg ratio) ratio))
958 (math-simplify-units-prod))
960 (defun math-simplify-units-prod ()
961 (and math-simplifying-units
963 (Math-realp (nth 1 expr))
964 (let* ((num (math-float (nth 1 expr)))
965 (xpon (calcFunc-xpon num))
966 (unitp (cdr (cdr expr)))
968 (pow (if (eq (car expr) '*) 1 -1))
970 (and (eq (car-safe unit) '*)
971 (setq unitp (cdr unit)
973 (and (eq (car-safe unit) '^)
974 (integerp (nth 2 unit))
975 (setq pow (* pow (nth 2 unit))
978 (and (setq u (math-check-unit-name unit))
981 (>= xpon (if (eq (car u) 'm) 1 3)))
984 (reverse math-unit-prefixes)
988 (or (eq (car u) (nth 1 unit))
993 math-unit-prefixes))))))
994 (setq xpon (+ xpon uxpon))
996 (or (memq (car (car p)) '(?d ?D ?h ?H))
997 (and (eq (car (car p)) ?c)
998 (not (eq (car u) 'm)))
999 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1002 (setq pname (math-build-var-name
1003 (if (eq (car (car p)) 0)
1005 (concat (char-to-string
1009 (and (/= (car (car p)) 0)
1011 math-units-table)))))
1015 (or (not (eq p pref))
1016 (< xpon (+ pxpon (* (math-abs pow) 3))))
1019 (let ((calc-prefer-frac nil))
1020 (calcFunc-scf (nth 1 expr)
1022 (setcar unitp pname)
1026 (and math-simplifying-units
1027 (let ((np (cdr expr))
1028 (try-cancel-units 0)
1030 (setq n (if (eq (car-safe (nth 2 expr)) '*)
1033 (if (math-realp (car n))
1035 (setcar (cdr expr) (math-mul (nth 1 expr)
1036 (let ((calc-prefer-frac nil))
1037 (math-div 1 (car n)))))
1039 (while (eq (car-safe (setq n (car np))) '*)
1040 (math-simplify-units-divisor (cdr n) (cdr (cdr expr)))
1041 (setq np (cdr (cdr n))))
1042 (math-simplify-units-divisor np (cdr (cdr expr)))
1043 (if (eq try-cancel-units 0)
1044 (let* ((math-simplifying-units nil)
1045 (base (math-simplify (math-to-standard-units expr nil))))
1046 (if (Math-numberp base)
1048 (if (eq (car-safe expr) '/)
1049 (math-simplify-units-prod))
1052 (defun math-simplify-units-divisor (np dp)
1055 (while (eq (car-safe (setq d (car dp))) '*)
1056 (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1057 (setcar np (setq n temp))
1059 (setq dp (cdr (cdr d))))
1060 (when (setq temp (math-simplify-units-quotient n d))
1061 (setcar np (setq n temp))
1064 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1065 (defun math-simplify-units-quotient (n d)
1068 (when (and (eq (car-safe n) '^)
1069 (integerp (nth 2 n)))
1070 (setq pow1 (nth 2 n) n (nth 1 n)))
1071 (when (and (eq (car-safe d) '^)
1072 (integerp (nth 2 d)))
1073 (setq pow2 (nth 2 d) d (nth 1 d)))
1074 (let ((un (math-check-unit-name n))
1075 (ud (math-check-unit-name d)))
1077 (if (and (equal (nth 4 un) (nth 4 ud))
1079 (math-to-standard-units (list '/ n d) nil)
1086 (and (eq (car (car un)) (car (car ud1)))
1087 (setq try-cancel-units
1089 (- (* (cdr (car un)) pow1)
1090 (* (cdr (car ud)) pow2)))))
1091 (setq ud1 (cdr ud1)))
1096 (and math-simplifying-units
1097 (math-realp (nth 2 expr))
1098 (if (memq (car-safe (nth 1 expr)) '(* /))
1099 (list (car (nth 1 expr))
1100 (list '^ (nth 1 (nth 1 expr)) (nth 2 expr))
1101 (list '^ (nth 2 (nth 1 expr)) (nth 2 expr)))
1102 (math-simplify-units-pow (nth 1 expr) (nth 2 expr)))))
1104 (math-defsimplify calcFunc-sqrt
1105 (and math-simplifying-units
1106 (if (memq (car-safe (nth 1 expr)) '(* /))
1107 (list (car (nth 1 expr))
1108 (list 'calcFunc-sqrt (nth 1 (nth 1 expr)))
1109 (list 'calcFunc-sqrt (nth 2 (nth 1 expr))))
1110 (math-simplify-units-pow (nth 1 expr) '(frac 1 2)))))
1112 (math-defsimplify (calcFunc-floor
1122 (and math-simplifying-units
1124 (if (math-only-units-in-expr-p (nth 1 expr))
1126 (if (and (memq (car-safe (nth 1 expr)) '(* /))
1127 (or (math-only-units-in-expr-p
1128 (nth 1 (nth 1 expr)))
1129 (math-only-units-in-expr-p
1130 (nth 2 (nth 1 expr)))))
1131 (list (car (nth 1 expr))
1133 (cons (nth 1 (nth 1 expr))
1136 (cons (nth 2 (nth 1 expr))
1137 (cdr (cdr expr)))))))))
1139 (defun math-simplify-units-pow (a pow)
1140 (if (and (eq (car-safe a) '^)
1141 (math-check-unit-name (nth 1 a))
1142 (math-realp (nth 2 a)))
1143 (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1144 (let* ((u (math-check-unit-name a))
1145 (pf (math-to-simple-fraction pow))
1146 (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1148 (math-units-are-multiple u d)
1149 (list '^ (math-to-standard-units a nil) pow)))))
1152 (defun math-units-are-multiple (u n)
1154 (while (and u (= (% (cdr (car u)) n) 0))
1158 (math-defsimplify calcFunc-sin
1159 (and math-simplifying-units
1160 (math-units-in-expr-p (nth 1 expr) nil)
1161 (let ((rad (math-simplify-units
1163 (math-to-standard-units (nth 1 expr) nil))))
1164 (calc-angle-mode 'rad))
1165 (and (eq (car-safe rad) '*)
1166 (math-realp (nth 1 rad))
1167 (eq (car-safe (nth 2 rad)) 'var)
1168 (eq (nth 1 (nth 2 rad)) 'rad)
1169 (list 'calcFunc-sin (nth 1 rad))))))
1171 (math-defsimplify calcFunc-cos
1172 (and math-simplifying-units
1173 (math-units-in-expr-p (nth 1 expr) nil)
1174 (let ((rad (math-simplify-units
1176 (math-to-standard-units (nth 1 expr) nil))))
1177 (calc-angle-mode 'rad))
1178 (and (eq (car-safe rad) '*)
1179 (math-realp (nth 1 rad))
1180 (eq (car-safe (nth 2 rad)) 'var)
1181 (eq (nth 1 (nth 2 rad)) 'rad)
1182 (list 'calcFunc-cos (nth 1 rad))))))
1184 (math-defsimplify calcFunc-tan
1185 (and math-simplifying-units
1186 (math-units-in-expr-p (nth 1 expr) nil)
1187 (let ((rad (math-simplify-units
1189 (math-to-standard-units (nth 1 expr) nil))))
1190 (calc-angle-mode 'rad))
1191 (and (eq (car-safe rad) '*)
1192 (math-realp (nth 1 rad))
1193 (eq (car-safe (nth 2 rad)) 'var)
1194 (eq (nth 1 (nth 2 rad)) 'rad)
1195 (list 'calcFunc-tan (nth 1 rad))))))
1198 (defun math-remove-units (expr)
1199 (if (math-check-unit-name expr)
1201 (if (Math-primp expr)
1204 (mapcar 'math-remove-units (cdr expr))))))
1206 (defun math-extract-units (expr)
1207 (if (memq (car-safe expr) '(* /))
1209 (mapcar 'math-extract-units (cdr expr)))
1210 (if (math-check-unit-name expr) expr 1)))
1212 (defun math-build-units-table-buffer (enter-buffer)
1213 (if (not (and math-units-table math-units-table-buffer-valid
1214 (get-buffer "*Units Table*")))
1215 (let ((buf (get-buffer-create "*Units Table*"))
1216 (uptr (math-build-units-table))
1217 (calc-language (if (eq calc-language 'big) nil calc-language))
1218 (calc-float-format '(float 0))
1219 (calc-group-digits nil)
1220 (calc-number-radix 10)
1221 (calc-point-char ".")
1225 (message "Formatting units table...")
1227 (setq buffer-read-only nil)
1229 (insert "Calculator Units Table:\n\n")
1230 (insert "Unit Type Definition Description\n\n")
1234 (when (eq (car u) 'm)
1236 (setq shadowed (and std (assq (car u) math-additional-units)))
1239 (eq (aref name 0) ?\*))
1240 (unless (eq uptr math-units-table)
1242 (setq name (substring name 1)))
1244 (and shadowed (insert "("))
1245 (insert (symbol-name (car u)))
1246 (and shadowed (insert ")"))
1250 (insert (symbol-name (nth 3 u))))
1256 (and shadowed (insert "("))
1258 (insert (math-format-value (nth 1 u) 80))
1259 (insert (symbol-name (car u))))
1260 (and shadowed (insert ")"))
1266 (insert " (redefined above)")
1268 (insert " (base unit)")))
1270 (setq uptr (cdr uptr)))
1271 (insert "\n\nUnit Prefix Table:\n\n")
1272 (setq uptr math-unit-prefixes)
1275 (insert " " (char-to-string (car u)))
1276 (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1277 (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1280 (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1282 (insert " " (nth 2 u) "\n")
1283 (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1285 (setq buffer-read-only t)
1286 (message "Formatting units table...done"))
1287 (setq math-units-table-buffer-valid t)
1288 (let ((oldbuf (current-buffer)))
1290 (goto-char (point-min))
1291 (set-buffer oldbuf))
1294 (display-buffer buf)))
1296 (pop-to-buffer (get-buffer "*Units Table*"))
1297 (display-buffer (get-buffer "*Units Table*")))))
1300 ;; coding: iso-latin-1
1303 ;;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
1304 ;;; calc-units.el ends here