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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, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
5
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8
9 ;; This file is part of GNU Emacs.
10
11 ;; GNU Emacs is free software: you can redistribute it and/or modify
12 ;; it under the terms of the GNU General Public License as published by
13 ;; the Free Software Foundation, either version 3 of the License, or
14 ;; (at your option) any later version.
15
16 ;; GNU Emacs is distributed in the hope that it will be useful,
17 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
18 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 ;; GNU General Public License for more details.
20
21 ;; You should have received a copy of the GNU General Public License
22 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
23
24 ;;; Commentary:
25
26 ;;; Code:
27
28 ;; This file is autoloaded from calc-ext.el.
29
30 (require 'calc-ext)
31 (require 'calc-macs)
32 (eval-when-compile
33 (require 'calc-alg))
34
35 ;;; Units operations.
36
37 ;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
38 ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)
39 ;;; Updated April 2002 by Jochen Küpper
40
41 ;;; Updated August 2007, using
42 ;;; CODATA (http://physics.nist.gov/cuu/Constants/index.html)
43 ;;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
44 ;;; ESUWM (Encyclopaedia of Scientific Units, Weights and
45 ;;; Measures, by François Cardarelli)
46 ;;; All conversions are exact unless otherwise noted.
47
48 (defvar math-standard-units
49 '( ;; Length
50 ( m nil "*Meter" )
51 ( in "254*10^(-2) cm" "Inch" nil
52 "2.54 cm")
53 ( ft "12 in" "Foot")
54 ( yd "3 ft" "Yard" )
55 ( mi "5280 ft" "Mile" )
56 ( au "149597870691. m" "Astronomical Unit" nil
57 "149597870691 m (*)")
58 ;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
59 ( lyr "c yr" "Light Year" )
60 ( pc "3.0856775854*10^16 m" "Parsec (**)" nil
61 "3.0856775854 10^16 m (*)") ;; (approx) ESUWM
62 ( nmi "1852 m" "Nautical Mile" )
63 ( fath "6 ft" "Fathom" )
64 ( fur "660 ft" "Furlong")
65 ( mu "1 um" "Micron" )
66 ( mil "(1/1000) in" "Mil" )
67 ( point "(1/72) in" "Point (PostScript convention)" )
68 ( Ang "10^(-10) m" "Angstrom" )
69 ( mfi "mi+ft+in" "Miles + feet + inches" )
70 ;; TeX lengths
71 ( texpt "(100/7227) in" "Point (TeX convention) (**)" )
72 ( texpc "12 texpt" "Pica (TeX convention) (**)" )
73 ( texbp "point" "Big point (TeX convention) (**)" )
74 ( texdd "(1238/1157) texpt" "Didot point (TeX convention) (**)" )
75 ( texcc "12 texdd" "Cicero (TeX convention) (**)" )
76 ( texsp "(1/65536) texpt" "Scaled TeX point (TeX convention) (**)" )
77
78 ;; Area
79 ( hect "10000 m^2" "*Hectare" )
80 ( a "100 m^2" "Are")
81 ( acre "(1/640) mi^2" "Acre" )
82 ( b "10^(-28) m^2" "Barn" )
83
84 ;; Volume
85 ( L "10^(-3) m^3" "*Liter" )
86 ( l "L" "Liter" )
87 ( gal "4 qt" "US Gallon" )
88 ( qt "2 pt" "Quart" )
89 ( pt "2 cup" "Pint (**)" )
90 ( cup "8 ozfl" "Cup" )
91 ( ozfl "2 tbsp" "Fluid Ounce" )
92 ( floz "2 tbsp" "Fluid Ounce" )
93 ( tbsp "3 tsp" "Tablespoon" )
94 ;; ESUWM defines a US gallon as 231 in^3.
95 ;; That gives the following exact value for tsp.
96 ( tsp "492892159375*10^(-11) ml" "Teaspoon" nil
97 "4.92892159375 ml")
98 ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" nil
99 "tsp+tbsp+ozfl+cup+pt+qt+gal")
100 ( galC "galUK" "Canadian Gallon" )
101 ( galUK "454609*10^(-5) L" "UK Gallon" nil
102 "4.54609 L") ;; NIST
103
104 ;; Time
105 ( s nil "*Second" )
106 ( sec "s" "Second" )
107 ( min "60 s" "Minute" )
108 ( hr "60 min" "Hour" )
109 ( day "24 hr" "Day" )
110 ( wk "7 day" "Week" )
111 ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" )
112 ( yr "36525*10^(-2) day" "Year (Julian)" nil
113 "365.25 day")
114 ( Hz "1/s" "Hertz" )
115
116 ;; Speed
117 ( mph "mi/hr" "*Miles per hour" )
118 ( kph "km/hr" "Kilometers per hour" )
119 ( knot "nmi/hr" "Knot" )
120 ( c "299792458 m/s" "Speed of light" ) ;;; CODATA
121
122 ;; Acceleration
123 ( ga "980665*10^(-5) m/s^2" "*\"g\" acceleration" nil
124 "9.80665 m / s^2") ;; CODATA
125
126 ;; Mass
127 ( g nil "*Gram" )
128 ( lb "16 oz" "Pound (mass)" )
129 ( oz "28349523125*10^(-9) g" "Ounce (mass)" nil
130 "28.349523125 g") ;; ESUWM
131 ( ton "2000 lb" "Ton" )
132 ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
133 ( t "1000 kg" "Metric ton" )
134 ( tonUK "10160469088*10^(-7) kg" "UK ton" nil
135 "1016.0469088 kg") ;; ESUWM
136 ( lbt "12 ozt" "Troy pound" )
137 ( ozt "311034768*10^(-7) g" "Troy ounce" nil
138 "31.10347680 g") ;; ESUWM, 1/12 exact value for lbt
139 ( ct "(2/10) g" "Carat" nil
140 "0.2 g") ;; ESUWM
141 ( u "1.660538782*10^(-27) kg" "Unified atomic mass" nil
142 "1.660538782 10^-27 kg (*)");;(approx) CODATA
143
144 ;; Force
145 ( N "m kg/s^2" "*Newton" )
146 ( dyn "10^(-5) N" "Dyne" )
147 ( gf "ga g" "Gram (force)" )
148 ( lbf "ga lb" "Pound (force)" )
149 ( kip "1000 lbf" "Kilopound (force)" )
150 ( pdl "138254954376*10^(-12) N" "Poundal" nil
151 "0.138254954376 N") ;; ESUWM
152
153 ;; Energy
154 ( J "N m" "*Joule" )
155 ( erg "10^(-7) J" "Erg" )
156 ( cal "41868*10^(-4) J" "International Table Calorie" nil
157 "4.1868 J") ;; NIST
158 ( calth "4184*10^(-3) J" "Thermochemical Calorie" nil
159 "4.184 J") ;; NIST
160 ( Cal "1000 cal" "Large Calorie")
161 ( Btu "105505585262*10^(-8) J" "International Table Btu" nil
162 "1055.05585262 J") ;; ESUWM
163 ( eV "ech V" "Electron volt" )
164 ( ev "eV" "Electron volt" )
165 ( therm "105506000 J" "EEC therm" )
166 ( invcm "h c/cm" "Energy in inverse centimeters" )
167 ( Kayser "invcm" "Kayser (inverse centimeter energy)" )
168 ( men "100/invcm" "Inverse energy in meters" )
169 ( Hzen "h Hz" "Energy in Hertz")
170 ( Ken "k K" "Energy in Kelvins")
171 ( Wh "W hr" "Watt hour")
172 ( Ws "W s" "Watt second")
173
174 ;; Power
175 ( W "J/s" "*Watt" )
176 ( hp "550 ft lbf/s" "Horsepower") ;;ESUWM
177 ( hpm "75 m kgf/s" "Metric Horsepower") ;;ESUWM
178
179 ;; Temperature
180 ( K nil "*Degree Kelvin" K )
181 ( dK "K" "Degree Kelvin" K )
182 ( degK "K" "Degree Kelvin" K )
183 ( dC "K" "Degree Celsius" C )
184 ( degC "K" "Degree Celsius" C )
185 ( dF "(5/9) K" "Degree Fahrenheit" F )
186 ( degF "(5/9) K" "Degree Fahrenheit" F )
187
188 ;; Pressure
189 ( Pa "N/m^2" "*Pascal" )
190 ( bar "10^5 Pa" "Bar" )
191 ( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA
192 ( Torr "(1/760) atm" "Torr")
193 ( mHg "1000 Torr" "Meter of mercury" )
194 ( inHg "254*10^(-1) mmHg" "Inch of mercury" nil
195 "25.4 mmHg")
196 ( inH2O "2.490889*10^2 Pa" "Inch of water" nil
197 "2.490889 10^2 Pa (*)") ;;(approx) NIST
198 ( psi "lbf/in^2" "Pounds per square inch" )
199
200 ;; Viscosity
201 ( P "(1/10) Pa s" "*Poise" )
202 ( St "10^(-4) m^2/s" "Stokes" )
203
204 ;; Electromagnetism
205 ( A nil "*Ampere" )
206 ( C "A s" "Coulomb" )
207 ( Fdy "ech Nav" "Faraday" )
208 ( e "ech" "Elementary charge" )
209 ( ech "1.602176487*10^(-19) C" "Elementary charge" nil
210 "1.602176487 10^-19 C (*)") ;;(approx) CODATA
211 ( V "W/A" "Volt" )
212 ( ohm "V/A" "Ohm" )
213 ( Ω "ohm" "Ohm" )
214 ( mho "A/V" "Mho" )
215 ( S "A/V" "Siemens" )
216 ( F "C/V" "Farad" )
217 ( H "Wb/A" "Henry" )
218 ( T "Wb/m^2" "Tesla" )
219 ( Gs "10^(-4) T" "Gauss" )
220 ( Wb "V s" "Weber" )
221
222 ;; Luminous intensity
223 ( cd nil "*Candela" )
224 ( sb "10000 cd/m^2" "Stilb" )
225 ( lm "cd sr" "Lumen" )
226 ( lx "lm/m^2" "Lux" )
227 ( ph "10000 lx" "Phot" )
228 ( fc "lm/ft^2" "Footcandle") ;; ESUWM
229 ( lam "10000 lm/m^2" "Lambert" )
230 ( flam "(1/pi) cd/ft^2" "Footlambert") ;; ESUWM
231
232 ;; Radioactivity
233 ( Bq "1/s" "*Becquerel" )
234 ( Ci "37*10^9 Bq" "Curie" ) ;; ESUWM
235 ( Gy "J/kg" "Gray" )
236 ( Sv "Gy" "Sievert" )
237 ( R "258*10^(-6) C/kg" "Roentgen" ) ;; NIST
238 ( rd "(1/100) Gy" "Rad" )
239 ( rem "rd" "Rem" )
240
241 ;; Amount of substance
242 ( mol nil "*Mole" )
243
244 ;; Plane angle
245 ( rad nil "*Radian" )
246 ( circ "2 pi rad" "Full circle" )
247 ( rev "circ" "Full revolution" )
248 ( deg "circ/360" "Degree" )
249 ( arcmin "deg/60" "Arc minute" )
250 ( arcsec "arcmin/60" "Arc second" )
251 ( grad "circ/400" "Grade" )
252 ( rpm "rev/min" "Revolutions per minute" )
253
254 ;; Solid angle
255 ( sr nil "*Steradian" )
256
257 ;; Other physical quantities
258 ;; The values are from CODATA, and are approximate.
259 ( h "6.62606896*10^(-34) J s" "*Planck's constant" nil
260 "6.62606896 10^-34 J s (*)")
261 ( hbar "h / (2 pi)" "Planck's constant" ) ;; Exact
262 ( mu0 "4 pi 10^(-7) H/m" "Permeability of vacuum") ;; Exact
263 ( μ0 "mu0" "Permeability of vacuum") ;; Exact
264 ( eps0 "1 / (mu0 c^2)" "Permittivity of vacuum" )
265 ( ε0 "eps0" "Permittivity of vacuum" )
266 ( G "6.67428*10^(-11) m^3/(kg s^2)" "Gravitational constant" nil
267 "6.67428 10^-11 m^3/(kg s^2) (*)")
268 ( Nav "6.02214179*10^(23) / mol" "Avogadro's constant" nil
269 "6.02214179 10^23 / mol (*)")
270 ( me "9.10938215*10^(-31) kg" "Electron rest mass" nil
271 "9.10938215 10^-31 kg (*)")
272 ( mp "1.672621637*10^(-27) kg" "Proton rest mass" nil
273 "1.672621637 10^-27 kg (*)")
274 ( mn "1.674927211*10^(-27) kg" "Neutron rest mass" nil
275 "1.674927211 10^-27 kg (*)")
276 ( mmu "1.88353130*10^(-28) kg" "Muon rest mass" nil
277 "1.88353130 10^-28 kg (*)")
278 ( mμ "mmu" "Muon rest mass" nil
279 "1.88353130 10^-28 kg (*)")
280 ( Ryd "10973731.568527 /m" "Rydberg's constant" nil
281 "10973731.568527 /m (*)")
282 ( k "1.3806504*10^(-23) J/K" "Boltzmann's constant" nil
283 "1.3806504 10^-23 J/K (*)")
284 ( alpha "7.2973525376*10^(-3)" "Fine structure constant" nil
285 "7.2973525376 10^-3 (*)")
286 ( α "alpha" "Fine structure constant" nil
287 "7.2973525376 10^-3 (*)")
288 ( muB "927.400915*10^(-26) J/T" "Bohr magneton" nil
289 "927.400915 10^-26 J/T (*)")
290 ( muN "5.05078324*10^(-27) J/T" "Nuclear magneton" nil
291 "5.05078324 10^-27 J/T (*)")
292 ( mue "-928.476377*10^(-26) J/T" "Electron magnetic moment" nil
293 "-928.476377 10^-26 J/T (*)")
294 ( mup "1.410606662*10^(-26) J/T" "Proton magnetic moment" nil
295 "1.410606662 10^-26 J/T (*)")
296 ( R0 "8.314472 J/(mol K)" "Molar gas constant" nil
297 "8.314472 J/(mol K) (*)")
298 ( V0 "22.710981*10^(-3) m^3/mol" "Standard volume of ideal gas" nil
299 "22.710981 10^-3 m^3/mol (*)")))
300
301
302 (defvar math-additional-units nil
303 "*Additional units table for user-defined units.
304 Must be formatted like `math-standard-units'.
305 If you change this, be sure to set `math-units-table' to nil to ensure
306 that the combined units table will be rebuilt.")
307
308 (defvar math-unit-prefixes
309 '( ( ?Y (^ 10 24) "Yotta" )
310 ( ?Z (^ 10 21) "Zetta" )
311 ( ?E (^ 10 18) "Exa" )
312 ( ?P (^ 10 15) "Peta" )
313 ( ?T (^ 10 12) "Tera" )
314 ( ?G (^ 10 9) "Giga" )
315 ( ?M (^ 10 6) "Mega" )
316 ( ?k (^ 10 3) "Kilo" )
317 ( ?K (^ 10 3) "Kilo" )
318 ( ?h (^ 10 2) "Hecto" )
319 ( ?H (^ 10 2) "Hecto" )
320 ( ?D (^ 10 1) "Deka" )
321 ( 0 (^ 10 0) nil )
322 ( ?d (^ 10 -1) "Deci" )
323 ( ?c (^ 10 -2) "Centi" )
324 ( ?m (^ 10 -3) "Milli" )
325 ( ?u (^ 10 -6) "Micro" )
326 ( ?μ (^ 10 -6) "Micro" )
327 ( ?n (^ 10 -9) "Nano" )
328 ( ?p (^ 10 -12) "Pico" )
329 ( ?f (^ 10 -15) "Femto" )
330 ( ?a (^ 10 -18) "Atto" )
331 ( ?z (^ 10 -21) "zepto" )
332 ( ?y (^ 10 -24) "yocto" )))
333
334 (defvar math-standard-units-systems
335 '( ( base nil )
336 ( si ( ( g '(/ (var kg var-kg) 1000) ) ) )
337 ( mks ( ( g '(/ (var kg var-kg) 1000) ) ) )
338 ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
339
340 (defvar math-units-table nil
341 "Internal units table.
342 Derived from `math-standard-units' and `math-additional-units'.
343 Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
344
345 (defvar math-units-table-buffer-valid nil)
346
347 ;;; Units commands.
348
349 (defun calc-base-units ()
350 (interactive)
351 (calc-slow-wrapper
352 (let ((calc-autorange-units nil))
353 (calc-enter-result 1 "bsun" (math-simplify-units
354 (math-to-standard-units (calc-top-n 1)
355 nil))))))
356
357 (defun calc-quick-units ()
358 (interactive)
359 (calc-slow-wrapper
360 (let* ((num (- last-command-event ?0))
361 (pos (if (= num 0) 10 num))
362 (units (calc-var-value 'var-Units))
363 (expr (calc-top-n 1)))
364 (unless (and (>= num 0) (<= num 9))
365 (error "Bad unit number"))
366 (unless (math-vectorp units)
367 (error "No \"quick units\" are defined"))
368 (unless (< pos (length units))
369 (error "Unit number %d not defined" pos))
370 (if (math-units-in-expr-p expr nil)
371 (calc-enter-result 1 (format "cun%d" num)
372 (math-convert-units expr (nth pos units)))
373 (calc-enter-result 1 (format "*un%d" num)
374 (math-simplify-units
375 (math-mul expr (nth pos units))))))))
376
377 (defun math-get-standard-units (expr)
378 "Return the standard units in EXPR."
379 (math-simplify-units
380 (math-extract-units
381 (math-to-standard-units expr nil))))
382
383 (defun math-get-units (expr)
384 "Return the units in EXPR."
385 (math-simplify-units
386 (math-extract-units expr)))
387
388 (defun math-make-unit-string (expr)
389 "Return EXPR in string form.
390 If EXPR is nil, return nil."
391 (if expr
392 (let ((cexpr (math-compose-expr expr 0)))
393 (replace-regexp-in-string
394 " / " "/"
395 (if (stringp cexpr)
396 cexpr
397 (math-composition-to-string cexpr))))))
398
399 (defvar math-default-units-table
400 (make-hash-table :test 'equal)
401 "A table storing previously converted units.")
402
403 (defun math-get-default-units (expr)
404 "Get default units to use when converting the units in EXPR."
405 (let* ((units (math-get-units expr))
406 (standard-units (math-get-standard-units expr))
407 (default-units (gethash
408 standard-units
409 math-default-units-table)))
410 (if (equal units (car default-units))
411 (math-make-unit-string (cadr default-units))
412 (math-make-unit-string (car default-units)))))
413
414 (defun math-put-default-units (expr)
415 "Put the units in EXPR in the default units table."
416 (let* ((units (math-get-units expr))
417 (standard-units (math-get-standard-units expr))
418 (default-units (gethash
419 standard-units
420 math-default-units-table)))
421 (cond
422 ((not default-units)
423 (puthash standard-units (list units) math-default-units-table))
424 ((not (equal units (car default-units)))
425 (puthash standard-units
426 (list units (car default-units))
427 math-default-units-table)))))
428
429
430 (defun calc-convert-units (&optional old-units new-units)
431 (interactive)
432 (calc-slow-wrapper
433 (let ((expr (calc-top-n 1))
434 (uoldname nil)
435 unew
436 units
437 defunits)
438 (unless (math-units-in-expr-p expr t)
439 (let ((uold (or old-units
440 (progn
441 (setq uoldname (read-string "Old units: "))
442 (if (equal uoldname "")
443 (progn
444 (setq uoldname "1")
445 1)
446 (if (string-match "\\` */" uoldname)
447 (setq uoldname (concat "1" uoldname)))
448 (math-read-expr uoldname))))))
449 (when (eq (car-safe uold) 'error)
450 (error "Bad format in units expression: %s" (nth 1 uold)))
451 (setq expr (math-mul expr uold))))
452 (unless new-units
453 (setq defunits (math-get-default-units expr))
454 (setq new-units
455 (read-string (concat
456 (if uoldname
457 (concat "Old units: "
458 uoldname
459 ", new units")
460 "New units")
461 (if defunits
462 (concat
463 " (default "
464 defunits
465 "): ")
466 ": "))))
467
468 (if (and
469 (string= new-units "")
470 defunits)
471 (setq new-units defunits)))
472 (when (string-match "\\` */" new-units)
473 (setq new-units (concat "1" new-units)))
474 (setq units (math-read-expr new-units))
475 (when (eq (car-safe units) 'error)
476 (error "Bad format in units expression: %s" (nth 2 units)))
477 (math-put-default-units units)
478 (let ((unew (math-units-in-expr-p units t))
479 (std (and (eq (car-safe units) 'var)
480 (assq (nth 1 units) math-standard-units-systems))))
481 (if std
482 (calc-enter-result 1 "cvun" (math-simplify-units
483 (math-to-standard-units expr
484 (nth 1 std))))
485 (unless unew
486 (error "No units specified"))
487 (calc-enter-result 1 "cvun"
488 (math-convert-units
489 expr units
490 (and uoldname (not (equal uoldname "1"))))))))))
491
492 (defun calc-autorange-units (arg)
493 (interactive "P")
494 (calc-wrapper
495 (calc-change-mode 'calc-autorange-units arg nil t)
496 (message (if calc-autorange-units
497 "Adjusting target unit prefix automatically"
498 "Using target units exactly"))))
499
500 (defun calc-convert-temperature (&optional old-units new-units)
501 (interactive)
502 (calc-slow-wrapper
503 (let ((expr (calc-top-n 1))
504 (uold nil)
505 (uoldname nil)
506 unew
507 defunits)
508 (setq uold (or old-units
509 (let ((units (math-single-units-in-expr-p expr)))
510 (if units
511 (if (consp units)
512 (list 'var (car units)
513 (intern (concat "var-"
514 (symbol-name
515 (car units)))))
516 (error "Not a pure temperature expression"))
517 (math-read-expr
518 (setq uoldname (read-string
519 "Old temperature units: ")))))))
520 (when (eq (car-safe uold) 'error)
521 (error "Bad format in units expression: %s" (nth 2 uold)))
522 (or (math-units-in-expr-p expr nil)
523 (setq expr (math-mul expr uold)))
524 (setq defunits (math-get-default-units expr))
525 (setq unew (or new-units
526 (read-string
527 (concat
528 (if uoldname
529 (concat "Old temperature units: "
530 uoldname
531 ", new units")
532 "New temperature units")
533 (if defunits
534 (concat " (default "
535 defunits
536 "): ")
537 ": ")))))
538 (setq unew (math-read-expr (if (string= unew "") defunits unew)))
539 (when (eq (car-safe unew) 'error)
540 (error "Bad format in units expression: %s" (nth 2 unew)))
541 (math-put-default-units unew)
542 (let ((ntemp (calc-normalize
543 (math-simplify-units
544 (math-convert-temperature expr uold unew
545 uoldname)))))
546 (if (Math-zerop ntemp)
547 (setq ntemp (list '* ntemp unew)))
548 (let ((calc-simplify-mode 'none))
549 (calc-enter-result 1 "cvtm" ntemp))))))
550
551 (defun calc-remove-units ()
552 (interactive)
553 (calc-slow-wrapper
554 (calc-enter-result 1 "rmun" (math-simplify-units
555 (math-remove-units (calc-top-n 1))))))
556
557 (defun calc-extract-units ()
558 (interactive)
559 (calc-slow-wrapper
560 (calc-enter-result 1 "rmun" (math-simplify-units
561 (math-extract-units (calc-top-n 1))))))
562
563 ;; The variables calc-num-units and calc-den-units are local to
564 ;; calc-explain-units, but are used by calc-explain-units-rec,
565 ;; which is called by calc-explain-units.
566 (defvar calc-num-units)
567 (defvar calc-den-units)
568
569 (defun calc-explain-units ()
570 (interactive)
571 (calc-wrapper
572 (let ((calc-num-units nil)
573 (calc-den-units nil))
574 (calc-explain-units-rec (calc-top-n 1) 1)
575 (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
576 (setq calc-den-units (concat "(" calc-den-units ")")))
577 (if calc-num-units
578 (if calc-den-units
579 (message "%s per %s" calc-num-units calc-den-units)
580 (message "%s" calc-num-units))
581 (if calc-den-units
582 (message "1 per %s" calc-den-units)
583 (message "No units in expression"))))))
584
585 (defun calc-explain-units-rec (expr pow)
586 (let ((u (math-check-unit-name expr))
587 pos)
588 (if (and u (not (math-zerop pow)))
589 (let ((name (or (nth 2 u) (symbol-name (car u)))))
590 (if (eq (aref name 0) ?\*)
591 (setq name (substring name 1)))
592 (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
593 (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name)
594 (while (setq pos (string-match "[ ()]" name))
595 (setq name (concat (substring name 0 pos)
596 (if (eq (aref name pos) 32) "-" "")
597 (substring name (1+ pos)))))
598 (setq name (concat "(" name ")"))))
599 (or (eq (nth 1 expr) (car u))
600 (setq name (concat (nth 2 (assq (aref (symbol-name
601 (nth 1 expr)) 0)
602 math-unit-prefixes))
603 (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
604 (not (memq (car u) '(mHg gf))))
605 (concat "-" name)
606 (downcase name)))))
607 (cond ((or (math-equal-int pow 1)
608 (math-equal-int pow -1)))
609 ((or (math-equal-int pow 2)
610 (math-equal-int pow -2))
611 (if (equal (nth 4 u) '((m . 1)))
612 (setq name (concat "Square-" name))
613 (setq name (concat name "-squared"))))
614 ((or (math-equal-int pow 3)
615 (math-equal-int pow -3))
616 (if (equal (nth 4 u) '((m . 1)))
617 (setq name (concat "Cubic-" name))
618 (setq name (concat name "-cubed"))))
619 (t
620 (setq name (concat name "^"
621 (math-format-number (math-abs pow))))))
622 (if (math-posp pow)
623 (setq calc-num-units (if calc-num-units
624 (concat calc-num-units " " name)
625 name))
626 (setq calc-den-units (if calc-den-units
627 (concat calc-den-units " " name)
628 name))))
629 (cond ((eq (car-safe expr) '*)
630 (calc-explain-units-rec (nth 1 expr) pow)
631 (calc-explain-units-rec (nth 2 expr) pow))
632 ((eq (car-safe expr) '/)
633 (calc-explain-units-rec (nth 1 expr) pow)
634 (calc-explain-units-rec (nth 2 expr) (- pow)))
635 ((memq (car-safe expr) '(neg + -))
636 (calc-explain-units-rec (nth 1 expr) pow))
637 ((and (eq (car-safe expr) '^)
638 (math-realp (nth 2 expr)))
639 (calc-explain-units-rec (nth 1 expr)
640 (math-mul pow (nth 2 expr))))))))
641
642 (defun calc-simplify-units ()
643 (interactive)
644 (calc-slow-wrapper
645 (calc-with-default-simplification
646 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
647
648 (defun calc-view-units-table (n)
649 (interactive "P")
650 (and n (setq math-units-table-buffer-valid nil))
651 (let ((win (get-buffer-window "*Units Table*")))
652 (if (and win
653 math-units-table
654 math-units-table-buffer-valid)
655 (progn
656 (bury-buffer (window-buffer win))
657 (let ((curwin (selected-window)))
658 (select-window win)
659 (switch-to-buffer nil)
660 (select-window curwin)))
661 (math-build-units-table-buffer nil))))
662
663 (defun calc-enter-units-table (n)
664 (interactive "P")
665 (and n (setq math-units-table-buffer-valid nil))
666 (math-build-units-table-buffer t)
667 (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
668
669 (defun calc-define-unit (uname desc &optional disp)
670 (interactive "SDefine unit name: \nsDescription: \nP")
671 (if disp (setq disp (read-string "Display definition: ")))
672 (calc-wrapper
673 (let ((form (calc-top-n 1))
674 (unit (assq uname math-additional-units)))
675 (or unit
676 (setq math-additional-units
677 (cons (setq unit (list uname nil nil nil nil))
678 math-additional-units)
679 math-units-table nil))
680 (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
681 (eq (nth 1 form) uname)))
682 (not (math-equal-int form 1))
683 (math-format-flat-expr form 0)))
684 (setcar (cdr (cdr unit)) (and (not (equal desc ""))
685 desc))
686 (if disp
687 (setcar (cdr (cdr (cdr (cdr unit)))) disp))))
688 (calc-invalidate-units-table))
689
690 (defun calc-undefine-unit (uname)
691 (interactive "SUndefine unit name: ")
692 (calc-wrapper
693 (let ((unit (assq uname math-additional-units)))
694 (or unit
695 (if (assq uname math-standard-units)
696 (error "\"%s\" is a predefined unit name" uname)
697 (error "Unit name \"%s\" not found" uname)))
698 (setq math-additional-units (delq unit math-additional-units)
699 math-units-table nil)))
700 (calc-invalidate-units-table))
701
702 (defun calc-invalidate-units-table ()
703 (setq math-units-table nil)
704 (let ((buf (get-buffer "*Units Table*")))
705 (and buf
706 (with-current-buffer buf
707 (save-excursion
708 (goto-char (point-min))
709 (if (looking-at "Calculator Units Table")
710 (let ((inhibit-read-only t))
711 (insert "(Obsolete) "))))))))
712
713 (defun calc-get-unit-definition (uname)
714 (interactive "SGet definition for unit: ")
715 (calc-wrapper
716 (math-build-units-table)
717 (let ((unit (assq uname math-units-table)))
718 (or unit
719 (error "Unit name \"%s\" not found" uname))
720 (let ((msg (nth 2 unit)))
721 (if (stringp msg)
722 (if (string-match "^\\*" msg)
723 (setq msg (substring msg 1)))
724 (setq msg (symbol-name uname)))
725 (if (nth 1 unit)
726 (progn
727 (calc-enter-result 0 "ugdf" (nth 1 unit))
728 (message "Derived unit: %s" msg))
729 (calc-enter-result 0 "ugdf" (list 'var uname
730 (intern
731 (concat "var-"
732 (symbol-name uname)))))
733 (message "Base unit: %s" msg))))))
734
735 (defun calc-permanent-units ()
736 (interactive)
737 (calc-wrapper
738 (let (pos)
739 (set-buffer (find-file-noselect (substitute-in-file-name
740 calc-settings-file)))
741 (goto-char (point-min))
742 (if (and (search-forward ";;; Custom units stored by Calc" nil t)
743 (progn
744 (beginning-of-line)
745 (setq pos (point))
746 (search-forward "\n;;; End of custom units" nil t)))
747 (progn
748 (beginning-of-line)
749 (forward-line 1)
750 (delete-region pos (point)))
751 (goto-char (point-max))
752 (insert "\n\n")
753 (forward-char -1))
754 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
755 (if math-additional-units
756 (progn
757 (insert "(setq math-additional-units '(\n")
758 (let ((list math-additional-units))
759 (while list
760 (insert " (" (symbol-name (car (car list))) " "
761 (if (nth 1 (car list))
762 (if (stringp (nth 1 (car list)))
763 (prin1-to-string (nth 1 (car list)))
764 (prin1-to-string (math-format-flat-expr
765 (nth 1 (car list)) 0)))
766 "nil")
767 " "
768 (prin1-to-string (nth 2 (car list)))
769 ")\n")
770 (setq list (cdr list))))
771 (insert "))\n"))
772 (insert ";;; (no custom units defined)\n"))
773 (insert ";;; End of custom units\n")
774 (save-buffer))))
775
776
777 ;; The variable math-cu-unit-list is local to math-build-units-table,
778 ;; but is used by math-compare-unit-names, which is called (indirectly)
779 ;; by math-build-units-table.
780 ;; math-cu-unit-list is also local to math-convert-units, but is used
781 ;; by math-convert-units-rec, which is called by math-convert-units.
782 (defvar math-cu-unit-list)
783
784 (defun math-build-units-table ()
785 (or math-units-table
786 (let* ((combined-units (append math-additional-units
787 math-standard-units))
788 (math-cu-unit-list (mapcar 'car combined-units))
789 tab)
790 (message "Building units table...")
791 (setq math-units-table-buffer-valid nil)
792 (setq tab (mapcar (function
793 (lambda (x)
794 (list (car x)
795 (and (nth 1 x)
796 (if (stringp (nth 1 x))
797 (let ((exp (math-read-plain-expr
798 (nth 1 x))))
799 (if (eq (car-safe exp) 'error)
800 (error "Format error in definition of %s in units table: %s"
801 (car x) (nth 2 exp))
802 exp))
803 (nth 1 x)))
804 (nth 2 x)
805 (nth 3 x)
806 (and (not (nth 1 x))
807 (list (cons (car x) 1)))
808 (nth 4 x))))
809 combined-units))
810 (let ((math-units-table tab))
811 (mapc 'math-find-base-units tab))
812 (message "Building units table...done")
813 (setq math-units-table tab))))
814
815 ;; The variables math-fbu-base and math-fbu-entry are local to
816 ;; math-find-base-units, but are used by math-find-base-units-rec,
817 ;; which is called by math-find-base-units.
818 (defvar math-fbu-base)
819 (defvar math-fbu-entry)
820
821 (defun math-find-base-units (math-fbu-entry)
822 (if (eq (nth 4 math-fbu-entry) 'boom)
823 (error "Circular definition involving unit %s" (car math-fbu-entry)))
824 (or (nth 4 math-fbu-entry)
825 (let (math-fbu-base)
826 (setcar (nthcdr 4 math-fbu-entry) 'boom)
827 (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
828 '(or math-fbu-base
829 (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
830 (while (eq (cdr (car math-fbu-base)) 0)
831 (setq math-fbu-base (cdr math-fbu-base)))
832 (let ((b math-fbu-base))
833 (while (cdr b)
834 (if (eq (cdr (car (cdr b))) 0)
835 (setcdr b (cdr (cdr b)))
836 (setq b (cdr b)))))
837 (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
838 (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
839 math-fbu-base)))
840
841 (defun math-compare-unit-names (a b)
842 (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
843
844 (defun math-find-base-units-rec (expr pow)
845 (let ((u (math-check-unit-name expr)))
846 (cond (u
847 (let ((ulist (math-find-base-units u)))
848 (while ulist
849 (let ((p (* (cdr (car ulist)) pow))
850 (old (assq (car (car ulist)) math-fbu-base)))
851 (if old
852 (setcdr old (+ (cdr old) p))
853 (setq math-fbu-base
854 (cons (cons (car (car ulist)) p) math-fbu-base))))
855 (setq ulist (cdr ulist)))))
856 ((math-scalarp expr))
857 ((and (eq (car expr) '^)
858 (integerp (nth 2 expr)))
859 (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
860 ((eq (car expr) '*)
861 (math-find-base-units-rec (nth 1 expr) pow)
862 (math-find-base-units-rec (nth 2 expr) pow))
863 ((eq (car expr) '/)
864 (math-find-base-units-rec (nth 1 expr) pow)
865 (math-find-base-units-rec (nth 2 expr) (- pow)))
866 ((eq (car expr) 'neg)
867 (math-find-base-units-rec (nth 1 expr) pow))
868 ((eq (car expr) '+)
869 (math-find-base-units-rec (nth 1 expr) pow))
870 ((eq (car expr) 'var)
871 (or (eq (nth 1 expr) 'pi)
872 (error "Unknown name %s in defining expression for unit %s"
873 (nth 1 expr) (car math-fbu-entry))))
874 (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
875
876
877 (defun math-units-in-expr-p (expr sub-exprs)
878 (and (consp expr)
879 (if (eq (car expr) 'var)
880 (math-check-unit-name expr)
881 (and (or sub-exprs
882 (memq (car expr) '(* / ^)))
883 (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
884 (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
885
886 (defun math-only-units-in-expr-p (expr)
887 (and (consp expr)
888 (if (eq (car expr) 'var)
889 (math-check-unit-name expr)
890 (if (memq (car expr) '(* /))
891 (and (math-only-units-in-expr-p (nth 1 expr))
892 (math-only-units-in-expr-p (nth 2 expr)))
893 (and (eq (car expr) '^)
894 (and (math-only-units-in-expr-p (nth 1 expr))
895 (math-realp (nth 2 expr))))))))
896
897 (defun math-single-units-in-expr-p (expr)
898 (cond ((math-scalarp expr) nil)
899 ((eq (car expr) 'var)
900 (math-check-unit-name expr))
901 ((eq (car expr) '*)
902 (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
903 (u2 (math-single-units-in-expr-p (nth 2 expr))))
904 (or (and u1 u2 'wrong)
905 u1
906 u2)))
907 ((eq (car expr) '/)
908 (if (math-units-in-expr-p (nth 2 expr) nil)
909 'wrong
910 (math-single-units-in-expr-p (nth 1 expr))))
911 (t 'wrong)))
912
913 (defun math-check-unit-name (v)
914 (and (eq (car-safe v) 'var)
915 (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
916 (let ((name (symbol-name (nth 1 v))))
917 (and (> (length name) 1)
918 (assq (aref name 0) math-unit-prefixes)
919 (or (assq (intern (substring name 1)) math-units-table)
920 (and (eq (aref name 0) ?M)
921 (> (length name) 3)
922 (eq (aref name 1) ?e)
923 (eq (aref name 2) ?g)
924 (assq (intern (substring name 3))
925 math-units-table))))))))
926
927 ;; The variable math-which-standard is local to math-to-standard-units,
928 ;; but is used by math-to-standard-rec, which is called by
929 ;; math-to-standard-units.
930 (defvar math-which-standard)
931
932 (defun math-to-standard-units (expr math-which-standard)
933 (math-to-standard-rec expr))
934
935 (defun math-to-standard-rec (expr)
936 (if (eq (car-safe expr) 'var)
937 (let ((u (math-check-unit-name expr))
938 (base (nth 1 expr)))
939 (if u
940 (progn
941 (if (nth 1 u)
942 (setq expr (math-to-standard-rec (nth 1 u)))
943 (let ((st (assq (car u) math-which-standard)))
944 (if st
945 (setq expr (nth 1 st))
946 (setq expr (list 'var (car u)
947 (intern (concat "var-"
948 (symbol-name
949 (car u)))))))))
950 (or (null u)
951 (eq base (car u))
952 (setq expr (list '*
953 (nth 1 (assq (aref (symbol-name base) 0)
954 math-unit-prefixes))
955 expr)))
956 expr)
957 (if (eq base 'pi)
958 (math-pi)
959 expr)))
960 (if (Math-primp expr)
961 expr
962 (cons (car expr)
963 (mapcar 'math-to-standard-rec (cdr expr))))))
964
965 (defun math-apply-units (expr units ulist &optional pure)
966 (setq expr (math-simplify-units expr))
967 (if ulist
968 (let ((new 0)
969 value)
970 (or (math-numberp expr)
971 (error "Incompatible units"))
972 (while (cdr ulist)
973 (setq value (math-div expr (nth 1 (car ulist)))
974 value (math-floor (let ((calc-internal-prec
975 (1- calc-internal-prec)))
976 (math-normalize value)))
977 new (math-add new (math-mul value (car (car ulist))))
978 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
979 ulist (cdr ulist)))
980 (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
981 (car (car ulist)))))
982 (if pure
983 expr
984 (math-simplify-units (list '* expr units)))))
985
986 (defvar math-decompose-units-cache nil)
987 (defun math-decompose-units (units)
988 (let ((u (math-check-unit-name units)))
989 (and u (eq (car-safe (nth 1 u)) '+)
990 (setq units (nth 1 u))))
991 (setq units (calcFunc-expand units))
992 (and (eq (car-safe units) '+)
993 (let ((entry (list units calc-internal-prec calc-prefer-frac)))
994 (or (equal entry (car math-decompose-units-cache))
995 (let ((ulist nil)
996 (utemp units)
997 qty unit)
998 (while (eq (car-safe utemp) '+)
999 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
1000 ulist)
1001 utemp (nth 1 utemp)))
1002 (setq ulist (cons (math-decompose-unit-part utemp) ulist)
1003 utemp ulist)
1004 (while (setq utemp (cdr utemp))
1005 (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
1006 (error "Inconsistent units in sum")))
1007 (setq math-decompose-units-cache
1008 (cons entry
1009 (sort ulist
1010 (function
1011 (lambda (x y)
1012 (not (Math-lessp (nth 1 x)
1013 (nth 1 y))))))))))
1014 (cdr math-decompose-units-cache))))
1015
1016 (defun math-decompose-unit-part (unit)
1017 (cons unit
1018 (math-is-multiple (math-simplify-units (math-to-standard-units
1019 unit nil))
1020 t)))
1021
1022 ;; The variable math-fcu-u is local to math-find-compatible-unit,
1023 ;; but is used by math-find-compatible-rec which is called by
1024 ;; math-find-compatible-unit.
1025 (defvar math-fcu-u)
1026
1027 (defun math-find-compatible-unit (expr unit)
1028 (let ((math-fcu-u (math-check-unit-name unit)))
1029 (if math-fcu-u
1030 (math-find-compatible-unit-rec expr 1))))
1031
1032 (defun math-find-compatible-unit-rec (expr pow)
1033 (cond ((eq (car-safe expr) '*)
1034 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1035 (math-find-compatible-unit-rec (nth 2 expr) pow)))
1036 ((eq (car-safe expr) '/)
1037 (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1038 (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
1039 ((and (eq (car-safe expr) '^)
1040 (integerp (nth 2 expr)))
1041 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
1042 (t
1043 (let ((u2 (math-check-unit-name expr)))
1044 (if (equal (nth 4 math-fcu-u) (nth 4 u2))
1045 (cons expr pow))))))
1046
1047 ;; The variables math-cu-new-units and math-cu-pure are local to
1048 ;; math-convert-units, but are used by math-convert-units-rec,
1049 ;; which is called by math-convert-units.
1050 (defvar math-cu-new-units)
1051 (defvar math-cu-pure)
1052
1053 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
1054 (if (eq (car-safe math-cu-new-units) 'var)
1055 (let ((unew (assq (nth 1 math-cu-new-units)
1056 (math-build-units-table))))
1057 (if (eq (car-safe (nth 1 unew)) '+)
1058 (setq math-cu-new-units (nth 1 unew)))))
1059 (math-with-extra-prec 2
1060 (let ((compat (and (not math-cu-pure)
1061 (math-find-compatible-unit expr math-cu-new-units)))
1062 (math-cu-unit-list nil)
1063 (math-combining-units nil))
1064 (if compat
1065 (math-simplify-units
1066 (math-mul (math-mul (math-simplify-units
1067 (math-div expr (math-pow (car compat)
1068 (cdr compat))))
1069 (math-pow math-cu-new-units (cdr compat)))
1070 (math-simplify-units
1071 (math-to-standard-units
1072 (math-pow (math-div (car compat) math-cu-new-units)
1073 (cdr compat))
1074 nil))))
1075 (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
1076 (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
1077 (when (eq (car-safe expr) '+)
1078 (setq expr (math-simplify-units expr)))
1079 (if (math-units-in-expr-p expr t)
1080 (math-convert-units-rec expr)
1081 (math-apply-units (math-to-standard-units
1082 (list '/ expr math-cu-new-units) nil)
1083 math-cu-new-units math-cu-unit-list math-cu-pure))))))
1084
1085 (defun math-convert-units-rec (expr)
1086 (if (math-units-in-expr-p expr nil)
1087 (math-apply-units (math-to-standard-units
1088 (list '/ expr math-cu-new-units) nil)
1089 math-cu-new-units math-cu-unit-list math-cu-pure)
1090 (if (Math-primp expr)
1091 expr
1092 (cons (car expr)
1093 (mapcar 'math-convert-units-rec (cdr expr))))))
1094
1095 (defun math-convert-temperature (expr old new &optional pure)
1096 (let* ((units (math-single-units-in-expr-p expr))
1097 (uold (if old
1098 (if (or (null units)
1099 (equal (nth 1 old) (car units)))
1100 (math-check-unit-name old)
1101 (error "Inconsistent temperature units"))
1102 units))
1103 (unew (math-check-unit-name new)))
1104 (unless (and (consp unew) (nth 3 unew))
1105 (error "Not a valid temperature unit"))
1106 (unless (and (consp uold) (nth 3 uold))
1107 (error "Not a pure temperature expression"))
1108 (let ((v (car uold)))
1109 (setq expr (list '/ expr (list 'var v
1110 (intern (concat "var-"
1111 (symbol-name v)))))))
1112 (or (eq (nth 3 uold) (nth 3 unew))
1113 (cond ((eq (nth 3 uold) 'K)
1114 (setq expr (list '- expr '(/ 27315 100)))
1115 (if (eq (nth 3 unew) 'F)
1116 (setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
1117 ((eq (nth 3 uold) 'C)
1118 (if (eq (nth 3 unew) 'F)
1119 (setq expr (list '+ (list '* expr '(/ 9 5)) 32))
1120 (setq expr (list '+ expr '(/ 27315 100)))))
1121 (t
1122 (setq expr (list '* (list '- expr 32) '(/ 5 9)))
1123 (if (eq (nth 3 unew) 'K)
1124 (setq expr (list '+ expr '(/ 27315 100)))))))
1125 (if pure
1126 expr
1127 (list '* expr new))))
1128
1129
1130
1131 (defun math-simplify-units (a)
1132 (let ((math-simplifying-units t)
1133 (calc-matrix-mode 'scalar))
1134 (math-simplify a)))
1135 (defalias 'calcFunc-usimplify 'math-simplify-units)
1136
1137 ;; The function created by math-defsimplify uses the variable
1138 ;; math-simplify-expr, and so is used by functions in math-defsimplify
1139 (defvar math-simplify-expr)
1140
1141 (math-defsimplify (+ -)
1142 (and math-simplifying-units
1143 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1144 (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1145 (ratio (math-simplify (math-to-standard-units
1146 (list '/ (nth 2 math-simplify-expr) units) nil))))
1147 (if (math-units-in-expr-p ratio nil)
1148 (progn
1149 (calc-record-why "*Inconsistent units" math-simplify-expr)
1150 math-simplify-expr)
1151 (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1152 (if (eq (car math-simplify-expr) '-)
1153 (math-neg ratio) ratio))
1154 units)))))
1155
1156 (math-defsimplify *
1157 (math-simplify-units-prod))
1158
1159 (defun math-simplify-units-prod ()
1160 (and math-simplifying-units
1161 calc-autorange-units
1162 (Math-realp (nth 1 math-simplify-expr))
1163 (let* ((num (math-float (nth 1 math-simplify-expr)))
1164 (xpon (calcFunc-xpon num))
1165 (unitp (cdr (cdr math-simplify-expr)))
1166 (unit (car unitp))
1167 (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1168 u)
1169 (and (eq (car-safe unit) '*)
1170 (setq unitp (cdr unit)
1171 unit (car unitp)))
1172 (and (eq (car-safe unit) '^)
1173 (integerp (nth 2 unit))
1174 (setq pow (* pow (nth 2 unit))
1175 unitp (cdr unit)
1176 unit (car unitp)))
1177 (and (setq u (math-check-unit-name unit))
1178 (integerp xpon)
1179 (or (< xpon 0)
1180 (>= xpon (if (eq (car u) 'm) 1 3)))
1181 (let* ((uxpon 0)
1182 (pref (if (< pow 0)
1183 (reverse math-unit-prefixes)
1184 math-unit-prefixes))
1185 (p pref)
1186 pxpon pname)
1187 (or (eq (car u) (nth 1 unit))
1188 (setq uxpon (* pow
1189 (nth 2 (nth 1 (assq
1190 (aref (symbol-name
1191 (nth 1 unit)) 0)
1192 math-unit-prefixes))))))
1193 (setq xpon (+ xpon uxpon))
1194 (while (and p
1195 (or (memq (car (car p)) '(?d ?D ?h ?H))
1196 (and (eq (car (car p)) ?c)
1197 (not (eq (car u) 'm)))
1198 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1199 pow)))
1200 (progn
1201 (setq pname (math-build-var-name
1202 (if (eq (car (car p)) 0)
1203 (car u)
1204 (concat (char-to-string
1205 (car (car p)))
1206 (symbol-name
1207 (car u))))))
1208 (and (/= (car (car p)) 0)
1209 (assq (nth 1 pname)
1210 math-units-table)))))
1211 (setq p (cdr p)))
1212 (and p
1213 (/= pxpon uxpon)
1214 (or (not (eq p pref))
1215 (< xpon (+ pxpon (* (math-abs pow) 3))))
1216 (progn
1217 (setcar (cdr math-simplify-expr)
1218 (let ((calc-prefer-frac nil))
1219 (calcFunc-scf (nth 1 math-simplify-expr)
1220 (- uxpon pxpon))))
1221 (setcar unitp pname)
1222 math-simplify-expr)))))))
1223
1224 (defvar math-try-cancel-units)
1225
1226 (math-defsimplify /
1227 (and math-simplifying-units
1228 (let ((np (cdr math-simplify-expr))
1229 (math-try-cancel-units 0)
1230 n nn)
1231 (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1232 (cdr (nth 2 math-simplify-expr))
1233 (nthcdr 2 math-simplify-expr)))
1234 (if (math-realp (car n))
1235 (progn
1236 (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1237 (let ((calc-prefer-frac nil))
1238 (math-div 1 (car n)))))
1239 (setcar n 1)))
1240 (while (eq (car-safe (setq n (car np))) '*)
1241 (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1242 (setq np (cdr (cdr n))))
1243 (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1244 (if (eq math-try-cancel-units 0)
1245 (let* ((math-simplifying-units nil)
1246 (base (math-simplify
1247 (math-to-standard-units math-simplify-expr nil))))
1248 (if (Math-numberp base)
1249 (setq math-simplify-expr base))))
1250 (if (eq (car-safe math-simplify-expr) '/)
1251 (math-simplify-units-prod))
1252 math-simplify-expr)))
1253
1254 (defun math-simplify-units-divisor (np dp)
1255 (let ((n (car np))
1256 d dd temp)
1257 (while (eq (car-safe (setq d (car dp))) '*)
1258 (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1259 (setcar np (setq n temp))
1260 (setcar (cdr d) 1))
1261 (setq dp (cdr (cdr d))))
1262 (when (setq temp (math-simplify-units-quotient n d))
1263 (setcar np (setq n temp))
1264 (setcar dp 1))))
1265
1266 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1267 (defun math-simplify-units-quotient (n d)
1268 (let ((pow1 1)
1269 (pow2 1))
1270 (when (and (eq (car-safe n) '^)
1271 (integerp (nth 2 n)))
1272 (setq pow1 (nth 2 n) n (nth 1 n)))
1273 (when (and (eq (car-safe d) '^)
1274 (integerp (nth 2 d)))
1275 (setq pow2 (nth 2 d) d (nth 1 d)))
1276 (let ((un (math-check-unit-name n))
1277 (ud (math-check-unit-name d)))
1278 (and un ud
1279 (if (and (equal (nth 4 un) (nth 4 ud))
1280 (eq pow1 pow2))
1281 (if (eq pow1 1)
1282 (math-to-standard-units (list '/ n d) nil)
1283 (list '^ (math-to-standard-units (list '/ n d) nil) pow1))
1284 (let (ud1)
1285 (setq un (nth 4 un)
1286 ud (nth 4 ud))
1287 (while un
1288 (setq ud1 ud)
1289 (while ud1
1290 (and (eq (car (car un)) (car (car ud1)))
1291 (setq math-try-cancel-units
1292 (+ math-try-cancel-units
1293 (- (* (cdr (car un)) pow1)
1294 (* (cdr (car ud)) pow2)))))
1295 (setq ud1 (cdr ud1)))
1296 (setq un (cdr un)))
1297 nil))))))
1298
1299 (math-defsimplify ^
1300 (and math-simplifying-units
1301 (math-realp (nth 2 math-simplify-expr))
1302 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1303 (list (car (nth 1 math-simplify-expr))
1304 (list '^ (nth 1 (nth 1 math-simplify-expr))
1305 (nth 2 math-simplify-expr))
1306 (list '^ (nth 2 (nth 1 math-simplify-expr))
1307 (nth 2 math-simplify-expr)))
1308 (math-simplify-units-pow (nth 1 math-simplify-expr)
1309 (nth 2 math-simplify-expr)))))
1310
1311 (math-defsimplify calcFunc-sqrt
1312 (and math-simplifying-units
1313 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1314 (list (car (nth 1 math-simplify-expr))
1315 (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1316 (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1317 (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1318
1319 (math-defsimplify (calcFunc-floor
1320 calcFunc-ceil
1321 calcFunc-round
1322 calcFunc-rounde
1323 calcFunc-roundu
1324 calcFunc-trunc
1325 calcFunc-float
1326 calcFunc-frac
1327 calcFunc-abs
1328 calcFunc-clean)
1329 (and math-simplifying-units
1330 (= (length math-simplify-expr) 2)
1331 (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1332 (nth 1 math-simplify-expr)
1333 (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1334 (or (math-only-units-in-expr-p
1335 (nth 1 (nth 1 math-simplify-expr)))
1336 (math-only-units-in-expr-p
1337 (nth 2 (nth 1 math-simplify-expr)))))
1338 (list (car (nth 1 math-simplify-expr))
1339 (cons (car math-simplify-expr)
1340 (cons (nth 1 (nth 1 math-simplify-expr))
1341 (cdr (cdr math-simplify-expr))))
1342 (cons (car math-simplify-expr)
1343 (cons (nth 2 (nth 1 math-simplify-expr))
1344 (cdr (cdr math-simplify-expr)))))))))
1345
1346 (defun math-simplify-units-pow (a pow)
1347 (if (and (eq (car-safe a) '^)
1348 (math-check-unit-name (nth 1 a))
1349 (math-realp (nth 2 a)))
1350 (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1351 (let* ((u (math-check-unit-name a))
1352 (pf (math-to-simple-fraction pow))
1353 (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1354 (and u d
1355 (math-units-are-multiple u d)
1356 (list '^ (math-to-standard-units a nil) pow)))))
1357
1358
1359 (defun math-units-are-multiple (u n)
1360 (setq u (nth 4 u))
1361 (while (and u (= (% (cdr (car u)) n) 0))
1362 (setq u (cdr u)))
1363 (null u))
1364
1365 (math-defsimplify calcFunc-sin
1366 (and math-simplifying-units
1367 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1368 (let ((rad (math-simplify-units
1369 (math-evaluate-expr
1370 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1371 (calc-angle-mode 'rad))
1372 (and (eq (car-safe rad) '*)
1373 (math-realp (nth 1 rad))
1374 (eq (car-safe (nth 2 rad)) 'var)
1375 (eq (nth 1 (nth 2 rad)) 'rad)
1376 (list 'calcFunc-sin (nth 1 rad))))))
1377
1378 (math-defsimplify calcFunc-cos
1379 (and math-simplifying-units
1380 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1381 (let ((rad (math-simplify-units
1382 (math-evaluate-expr
1383 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1384 (calc-angle-mode 'rad))
1385 (and (eq (car-safe rad) '*)
1386 (math-realp (nth 1 rad))
1387 (eq (car-safe (nth 2 rad)) 'var)
1388 (eq (nth 1 (nth 2 rad)) 'rad)
1389 (list 'calcFunc-cos (nth 1 rad))))))
1390
1391 (math-defsimplify calcFunc-tan
1392 (and math-simplifying-units
1393 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1394 (let ((rad (math-simplify-units
1395 (math-evaluate-expr
1396 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1397 (calc-angle-mode 'rad))
1398 (and (eq (car-safe rad) '*)
1399 (math-realp (nth 1 rad))
1400 (eq (car-safe (nth 2 rad)) 'var)
1401 (eq (nth 1 (nth 2 rad)) 'rad)
1402 (list 'calcFunc-tan (nth 1 rad))))))
1403
1404 (math-defsimplify calcFunc-sec
1405 (and math-simplifying-units
1406 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1407 (let ((rad (math-simplify-units
1408 (math-evaluate-expr
1409 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1410 (calc-angle-mode 'rad))
1411 (and (eq (car-safe rad) '*)
1412 (math-realp (nth 1 rad))
1413 (eq (car-safe (nth 2 rad)) 'var)
1414 (eq (nth 1 (nth 2 rad)) 'rad)
1415 (list 'calcFunc-sec (nth 1 rad))))))
1416
1417 (math-defsimplify calcFunc-csc
1418 (and math-simplifying-units
1419 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1420 (let ((rad (math-simplify-units
1421 (math-evaluate-expr
1422 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1423 (calc-angle-mode 'rad))
1424 (and (eq (car-safe rad) '*)
1425 (math-realp (nth 1 rad))
1426 (eq (car-safe (nth 2 rad)) 'var)
1427 (eq (nth 1 (nth 2 rad)) 'rad)
1428 (list 'calcFunc-csc (nth 1 rad))))))
1429
1430 (math-defsimplify calcFunc-cot
1431 (and math-simplifying-units
1432 (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1433 (let ((rad (math-simplify-units
1434 (math-evaluate-expr
1435 (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1436 (calc-angle-mode 'rad))
1437 (and (eq (car-safe rad) '*)
1438 (math-realp (nth 1 rad))
1439 (eq (car-safe (nth 2 rad)) 'var)
1440 (eq (nth 1 (nth 2 rad)) 'rad)
1441 (list 'calcFunc-cot (nth 1 rad))))))
1442
1443
1444 (defun math-remove-units (expr)
1445 (if (math-check-unit-name expr)
1446 1
1447 (if (Math-primp expr)
1448 expr
1449 (cons (car expr)
1450 (mapcar 'math-remove-units (cdr expr))))))
1451
1452 (defun math-extract-units (expr)
1453 (if (memq (car-safe expr) '(* /))
1454 (cons (car expr)
1455 (mapcar 'math-extract-units (cdr expr)))
1456 (if (math-check-unit-name expr) expr 1)))
1457
1458 (defun math-build-units-table-buffer (enter-buffer)
1459 (if (not (and math-units-table math-units-table-buffer-valid
1460 (get-buffer "*Units Table*")))
1461 (let ((buf (get-buffer-create "*Units Table*"))
1462 (uptr (math-build-units-table))
1463 (calc-language (if (eq calc-language 'big) nil calc-language))
1464 (calc-float-format '(float 0))
1465 (calc-group-digits nil)
1466 (calc-number-radix 10)
1467 (calc-twos-complement-mode nil)
1468 (calc-point-char ".")
1469 (std nil)
1470 u name shadowed)
1471 (save-excursion
1472 (message "Formatting units table...")
1473 (set-buffer buf)
1474 (let ((inhibit-read-only t))
1475 (erase-buffer)
1476 (insert "Calculator Units Table:\n\n")
1477 (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n")
1478 (insert "Unit Type Definition Description\n\n")
1479 (while uptr
1480 (setq u (car uptr)
1481 name (nth 2 u))
1482 (when (eq (car u) 'm)
1483 (setq std t))
1484 (setq shadowed (and std (assq (car u) math-additional-units)))
1485 (when (and name
1486 (> (length name) 1)
1487 (eq (aref name 0) ?\*))
1488 (unless (eq uptr math-units-table)
1489 (insert "\n"))
1490 (setq name (substring name 1)))
1491 (insert " ")
1492 (and shadowed (insert "("))
1493 (insert (symbol-name (car u)))
1494 (and shadowed (insert ")"))
1495 (if (nth 3 u)
1496 (progn
1497 (indent-to 10)
1498 (insert (symbol-name (nth 3 u))))
1499 (or std
1500 (progn
1501 (indent-to 10)
1502 (insert "U"))))
1503 (indent-to 14)
1504 (and shadowed (insert "("))
1505 (if (nth 5 u)
1506 (insert (nth 5 u))
1507 (if (nth 1 u)
1508 (insert (math-format-value (nth 1 u) 80))
1509 (insert (symbol-name (car u)))))
1510 (and shadowed (insert ")"))
1511 (indent-to 41)
1512 (insert " ")
1513 (when name
1514 (insert name))
1515 (if shadowed
1516 (insert " (redefined above)")
1517 (unless (nth 1 u)
1518 (insert " (base unit)")))
1519 (insert "\n")
1520 (setq uptr (cdr uptr)))
1521 (insert "\n\nUnit Prefix Table:\n\n")
1522 (setq uptr math-unit-prefixes)
1523 (while uptr
1524 (setq u (car uptr))
1525 (insert " " (char-to-string (car u)))
1526 (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1527 (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1528 " ")
1529 (insert " "))
1530 (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1531 (indent-to 15)
1532 (insert " " (nth 2 u) "\n")
1533 (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1534 (insert "\n\n")
1535 (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
1536 "names will not use the `tex' prefix; the unit name for a\n"
1537 "TeX point will be `pt' instead of `texpt', for example.\n"
1538 "To avoid conflicts, the unit names for pint and parsec will\n"
1539 "be `pint' and `parsec' instead of `pt' and `pc'."))
1540 (view-mode)
1541 (message "Formatting units table...done"))
1542 (setq math-units-table-buffer-valid t)
1543 (let ((oldbuf (current-buffer)))
1544 (set-buffer buf)
1545 (goto-char (point-min))
1546 (set-buffer oldbuf))
1547 (if enter-buffer
1548 (pop-to-buffer buf)
1549 (display-buffer buf)))
1550 (if enter-buffer
1551 (pop-to-buffer (get-buffer "*Units Table*"))
1552 (display-buffer (get-buffer "*Units Table*")))))
1553
1554 (provide 'calc-units)
1555
1556 ;; Local variables:
1557 ;; coding: utf-8
1558 ;; End:
1559
1560 ;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
1561 ;;; calc-units.el ends here