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 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 2, or (at your option) 14;; 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; see the file COPYING. If not, write to the 23;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 24;; Boston, MA 02110-1301, USA. 25 26;;; Commentary: 27 28;;; Code: 29 30;; This file is autoloaded from calc-ext.el. 31 32(require 'calc-ext) 33(require 'calc-macs) 34(eval-when-compile 35 (require 'calc-alg)) 36 37;;; Units operations. 38 39;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch) 40;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov) 41;;; Updated April 2002 by Jochen K�pper 42 43;;; for CODATA 1998 see one of 44;;; - Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999. 45;;; - Reviews of Modern Physics, 72(2), 351-495, 2000. 46;;; for CODATA 2005 see 47;;; - http://physics.nist.gov/cuu/Constants/index.html 48 49(defvar math-standard-units 50 '( ;; Length 51 ( m nil "*Meter" ) 52 ( in "2.54 cm" "Inch" ) 53 ( ft "12 in" "Foot" ) 54 ( yd "3 ft" "Yard" ) 55 ( mi "5280 ft" "Mile" ) 56 ( au "149597870691 m" "Astronomical Unit" ) ;; NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html) 57 ( lyr "9460536207068016 m" "Light Year" ) 58 ( pc "206264.80625 au" "Parsec" ) 59 ( nmi "1852 m" "Nautical Mile" ) 60 ( fath "6 ft" "Fathom" ) 61 ( mu "1 um" "Micron" ) 62 ( mil "in/1000" "Mil" ) 63 ( point "in/72" "Point (1/72 inch)" ) 64 ( Ang "1e-10 m" "Angstrom" ) 65 ( mfi "mi+ft+in" "Miles + feet + inches" ) 66 ;; TeX lengths 67 ( texpt "in/72.27" "Point (TeX conventions)" ) 68 ( texpc "12 texpt" "Pica" ) 69 ( texbp "point" "Big point (TeX conventions)" ) 70 ( texdd "1238/1157 texpt" "Didot point" ) 71 ( texcc "12 texdd" "Cicero" ) 72 ( texsp "1/66536 texpt" "Scaled TeX point" ) 73 74 ;; Area 75 ( hect "10000 m^2" "*Hectare" ) 76 ( a "100 m^2" "Are") 77 ( acre "mi^2 / 640" "Acre" ) 78 ( b "1e-28 m^2" "Barn" ) 79 80 ;; Volume 81 ( L "1e-3 m^3" "*Liter" ) 82 ( l "L" "Liter" ) 83 ( gal "4 qt" "US Gallon" ) 84 ( qt "2 pt" "Quart" ) 85 ( pt "2 cup" "Pint" ) 86 ( cup "8 ozfl" "Cup" ) 87 ( ozfl "2 tbsp" "Fluid Ounce" ) 88 ( floz "2 tbsp" "Fluid Ounce" ) 89 ( tbsp "3 tsp" "Tablespoon" ) 90 ( tsp "4.92892159375 ml" "Teaspoon" ) 91 ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" ) 92 ( galC "4.54609 L" "Canadian Gallon" ) 93 ( galUK "4.546092 L" "UK Gallon" ) 94 95 ;; Time 96 ( s nil "*Second" ) 97 ( sec "s" "Second" ) 98 ( min "60 s" "Minute" ) 99 ( hr "60 min" "Hour" ) 100 ( day "24 hr" "Day" ) 101 ( wk "7 day" "Week" ) 102 ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" ) 103 ( yr "365.25 day" "Year" ) 104 ( Hz "1/s" "Hertz" ) 105 106 ;; Speed 107 ( mph "mi/hr" "*Miles per hour" ) 108 ( kph "km/hr" "Kilometers per hour" ) 109 ( knot "nmi/hr" "Knot" ) 110 ( c "299792458 m/s" "Speed of light" ) ;;; CODATA 2005 111 112 ;; Acceleration 113 ( ga "9.80665 m/s^2" "*\"g\" acceleration" ) ;; CODATA 2005 114 115 ;; Mass 116 ( g nil "*Gram" ) 117 ( lb "16 oz" "Pound (mass)" ) 118 ( oz "28.349523125 g" "Ounce (mass)" ) 119 ( ton "2000 lb" "Ton" ) 120 ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" ) 121 ( t "1000 kg" "Metric ton" ) 122 ( tonUK "1016.0469088 kg" "UK ton" ) 123 ( lbt "12 ozt" "Troy pound" ) 124 ( ozt "31.103475 g" "Troy ounce" ) 125 ( ct ".2 g" "Carat" ) 126 ( u "1.66053886e-27 kg" "Unified atomic mass" ) ;; CODATA 2005 127 128 ;; Force 129 ( N "m kg/s^2" "*Newton" ) 130 ( dyn "1e-5 N" "Dyne" ) 131 ( gf "ga g" "Gram (force)" ) 132 ( lbf "4.44822161526 N" "Pound (force)" ) 133 ( kip "1000 lbf" "Kilopound (force)" ) 134 ( pdl "0.138255 N" "Poundal" ) 135 136 ;; Energy 137 ( J "N m" "*Joule" ) 138 ( erg "1e-7 J" "Erg" ) 139 ( cal "4.1868 J" "International Table Calorie" ) 140 ( Btu "1055.05585262 J" "International Table Btu" ) 141 ( eV "ech V" "Electron volt" ) 142 ( ev "eV" "Electron volt" ) 143 ( therm "105506000 J" "EEC therm" ) 144 ( invcm "h c/cm" "Energy in inverse centimeters" ) 145 ( Kayser "invcm" "Kayser (inverse centimeter energy)" ) 146 ( men "100/invcm" "Inverse energy in meters" ) 147 ( Hzen "h Hz" "Energy in Hertz") 148 ( Ken "k K" "Energy in Kelvins") 149 ( Wh "W hr" "Watt hour") 150 ( Ws "W s" "Watt second") 151 152 ;; Power 153 ( W "J/s" "*Watt" ) 154 ( hp "745.7 W" "Horsepower" ) 155 156 ;; Temperature 157 ( K nil "*Degree Kelvin" K ) 158 ( dK "K" "Degree Kelvin" K ) 159 ( degK "K" "Degree Kelvin" K ) 160 ( dC "K" "Degree Celsius" C ) 161 ( degC "K" "Degree Celsius" C ) 162 ( dF "(5/9) K" "Degree Fahrenheit" F ) 163 ( degF "(5/9) K" "Degree Fahrenheit" F ) 164 165 ;; Pressure 166 ( Pa "N/m^2" "*Pascal" ) 167 ( bar "1e5 Pa" "Bar" ) 168 ( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA 2005 169 ( Torr " 1.333224e2 Pa" "Torr" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) 170 ( mHg "1000 Torr" "Meter of mercury" ) 171 ( inHg "25.4 mmHg" "Inch of mercury" ) 172 ( inH2O "2.490889e2 Pa" "Inch of water" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) 173 ( psi "6894.75729317 Pa" "Pound per square inch" ) 174 175 ;; Viscosity 176 ( P "0.1 Pa s" "*Poise" ) 177 ( St "1e-4 m^2/s" "Stokes" ) 178 179 ;; Electromagnetism 180 ( A nil "*Ampere" ) 181 ( C "A s" "Coulomb" ) 182 ( Fdy "ech Nav" "Faraday" ) 183 ( e "1.60217653e-19 C" "Elementary charge" ) ;; CODATA 2005 184 ( ech "1.60217653e-19 C" "Elementary charge" ) ;; CODATA 2005 185 ( V "W/A" "Volt" ) 186 ( ohm "V/A" "Ohm" ) 187 ( mho "A/V" "Mho" ) 188 ( S "A/V" "Siemens" ) 189 ( F "C/V" "Farad" ) 190 ( H "Wb/A" "Henry" ) 191 ( T "Wb/m^2" "Tesla" ) 192 ( Gs "1e-4 T" "Gauss" ) 193 ( Wb "V s" "Weber" ) 194 195 ;; Luminous intensity 196 ( cd nil "*Candela" ) 197 ( sb "1e4 cd/m^2" "Stilb" ) 198 ( lm "cd sr" "Lumen" ) 199 ( lx "lm/m^2" "Lux" ) 200 ( ph "1e4 lx" "Phot" ) 201 ( fc "10.76391 lx" "Footcandle" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) 202 ( lam "1e4 lm/m^2" "Lambert" ) 203 ( flam "3.426259 cd/m^2" "Footlambert" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) 204 205 ;; Radioactivity 206 ( Bq "1/s" "*Becquerel" ) 207 ( Ci "3.7e10 Bq" "Curie" ) 208 ( Gy "J/kg" "Gray" ) 209 ( Sv "Gy" "Sievert" ) 210 ( R "2.58e-4 C/kg" "Roentgen" ) 211 ( rd ".01 Gy" "Rad" ) 212 ( rem "rd" "Rem" ) 213 214 ;; Amount of substance 215 ( mol nil "*Mole" ) 216 217 ;; Plane angle 218 ( rad nil "*Radian" ) 219 ( circ "2 pi rad" "Full circle" ) 220 ( rev "circ" "Full revolution" ) 221 ( deg "circ/360" "Degree" ) 222 ( arcmin "deg/60" "Arc minute" ) 223 ( arcsec "arcmin/60" "Arc second" ) 224 ( grad "circ/400" "Grade" ) 225 ( rpm "rev/min" "Revolutions per minute" ) 226 227 ;; Solid angle 228 ( sr nil "*Steradian" ) 229 230 ;; Other physical quantities 231 ( h "6.6260693e-34 J s" "*Planck's constant" ) ;; CODATA 2005 232 ( hbar "h / 2 pi" "Planck's constant" ) 233 ( mu0 "4 pi 1e-7 H/m" "Permeability of vacuum" ) 234 ( G "6.6742e-11 m^3/kg^1/s^2" "Gravitational constant" ) ;; CODATA 2005 235 ( Nav "6.02214115e23 / mol" "Avagadro's constant" ) ;; CODATA 2005 236 ( me "9.1093826e-31 kg" "Electron rest mass" ) ;; CODATA 2005 237 ( mp "1.67262171e-27 kg" "Proton rest mass" ) ;; CODATA 2005 238 ( mn "1.67492728e-27 kg" "Neutron rest mass" ) ;; CODATA 2005 239 ( mmu "1.88353140e-28 kg" "Muon rest mass" ) ;; CODATA 2005 240 ( Ryd "10973731.568525 /m" "Rydberg's constant" ) ;; CODATA 2005 241 ( k "1.3806505e-23 J/K" "Boltzmann's constant" ) ;; CODATA 2005 242 ( alpha "7.297352568e-3" "Fine structure constant" ) ;; CODATA 2005 243 ( muB "927.400949e-26 J/T" "Bohr magneton" ) ;; CODATA 2005 244 ( muN "5.05078343e-27 J/T" "Nuclear magneton" ) ;; CODATA 2005 245 ( mue "-928.476412e-26 J/T" "Electron magnetic moment" ) ;; CODATA 2005 246 ( mup "1.41060671e-26 J/T" "Proton magnetic moment" ) ;; CODATA 2005 247 ( R0 "8.314472 J/mol/K" "Molar gas constant" ) ;; CODATA 2005 248 ( V0 "22.710981e-3 m^3/mol" "Standard volume of ideal gas" ))) 249 250 251(defvar math-additional-units nil 252 "*Additional units table for user-defined units. 253Must be formatted like math-standard-units. 254If this is changed, be sure to set math-units-table to nil to ensure 255that the combined units table will be rebuilt.") 256 257(defvar math-unit-prefixes 258 '( ( ?Y (float 1 24) "Yotta" ) 259 ( ?Z (float 1 21) "Zetta" ) 260 ( ?E (float 1 18) "Exa" ) 261 ( ?P (float 1 15) "Peta" ) 262 ( ?T (float 1 12) "Tera" ) 263 ( ?G (float 1 9) "Giga" ) 264 ( ?M (float 1 6) "Mega" ) 265 ( ?k (float 1 3) "Kilo" ) 266 ( ?K (float 1 3) "Kilo" ) 267 ( ?h (float 1 2) "Hecto" ) 268 ( ?H (float 1 2) "Hecto" ) 269 ( ?D (float 1 1) "Deka" ) 270 ( 0 (float 1 0) nil ) 271 ( ?d (float 1 -1) "Deci" ) 272 ( ?c (float 1 -2) "Centi" ) 273 ( ?m (float 1 -3) "Milli" ) 274 ( ?u (float 1 -6) "Micro" ) 275 ( ?n (float 1 -9) "Nano" ) 276 ( ?p (float 1 -12) "Pico" ) 277 ( ?f (float 1 -15) "Femto" ) 278 ( ?a (float 1 -18) "Atto" ) 279 ( ?z (float 1 -21) "zepto" ) 280 ( ?y (float 1 -24) "yocto" ))) 281 282(defvar math-standard-units-systems 283 '( ( base nil ) 284 ( si ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) ) 285 ( mks ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) ) 286 ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) ))) 287 288(defvar math-units-table nil 289 "Internal units table derived from math-defined-units. 290Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).") 291 292(defvar math-units-table-buffer-valid nil) 293 294;;; Units commands. 295 296(defun calc-base-units () 297 (interactive) 298 (calc-slow-wrapper 299 (let ((calc-autorange-units nil)) 300 (calc-enter-result 1 "bsun" (math-simplify-units 301 (math-to-standard-units (calc-top-n 1) 302 nil)))))) 303 304(defun calc-quick-units () 305 (interactive) 306 (calc-slow-wrapper 307 (let* ((num (- last-command-char ?0)) 308 (pos (if (= num 0) 10 num)) 309 (units (calc-var-value 'var-Units)) 310 (expr (calc-top-n 1))) 311 (unless (and (>= num 0) (<= num 9)) 312 (error "Bad unit number")) 313 (unless (math-vectorp units) 314 (error "No \"quick units\" are defined")) 315 (unless (< pos (length units)) 316 (error "Unit number %d not defined" pos)) 317 (if (math-units-in-expr-p expr nil) 318 (calc-enter-result 1 (format "cun%d" num) 319 (math-convert-units expr (nth pos units))) 320 (calc-enter-result 1 (format "*un%d" num) 321 (math-simplify-units 322 (math-mul expr (nth pos units)))))))) 323 324(defun calc-convert-units (&optional old-units new-units) 325 (interactive) 326 (calc-slow-wrapper 327 (let ((expr (calc-top-n 1)) 328 (uoldname nil) 329 unew 330 units) 331 (unless (math-units-in-expr-p expr t) 332 (let ((uold (or old-units 333 (progn 334 (setq uoldname (read-string "Old units: ")) 335 (if (equal uoldname "") 336 (progn 337 (setq uoldname "1") 338 1) 339 (if (string-match "\\` */" uoldname) 340 (setq uoldname (concat "1" uoldname))) 341 (math-read-expr uoldname)))))) 342 (when (eq (car-safe uold) 'error) 343 (error "Bad format in units expression: %s" (nth 1 uold))) 344 (setq expr (math-mul expr uold)))) 345 (unless new-units 346 (setq new-units (read-string (if uoldname 347 (concat "Old units: " 348 uoldname 349 ", new units: ") 350 "New units: ")))) 351 (when (string-match "\\` */" new-units) 352 (setq new-units (concat "1" new-units))) 353 (setq units (math-read-expr new-units)) 354 (when (eq (car-safe units) 'error) 355 (error "Bad format in units expression: %s" (nth 2 units))) 356 (let ((unew (math-units-in-expr-p units t)) 357 (std (and (eq (car-safe units) 'var) 358 (assq (nth 1 units) math-standard-units-systems)))) 359 (if std 360 (calc-enter-result 1 "cvun" (math-simplify-units 361 (math-to-standard-units expr 362 (nth 1 std)))) 363 (unless unew 364 (error "No units specified")) 365 (calc-enter-result 1 "cvun" 366 (math-convert-units 367 expr units 368 (and uoldname (not (equal uoldname "1")))))))))) 369 370(defun calc-autorange-units (arg) 371 (interactive "P") 372 (calc-wrapper 373 (calc-change-mode 'calc-autorange-units arg nil t) 374 (message (if calc-autorange-units 375 "Adjusting target unit prefix automatically" 376 "Using target units exactly")))) 377 378(defun calc-convert-temperature (&optional old-units new-units) 379 (interactive) 380 (calc-slow-wrapper 381 (let ((expr (calc-top-n 1)) 382 (uold nil) 383 (uoldname nil) 384 unew) 385 (setq uold (or old-units 386 (let ((units (math-single-units-in-expr-p expr))) 387 (if units 388 (if (consp units) 389 (list 'var (car units) 390 (intern (concat "var-" 391 (symbol-name 392 (car units))))) 393 (error "Not a pure temperature expression")) 394 (math-read-expr 395 (setq uoldname (read-string 396 "Old temperature units: "))))))) 397 (when (eq (car-safe uold) 'error) 398 (error "Bad format in units expression: %s" (nth 2 uold))) 399 (or (math-units-in-expr-p expr nil) 400 (setq expr (math-mul expr uold))) 401 (setq unew (or new-units 402 (math-read-expr 403 (read-string (if uoldname 404 (concat "Old temperature units: " 405 uoldname 406 ", new units: ") 407 "New temperature units: "))))) 408 (when (eq (car-safe unew) 'error) 409 (error "Bad format in units expression: %s" (nth 2 unew))) 410 (calc-enter-result 1 "cvtm" (math-simplify-units 411 (math-convert-temperature expr uold unew 412 uoldname)))))) 413 414(defun calc-remove-units () 415 (interactive) 416 (calc-slow-wrapper 417 (calc-enter-result 1 "rmun" (math-simplify-units 418 (math-remove-units (calc-top-n 1)))))) 419 420(defun calc-extract-units () 421 (interactive) 422 (calc-slow-wrapper 423 (calc-enter-result 1 "rmun" (math-simplify-units 424 (math-extract-units (calc-top-n 1)))))) 425 426;; The variables calc-num-units and calc-den-units are local to 427;; calc-explain-units, but are used by calc-explain-units-rec, 428;; which is called by calc-explain-units. 429(defvar calc-num-units) 430(defvar calc-den-units) 431 432(defun calc-explain-units () 433 (interactive) 434 (calc-wrapper 435 (let ((calc-num-units nil) 436 (calc-den-units nil)) 437 (calc-explain-units-rec (calc-top-n 1) 1) 438 (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units) 439 (setq calc-den-units (concat "(" calc-den-units ")"))) 440 (if calc-num-units 441 (if calc-den-units 442 (message "%s per %s" calc-num-units calc-den-units) 443 (message "%s" calc-num-units)) 444 (if calc-den-units 445 (message "1 per %s" calc-den-units) 446 (message "No units in expression")))))) 447 448(defun calc-explain-units-rec (expr pow) 449 (let ((u (math-check-unit-name expr)) 450 pos) 451 (if (and u (not (math-zerop pow))) 452 (let ((name (or (nth 2 u) (symbol-name (car u))))) 453 (if (eq (aref name 0) ?\*) 454 (setq name (substring name 1))) 455 (if (string-match "[^a-zA-Z0-9']" name) 456 (if (string-match "^[a-zA-Z0-9' ()]*$" name) 457 (while (setq pos (string-match "[ ()]" name)) 458 (setq name (concat (substring name 0 pos) 459 (if (eq (aref name pos) 32) "-" "") 460 (substring name (1+ pos))))) 461 (setq name (concat "(" name ")")))) 462 (or (eq (nth 1 expr) (car u)) 463 (setq name (concat (nth 2 (assq (aref (symbol-name 464 (nth 1 expr)) 0) 465 math-unit-prefixes)) 466 (if (and (string-match "[^a-zA-Z0-9']" name) 467 (not (memq (car u) '(mHg gf)))) 468 (concat "-" name) 469 (downcase name))))) 470 (cond ((or (math-equal-int pow 1) 471 (math-equal-int pow -1))) 472 ((or (math-equal-int pow 2) 473 (math-equal-int pow -2)) 474 (if (equal (nth 4 u) '((m . 1))) 475 (setq name (concat "Square-" name)) 476 (setq name (concat name "-squared")))) 477 ((or (math-equal-int pow 3) 478 (math-equal-int pow -3)) 479 (if (equal (nth 4 u) '((m . 1))) 480 (setq name (concat "Cubic-" name)) 481 (setq name (concat name "-cubed")))) 482 (t 483 (setq name (concat name "^" 484 (math-format-number (math-abs pow)))))) 485 (if (math-posp pow) 486 (setq calc-num-units (if calc-num-units 487 (concat calc-num-units " " name) 488 name)) 489 (setq calc-den-units (if calc-den-units 490 (concat calc-den-units " " name) 491 name)))) 492 (cond ((eq (car-safe expr) '*) 493 (calc-explain-units-rec (nth 1 expr) pow) 494 (calc-explain-units-rec (nth 2 expr) pow)) 495 ((eq (car-safe expr) '/) 496 (calc-explain-units-rec (nth 1 expr) pow) 497 (calc-explain-units-rec (nth 2 expr) (- pow))) 498 ((memq (car-safe expr) '(neg + -)) 499 (calc-explain-units-rec (nth 1 expr) pow)) 500 ((and (eq (car-safe expr) '^) 501 (math-realp (nth 2 expr))) 502 (calc-explain-units-rec (nth 1 expr) 503 (math-mul pow (nth 2 expr)))))))) 504 505(defun calc-simplify-units () 506 (interactive) 507 (calc-slow-wrapper 508 (calc-with-default-simplification 509 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1)))))) 510 511(defun calc-view-units-table (n) 512 (interactive "P") 513 (and n (setq math-units-table-buffer-valid nil)) 514 (let ((win (get-buffer-window "*Units Table*"))) 515 (if (and win 516 math-units-table 517 math-units-table-buffer-valid) 518 (progn 519 (bury-buffer (window-buffer win)) 520 (let ((curwin (selected-window))) 521 (select-window win) 522 (switch-to-buffer nil) 523 (select-window curwin))) 524 (math-build-units-table-buffer nil)))) 525 526(defun calc-enter-units-table (n) 527 (interactive "P") 528 (and n (setq math-units-table-buffer-valid nil)) 529 (math-build-units-table-buffer t) 530 (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator"))) 531 532(defun calc-define-unit (uname desc) 533 (interactive "SDefine unit name: \nsDescription: ") 534 (calc-wrapper 535 (let ((form (calc-top-n 1)) 536 (unit (assq uname math-additional-units))) 537 (or unit 538 (setq math-additional-units 539 (cons (setq unit (list uname nil nil)) 540 math-additional-units) 541 math-units-table nil)) 542 (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var) 543 (eq (nth 1 form) uname))) 544 (not (math-equal-int form 1)) 545 (math-format-flat-expr form 0))) 546 (setcar (cdr (cdr unit)) (and (not (equal desc "")) 547 desc)))) 548 (calc-invalidate-units-table)) 549 550(defun calc-undefine-unit (uname) 551 (interactive "SUndefine unit name: ") 552 (calc-wrapper 553 (let ((unit (assq uname math-additional-units))) 554 (or unit 555 (if (assq uname math-standard-units) 556 (error "\"%s\" is a predefined unit name" uname) 557 (error "Unit name \"%s\" not found" uname))) 558 (setq math-additional-units (delq unit math-additional-units) 559 math-units-table nil))) 560 (calc-invalidate-units-table)) 561 562(defun calc-invalidate-units-table () 563 (setq math-units-table nil) 564 (let ((buf (get-buffer "*Units Table*"))) 565 (and buf 566 (save-excursion 567 (set-buffer buf) 568 (save-excursion 569 (goto-char (point-min)) 570 (if (looking-at "Calculator Units Table") 571 (let ((inhibit-read-only t)) 572 (insert "(Obsolete) ")))))))) 573 574(defun calc-get-unit-definition (uname) 575 (interactive "SGet definition for unit: ") 576 (calc-wrapper 577 (math-build-units-table) 578 (let ((unit (assq uname math-units-table))) 579 (or unit 580 (error "Unit name \"%s\" not found" uname)) 581 (let ((msg (nth 2 unit))) 582 (if (stringp msg) 583 (if (string-match "^\\*" msg) 584 (setq msg (substring msg 1))) 585 (setq msg (symbol-name uname))) 586 (if (nth 1 unit) 587 (progn 588 (calc-enter-result 0 "ugdf" (nth 1 unit)) 589 (message "Derived unit: %s" msg)) 590 (calc-enter-result 0 "ugdf" (list 'var uname 591 (intern 592 (concat "var-" 593 (symbol-name uname))))) 594 (message "Base unit: %s" msg)))))) 595 596(defun calc-permanent-units () 597 (interactive) 598 (calc-wrapper 599 (let (pos) 600 (set-buffer (find-file-noselect (substitute-in-file-name 601 calc-settings-file))) 602 (goto-char (point-min)) 603 (if (and (search-forward ";;; Custom units stored by Calc" nil t) 604 (progn 605 (beginning-of-line) 606 (setq pos (point)) 607 (search-forward "\n;;; End of custom units" nil t))) 608 (progn 609 (beginning-of-line) 610 (forward-line 1) 611 (delete-region pos (point))) 612 (goto-char (point-max)) 613 (insert "\n\n") 614 (forward-char -1)) 615 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n") 616 (if math-additional-units 617 (progn 618 (insert "(setq math-additional-units '(\n") 619 (let ((list math-additional-units)) 620 (while list 621 (insert " (" (symbol-name (car (car list))) " " 622 (if (nth 1 (car list)) 623 (if (stringp (nth 1 (car list))) 624 (prin1-to-string (nth 1 (car list))) 625 (prin1-to-string (math-format-flat-expr 626 (nth 1 (car list)) 0))) 627 "nil") 628 " " 629 (prin1-to-string (nth 2 (car list))) 630 ")\n") 631 (setq list (cdr list)))) 632 (insert "))\n")) 633 (insert ";;; (no custom units defined)\n")) 634 (insert ";;; End of custom units\n") 635 (save-buffer)))) 636 637 638;; The variable math-cu-unit-list is local to math-build-units-table, 639;; but is used by math-compare-unit-names, which is called (indirectly) 640;; by math-build-units-table. 641;; math-cu-unit-list is also local to math-convert-units, but is used 642;; by math-convert-units-rec, which is called by math-convert-units. 643(defvar math-cu-unit-list) 644 645(defun math-build-units-table () 646 (or math-units-table 647 (let* ((combined-units (append math-additional-units 648 math-standard-units)) 649 (math-cu-unit-list (mapcar 'car combined-units)) 650 tab) 651 (message "Building units table...") 652 (setq math-units-table-buffer-valid nil) 653 (setq tab (mapcar (function 654 (lambda (x) 655 (list (car x) 656 (and (nth 1 x) 657 (if (stringp (nth 1 x)) 658 (let ((exp (math-read-plain-expr 659 (nth 1 x)))) 660 (if (eq (car-safe exp) 'error) 661 (error "Format error in definition of %s in units table: %s" 662 (car x) (nth 2 exp)) 663 exp)) 664 (nth 1 x))) 665 (nth 2 x) 666 (nth 3 x) 667 (and (not (nth 1 x)) 668 (list (cons (car x) 1)))))) 669 combined-units)) 670 (let ((math-units-table tab)) 671 (mapcar 'math-find-base-units tab)) 672 (message "Building units table...done") 673 (setq math-units-table tab)))) 674 675;; The variables math-fbu-base and math-fbu-entry are local to 676;; math-find-base-units, but are used by math-find-base-units-rec, 677;; which is called by math-find-base-units. 678(defvar math-fbu-base) 679(defvar math-fbu-entry) 680 681(defun math-find-base-units (math-fbu-entry) 682 (if (eq (nth 4 math-fbu-entry) 'boom) 683 (error "Circular definition involving unit %s" (car math-fbu-entry))) 684 (or (nth 4 math-fbu-entry) 685 (let (math-fbu-base) 686 (setcar (nthcdr 4 math-fbu-entry) 'boom) 687 (math-find-base-units-rec (nth 1 math-fbu-entry) 1) 688 '(or math-fbu-base 689 (error "Dimensionless definition for unit %s" (car math-fbu-entry))) 690 (while (eq (cdr (car math-fbu-base)) 0) 691 (setq math-fbu-base (cdr math-fbu-base))) 692 (let ((b math-fbu-base)) 693 (while (cdr b) 694 (if (eq (cdr (car (cdr b))) 0) 695 (setcdr b (cdr (cdr b))) 696 (setq b (cdr b))))) 697 (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names)) 698 (setcar (nthcdr 4 math-fbu-entry) math-fbu-base) 699 math-fbu-base))) 700 701(defun math-compare-unit-names (a b) 702 (memq (car b) (cdr (memq (car a) math-cu-unit-list)))) 703 704(defun math-find-base-units-rec (expr pow) 705 (let ((u (math-check-unit-name expr))) 706 (cond (u 707 (let ((ulist (math-find-base-units u))) 708 (while ulist 709 (let ((p (* (cdr (car ulist)) pow)) 710 (old (assq (car (car ulist)) math-fbu-base))) 711 (if old 712 (setcdr old (+ (cdr old) p)) 713 (setq math-fbu-base 714 (cons (cons (car (car ulist)) p) math-fbu-base)))) 715 (setq ulist (cdr ulist))))) 716 ((math-scalarp expr)) 717 ((and (eq (car expr) '^) 718 (integerp (nth 2 expr))) 719 (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr)))) 720 ((eq (car expr) '*) 721 (math-find-base-units-rec (nth 1 expr) pow) 722 (math-find-base-units-rec (nth 2 expr) pow)) 723 ((eq (car expr) '/) 724 (math-find-base-units-rec (nth 1 expr) pow) 725 (math-find-base-units-rec (nth 2 expr) (- pow))) 726 ((eq (car expr) 'neg) 727 (math-find-base-units-rec (nth 1 expr) pow)) 728 ((eq (car expr) '+) 729 (math-find-base-units-rec (nth 1 expr) pow)) 730 ((eq (car expr) 'var) 731 (or (eq (nth 1 expr) 'pi) 732 (error "Unknown name %s in defining expression for unit %s" 733 (nth 1 expr) (car math-fbu-entry)))) 734 (t (error "Malformed defining expression for unit %s" (car math-fbu-entry)))))) 735 736 737(defun math-units-in-expr-p (expr sub-exprs) 738 (and (consp expr) 739 (if (eq (car expr) 'var) 740 (math-check-unit-name expr) 741 (and (or sub-exprs 742 (memq (car expr) '(* / ^))) 743 (or (math-units-in-expr-p (nth 1 expr) sub-exprs) 744 (math-units-in-expr-p (nth 2 expr) sub-exprs)))))) 745 746(defun math-only-units-in-expr-p (expr) 747 (and (consp expr) 748 (if (eq (car expr) 'var) 749 (math-check-unit-name expr) 750 (if (memq (car expr) '(* /)) 751 (and (math-only-units-in-expr-p (nth 1 expr)) 752 (math-only-units-in-expr-p (nth 2 expr))) 753 (and (eq (car expr) '^) 754 (and (math-only-units-in-expr-p (nth 1 expr)) 755 (math-realp (nth 2 expr)))))))) 756 757(defun math-single-units-in-expr-p (expr) 758 (cond ((math-scalarp expr) nil) 759 ((eq (car expr) 'var) 760 (math-check-unit-name expr)) 761 ((eq (car expr) '*) 762 (let ((u1 (math-single-units-in-expr-p (nth 1 expr))) 763 (u2 (math-single-units-in-expr-p (nth 2 expr)))) 764 (or (and u1 u2 'wrong) 765 u1 766 u2))) 767 ((eq (car expr) '/) 768 (if (math-units-in-expr-p (nth 2 expr) nil) 769 'wrong 770 (math-single-units-in-expr-p (nth 1 expr)))) 771 (t 'wrong))) 772 773(defun math-check-unit-name (v) 774 (and (eq (car-safe v) 'var) 775 (or (assq (nth 1 v) (or math-units-table (math-build-units-table))) 776 (let ((name (symbol-name (nth 1 v)))) 777 (and (> (length name) 1) 778 (assq (aref name 0) math-unit-prefixes) 779 (or (assq (intern (substring name 1)) math-units-table) 780 (and (eq (aref name 0) ?M) 781 (> (length name) 3) 782 (eq (aref name 1) ?e) 783 (eq (aref name 2) ?g) 784 (assq (intern (substring name 3)) 785 math-units-table)))))))) 786 787;; The variable math-which-standard is local to math-to-standard-units, 788;; but is used by math-to-standard-rec, which is called by 789;; math-to-standard-units. 790(defvar math-which-standard) 791 792(defun math-to-standard-units (expr math-which-standard) 793 (math-to-standard-rec expr)) 794 795(defun math-to-standard-rec (expr) 796 (if (eq (car-safe expr) 'var) 797 (let ((u (math-check-unit-name expr)) 798 (base (nth 1 expr))) 799 (if u 800 (progn 801 (if (nth 1 u) 802 (setq expr (math-to-standard-rec (nth 1 u))) 803 (let ((st (assq (car u) math-which-standard))) 804 (if st 805 (setq expr (nth 1 st)) 806 (setq expr (list 'var (car u) 807 (intern (concat "var-" 808 (symbol-name 809 (car u))))))))) 810 (or (null u) 811 (eq base (car u)) 812 (setq expr (list '* 813 (nth 1 (assq (aref (symbol-name base) 0) 814 math-unit-prefixes)) 815 expr))) 816 expr) 817 (if (eq base 'pi) 818 (math-pi) 819 expr))) 820 (if (Math-primp expr) 821 expr 822 (cons (car expr) 823 (mapcar 'math-to-standard-rec (cdr expr)))))) 824 825(defun math-apply-units (expr units ulist &optional pure) 826 (setq expr (math-simplify-units expr)) 827 (if ulist 828 (let ((new 0) 829 value) 830 (or (math-numberp expr) 831 (error "Incompatible units")) 832 (while (cdr ulist) 833 (setq value (math-div expr (nth 1 (car ulist))) 834 value (math-floor (let ((calc-internal-prec 835 (1- calc-internal-prec))) 836 (math-normalize value))) 837 new (math-add new (math-mul value (car (car ulist)))) 838 expr (math-sub expr (math-mul value (nth 1 (car ulist)))) 839 ulist (cdr ulist))) 840 (math-add new (math-mul (math-div expr (nth 1 (car ulist))) 841 (car (car ulist))))) 842 (if pure 843 expr 844 (math-simplify-units (list '* expr units))))) 845 846(defvar math-decompose-units-cache nil) 847(defun math-decompose-units (units) 848 (let ((u (math-check-unit-name units))) 849 (and u (eq (car-safe (nth 1 u)) '+) 850 (setq units (nth 1 u)))) 851 (setq units (calcFunc-expand units)) 852 (and (eq (car-safe units) '+) 853 (let ((entry (list units calc-internal-prec calc-prefer-frac))) 854 (or (equal entry (car math-decompose-units-cache)) 855 (let ((ulist nil) 856 (utemp units) 857 qty unit) 858 (while (eq (car-safe utemp) '+) 859 (setq ulist (cons (math-decompose-unit-part (nth 2 utemp)) 860 ulist) 861 utemp (nth 1 utemp))) 862 (setq ulist (cons (math-decompose-unit-part utemp) ulist) 863 utemp ulist) 864 (while (setq utemp (cdr utemp)) 865 (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist))) 866 (error "Inconsistent units in sum"))) 867 (setq math-decompose-units-cache 868 (cons entry 869 (sort ulist 870 (function 871 (lambda (x y) 872 (not (Math-lessp (nth 1 x) 873 (nth 1 y)))))))))) 874 (cdr math-decompose-units-cache)))) 875 876(defun math-decompose-unit-part (unit) 877 (cons unit 878 (math-is-multiple (math-simplify-units (math-to-standard-units 879 unit nil)) 880 t))) 881 882;; The variable math-fcu-u is local to math-find-compatible-unit, 883;; but is used by math-find-compatible-rec which is called by 884;; math-find-compatible-unit. 885(defvar math-fcu-u) 886 887(defun math-find-compatible-unit (expr unit) 888 (let ((math-fcu-u (math-check-unit-name unit))) 889 (if math-fcu-u 890 (math-find-compatible-unit-rec expr 1)))) 891 892(defun math-find-compatible-unit-rec (expr pow) 893 (cond ((eq (car-safe expr) '*) 894 (or (math-find-compatible-unit-rec (nth 1 expr) pow) 895 (math-find-compatible-unit-rec (nth 2 expr) pow))) 896 ((eq (car-safe expr) '/) 897 (or (math-find-compatible-unit-rec (nth 1 expr) pow) 898 (math-find-compatible-unit-rec (nth 2 expr) (- pow)))) 899 ((and (eq (car-safe expr) '^) 900 (integerp (nth 2 expr))) 901 (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr)))) 902 (t 903 (let ((u2 (math-check-unit-name expr))) 904 (if (equal (nth 4 math-fcu-u) (nth 4 u2)) 905 (cons expr pow)))))) 906 907;; The variables math-cu-new-units and math-cu-pure are local to 908;; math-convert-units, but are used by math-convert-units-rec, 909;; which is called by math-convert-units. 910(defvar math-cu-new-units) 911(defvar math-cu-pure) 912 913(defun math-convert-units (expr math-cu-new-units &optional math-cu-pure) 914 (if (eq (car-safe math-cu-new-units) 'var) 915 (let ((unew (assq (nth 1 math-cu-new-units) 916 (math-build-units-table)))) 917 (if (eq (car-safe (nth 1 unew)) '+) 918 (setq math-cu-new-units (nth 1 unew))))) 919 (math-with-extra-prec 2 920 (let ((compat (and (not math-cu-pure) 921 (math-find-compatible-unit expr math-cu-new-units))) 922 (math-cu-unit-list nil) 923 (math-combining-units nil)) 924 (if compat 925 (math-simplify-units 926 (math-mul (math-mul (math-simplify-units 927 (math-div expr (math-pow (car compat) 928 (cdr compat)))) 929 (math-pow math-cu-new-units (cdr compat))) 930 (math-simplify-units 931 (math-to-standard-units 932 (math-pow (math-div (car compat) math-cu-new-units) 933 (cdr compat)) 934 nil)))) 935 (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units)) 936 (setq math-cu-new-units (nth 2 (car math-cu-unit-list)))) 937 (when (eq (car-safe expr) '+) 938 (setq expr (math-simplify-units expr))) 939 (if (math-units-in-expr-p expr t) 940 (math-convert-units-rec expr) 941 (math-apply-units (math-to-standard-units 942 (list '/ expr math-cu-new-units) nil) 943 math-cu-new-units math-cu-unit-list math-cu-pure)))))) 944 945(defun math-convert-units-rec (expr) 946 (if (math-units-in-expr-p expr nil) 947 (math-apply-units (math-to-standard-units 948 (list '/ expr math-cu-new-units) nil) 949 math-cu-new-units math-cu-unit-list math-cu-pure) 950 (if (Math-primp expr) 951 expr 952 (cons (car expr) 953 (mapcar 'math-convert-units-rec (cdr expr)))))) 954 955(defun math-convert-temperature (expr old new &optional pure) 956 (let* ((units (math-single-units-in-expr-p expr)) 957 (uold (if old 958 (if (or (null units) 959 (equal (nth 1 old) (car units))) 960 (math-check-unit-name old) 961 (error "Inconsistent temperature units")) 962 units)) 963 (unew (math-check-unit-name new))) 964 (unless (and (consp unew) (nth 3 unew)) 965 (error "Not a valid temperature unit")) 966 (unless (and (consp uold) (nth 3 uold)) 967 (error "Not a pure temperature expression")) 968 (let ((v (car uold))) 969 (setq expr (list '/ expr (list 'var v 970 (intern (concat "var-" 971 (symbol-name v))))))) 972 (or (eq (nth 3 uold) (nth 3 unew)) 973 (cond ((eq (nth 3 uold) 'K) 974 (setq expr (list '- expr '(float 27315 -2))) 975 (if (eq (nth 3 unew) 'F) 976 (setq expr (list '+ (list '* expr '(frac 9 5)) 32)))) 977 ((eq (nth 3 uold) 'C) 978 (if (eq (nth 3 unew) 'F) 979 (setq expr (list '+ (list '* expr '(frac 9 5)) 32)) 980 (setq expr (list '+ expr '(float 27315 -2))))) 981 (t 982 (setq expr (list '* (list '- expr 32) '(frac 5 9))) 983 (if (eq (nth 3 unew) 'K) 984 (setq expr (list '+ expr '(float 27315 -2))))))) 985 (if pure 986 expr 987 (list '* expr new)))) 988 989 990 991(defun math-simplify-units (a) 992 (let ((math-simplifying-units t) 993 (calc-matrix-mode 'scalar)) 994 (math-simplify a))) 995(defalias 'calcFunc-usimplify 'math-simplify-units) 996 997;; The function created by math-defsimplify uses the variable 998;; math-simplify-expr, and so is used by functions in math-defsimplify 999(defvar math-simplify-expr) 1000 1001(math-defsimplify (+ -) 1002 (and math-simplifying-units 1003 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1004 (let* ((units (math-extract-units (nth 1 math-simplify-expr))) 1005 (ratio (math-simplify (math-to-standard-units 1006 (list '/ (nth 2 math-simplify-expr) units) nil)))) 1007 (if (math-units-in-expr-p ratio nil) 1008 (progn 1009 (calc-record-why "*Inconsistent units" math-simplify-expr) 1010 math-simplify-expr) 1011 (list '* (math-add (math-remove-units (nth 1 math-simplify-expr)) 1012 (if (eq (car math-simplify-expr) '-) 1013 (math-neg ratio) ratio)) 1014 units))))) 1015 1016(math-defsimplify * 1017 (math-simplify-units-prod)) 1018 1019(defun math-simplify-units-prod () 1020 (and math-simplifying-units 1021 calc-autorange-units 1022 (Math-realp (nth 1 math-simplify-expr)) 1023 (let* ((num (math-float (nth 1 math-simplify-expr))) 1024 (xpon (calcFunc-xpon num)) 1025 (unitp (cdr (cdr math-simplify-expr))) 1026 (unit (car unitp)) 1027 (pow (if (eq (car math-simplify-expr) '*) 1 -1)) 1028 u) 1029 (and (eq (car-safe unit) '*) 1030 (setq unitp (cdr unit) 1031 unit (car unitp))) 1032 (and (eq (car-safe unit) '^) 1033 (integerp (nth 2 unit)) 1034 (setq pow (* pow (nth 2 unit)) 1035 unitp (cdr unit) 1036 unit (car unitp))) 1037 (and (setq u (math-check-unit-name unit)) 1038 (integerp xpon) 1039 (or (< xpon 0) 1040 (>= xpon (if (eq (car u) 'm) 1 3))) 1041 (let* ((uxpon 0) 1042 (pref (if (< pow 0) 1043 (reverse math-unit-prefixes) 1044 math-unit-prefixes)) 1045 (p pref) 1046 pxpon pname) 1047 (or (eq (car u) (nth 1 unit)) 1048 (setq uxpon (* pow 1049 (nth 2 (nth 1 (assq 1050 (aref (symbol-name 1051 (nth 1 unit)) 0) 1052 math-unit-prefixes)))))) 1053 (setq xpon (+ xpon uxpon)) 1054 (while (and p 1055 (or (memq (car (car p)) '(?d ?D ?h ?H)) 1056 (and (eq (car (car p)) ?c) 1057 (not (eq (car u) 'm))) 1058 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p))) 1059 pow))) 1060 (progn 1061 (setq pname (math-build-var-name 1062 (if (eq (car (car p)) 0) 1063 (car u) 1064 (concat (char-to-string 1065 (car (car p))) 1066 (symbol-name 1067 (car u)))))) 1068 (and (/= (car (car p)) 0) 1069 (assq (nth 1 pname) 1070 math-units-table))))) 1071 (setq p (cdr p))) 1072 (and p 1073 (/= pxpon uxpon) 1074 (or (not (eq p pref)) 1075 (< xpon (+ pxpon (* (math-abs pow) 3)))) 1076 (progn 1077 (setcar (cdr math-simplify-expr) 1078 (let ((calc-prefer-frac nil)) 1079 (calcFunc-scf (nth 1 math-simplify-expr) 1080 (- uxpon pxpon)))) 1081 (setcar unitp pname) 1082 math-simplify-expr))))))) 1083 1084(defvar math-try-cancel-units) 1085 1086(math-defsimplify / 1087 (and math-simplifying-units 1088 (let ((np (cdr math-simplify-expr)) 1089 (math-try-cancel-units 0) 1090 n nn) 1091 (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*) 1092 (cdr (nth 2 math-simplify-expr)) 1093 (nthcdr 2 math-simplify-expr))) 1094 (if (math-realp (car n)) 1095 (progn 1096 (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr) 1097 (let ((calc-prefer-frac nil)) 1098 (math-div 1 (car n))))) 1099 (setcar n 1))) 1100 (while (eq (car-safe (setq n (car np))) '*) 1101 (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr))) 1102 (setq np (cdr (cdr n)))) 1103 (math-simplify-units-divisor np (cdr (cdr math-simplify-expr))) 1104 (if (eq math-try-cancel-units 0) 1105 (let* ((math-simplifying-units nil) 1106 (base (math-simplify 1107 (math-to-standard-units math-simplify-expr nil)))) 1108 (if (Math-numberp base) 1109 (setq math-simplify-expr base)))) 1110 (if (eq (car-safe math-simplify-expr) '/) 1111 (math-simplify-units-prod)) 1112 math-simplify-expr))) 1113 1114(defun math-simplify-units-divisor (np dp) 1115 (let ((n (car np)) 1116 d dd temp) 1117 (while (eq (car-safe (setq d (car dp))) '*) 1118 (when (setq temp (math-simplify-units-quotient n (nth 1 d))) 1119 (setcar np (setq n temp)) 1120 (setcar (cdr d) 1)) 1121 (setq dp (cdr (cdr d)))) 1122 (when (setq temp (math-simplify-units-quotient n d)) 1123 (setcar np (setq n temp)) 1124 (setcar dp 1)))) 1125 1126;; Simplify, e.g., "in / cm" to "2.54" in a units expression. 1127(defun math-simplify-units-quotient (n d) 1128 (let ((pow1 1) 1129 (pow2 1)) 1130 (when (and (eq (car-safe n) '^) 1131 (integerp (nth 2 n))) 1132 (setq pow1 (nth 2 n) n (nth 1 n))) 1133 (when (and (eq (car-safe d) '^) 1134 (integerp (nth 2 d))) 1135 (setq pow2 (nth 2 d) d (nth 1 d))) 1136 (let ((un (math-check-unit-name n)) 1137 (ud (math-check-unit-name d))) 1138 (and un ud 1139 (if (and (equal (nth 4 un) (nth 4 ud)) 1140 (eq pow1 pow2)) 1141 (math-to-standard-units (list '/ n d) nil) 1142 (let (ud1) 1143 (setq un (nth 4 un) 1144 ud (nth 4 ud)) 1145 (while un 1146 (setq ud1 ud) 1147 (while ud1 1148 (and (eq (car (car un)) (car (car ud1))) 1149 (setq math-try-cancel-units 1150 (+ math-try-cancel-units 1151 (- (* (cdr (car un)) pow1) 1152 (* (cdr (car ud)) pow2))))) 1153 (setq ud1 (cdr ud1))) 1154 (setq un (cdr un))) 1155 nil)))))) 1156 1157(math-defsimplify ^ 1158 (and math-simplifying-units 1159 (math-realp (nth 2 math-simplify-expr)) 1160 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) 1161 (list (car (nth 1 math-simplify-expr)) 1162 (list '^ (nth 1 (nth 1 math-simplify-expr)) 1163 (nth 2 math-simplify-expr)) 1164 (list '^ (nth 2 (nth 1 math-simplify-expr)) 1165 (nth 2 math-simplify-expr))) 1166 (math-simplify-units-pow (nth 1 math-simplify-expr) 1167 (nth 2 math-simplify-expr))))) 1168 1169(math-defsimplify calcFunc-sqrt 1170 (and math-simplifying-units 1171 (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) 1172 (list (car (nth 1 math-simplify-expr)) 1173 (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr))) 1174 (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr)))) 1175 (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2))))) 1176 1177(math-defsimplify (calcFunc-floor 1178 calcFunc-ceil 1179 calcFunc-round 1180 calcFunc-rounde 1181 calcFunc-roundu 1182 calcFunc-trunc 1183 calcFunc-float 1184 calcFunc-frac 1185 calcFunc-abs 1186 calcFunc-clean) 1187 (and math-simplifying-units 1188 (= (length math-simplify-expr) 2) 1189 (if (math-only-units-in-expr-p (nth 1 math-simplify-expr)) 1190 (nth 1 math-simplify-expr) 1191 (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) 1192 (or (math-only-units-in-expr-p 1193 (nth 1 (nth 1 math-simplify-expr))) 1194 (math-only-units-in-expr-p 1195 (nth 2 (nth 1 math-simplify-expr))))) 1196 (list (car (nth 1 math-simplify-expr)) 1197 (cons (car math-simplify-expr) 1198 (cons (nth 1 (nth 1 math-simplify-expr)) 1199 (cdr (cdr math-simplify-expr)))) 1200 (cons (car math-simplify-expr) 1201 (cons (nth 2 (nth 1 math-simplify-expr)) 1202 (cdr (cdr math-simplify-expr))))))))) 1203 1204(defun math-simplify-units-pow (a pow) 1205 (if (and (eq (car-safe a) '^) 1206 (math-check-unit-name (nth 1 a)) 1207 (math-realp (nth 2 a))) 1208 (list '^ (nth 1 a) (math-mul pow (nth 2 a))) 1209 (let* ((u (math-check-unit-name a)) 1210 (pf (math-to-simple-fraction pow)) 1211 (d (and (eq (car-safe pf) 'frac) (nth 2 pf)))) 1212 (and u d 1213 (math-units-are-multiple u d) 1214 (list '^ (math-to-standard-units a nil) pow))))) 1215 1216 1217(defun math-units-are-multiple (u n) 1218 (setq u (nth 4 u)) 1219 (while (and u (= (% (cdr (car u)) n) 0)) 1220 (setq u (cdr u))) 1221 (null u)) 1222 1223(math-defsimplify calcFunc-sin 1224 (and math-simplifying-units 1225 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1226 (let ((rad (math-simplify-units 1227 (math-evaluate-expr 1228 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1229 (calc-angle-mode 'rad)) 1230 (and (eq (car-safe rad) '*) 1231 (math-realp (nth 1 rad)) 1232 (eq (car-safe (nth 2 rad)) 'var) 1233 (eq (nth 1 (nth 2 rad)) 'rad) 1234 (list 'calcFunc-sin (nth 1 rad)))))) 1235 1236(math-defsimplify calcFunc-cos 1237 (and math-simplifying-units 1238 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1239 (let ((rad (math-simplify-units 1240 (math-evaluate-expr 1241 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1242 (calc-angle-mode 'rad)) 1243 (and (eq (car-safe rad) '*) 1244 (math-realp (nth 1 rad)) 1245 (eq (car-safe (nth 2 rad)) 'var) 1246 (eq (nth 1 (nth 2 rad)) 'rad) 1247 (list 'calcFunc-cos (nth 1 rad)))))) 1248 1249(math-defsimplify calcFunc-tan 1250 (and math-simplifying-units 1251 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1252 (let ((rad (math-simplify-units 1253 (math-evaluate-expr 1254 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1255 (calc-angle-mode 'rad)) 1256 (and (eq (car-safe rad) '*) 1257 (math-realp (nth 1 rad)) 1258 (eq (car-safe (nth 2 rad)) 'var) 1259 (eq (nth 1 (nth 2 rad)) 'rad) 1260 (list 'calcFunc-tan (nth 1 rad)))))) 1261 1262(math-defsimplify calcFunc-sec 1263 (and math-simplifying-units 1264 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1265 (let ((rad (math-simplify-units 1266 (math-evaluate-expr 1267 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1268 (calc-angle-mode 'rad)) 1269 (and (eq (car-safe rad) '*) 1270 (math-realp (nth 1 rad)) 1271 (eq (car-safe (nth 2 rad)) 'var) 1272 (eq (nth 1 (nth 2 rad)) 'rad) 1273 (list 'calcFunc-sec (nth 1 rad)))))) 1274 1275(math-defsimplify calcFunc-csc 1276 (and math-simplifying-units 1277 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1278 (let ((rad (math-simplify-units 1279 (math-evaluate-expr 1280 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1281 (calc-angle-mode 'rad)) 1282 (and (eq (car-safe rad) '*) 1283 (math-realp (nth 1 rad)) 1284 (eq (car-safe (nth 2 rad)) 'var) 1285 (eq (nth 1 (nth 2 rad)) 'rad) 1286 (list 'calcFunc-csc (nth 1 rad)))))) 1287 1288(math-defsimplify calcFunc-cot 1289 (and math-simplifying-units 1290 (math-units-in-expr-p (nth 1 math-simplify-expr) nil) 1291 (let ((rad (math-simplify-units 1292 (math-evaluate-expr 1293 (math-to-standard-units (nth 1 math-simplify-expr) nil)))) 1294 (calc-angle-mode 'rad)) 1295 (and (eq (car-safe rad) '*) 1296 (math-realp (nth 1 rad)) 1297 (eq (car-safe (nth 2 rad)) 'var) 1298 (eq (nth 1 (nth 2 rad)) 'rad) 1299 (list 'calcFunc-cot (nth 1 rad)))))) 1300 1301 1302(defun math-remove-units (expr) 1303 (if (math-check-unit-name expr) 1304 1 1305 (if (Math-primp expr) 1306 expr 1307 (cons (car expr) 1308 (mapcar 'math-remove-units (cdr expr)))))) 1309 1310(defun math-extract-units (expr) 1311 (if (memq (car-safe expr) '(* /)) 1312 (cons (car expr) 1313 (mapcar 'math-extract-units (cdr expr))) 1314 (if (math-check-unit-name expr) expr 1))) 1315 1316(defun math-build-units-table-buffer (enter-buffer) 1317 (if (not (and math-units-table math-units-table-buffer-valid 1318 (get-buffer "*Units Table*"))) 1319 (let ((buf (get-buffer-create "*Units Table*")) 1320 (uptr (math-build-units-table)) 1321 (calc-language (if (eq calc-language 'big) nil calc-language)) 1322 (calc-float-format '(float 0)) 1323 (calc-group-digits nil) 1324 (calc-number-radix 10) 1325 (calc-point-char ".") 1326 (std nil) 1327 u name shadowed) 1328 (save-excursion 1329 (message "Formatting units table...") 1330 (set-buffer buf) 1331 (let ((inhibit-read-only t)) 1332 (erase-buffer) 1333 (insert "Calculator Units Table:\n\n") 1334 (insert "Unit Type Definition Description\n\n") 1335 (while uptr 1336 (setq u (car uptr) 1337 name (nth 2 u)) 1338 (when (eq (car u) 'm) 1339 (setq std t)) 1340 (setq shadowed (and std (assq (car u) math-additional-units))) 1341 (when (and name 1342 (> (length name) 1) 1343 (eq (aref name 0) ?\*)) 1344 (unless (eq uptr math-units-table) 1345 (insert "\n")) 1346 (setq name (substring name 1))) 1347 (insert " ") 1348 (and shadowed (insert "(")) 1349 (insert (symbol-name (car u))) 1350 (and shadowed (insert ")")) 1351 (if (nth 3 u) 1352 (progn 1353 (indent-to 10) 1354 (insert (symbol-name (nth 3 u)))) 1355 (or std 1356 (progn 1357 (indent-to 10) 1358 (insert "U")))) 1359 (indent-to 14) 1360 (and shadowed (insert "(")) 1361 (if (nth 1 u) 1362 (insert (math-format-value (nth 1 u) 80)) 1363 (insert (symbol-name (car u)))) 1364 (and shadowed (insert ")")) 1365 (indent-to 41) 1366 (insert " ") 1367 (when name 1368 (insert name)) 1369 (if shadowed 1370 (insert " (redefined above)") 1371 (unless (nth 1 u) 1372 (insert " (base unit)"))) 1373 (insert "\n") 1374 (setq uptr (cdr uptr))) 1375 (insert "\n\nUnit Prefix Table:\n\n") 1376 (setq uptr math-unit-prefixes) 1377 (while uptr 1378 (setq u (car uptr)) 1379 (insert " " (char-to-string (car u))) 1380 (if (equal (nth 1 u) (nth 1 (nth 1 uptr))) 1381 (insert " " (char-to-string (car (car (setq uptr (cdr uptr))))) 1382 " ") 1383 (insert " ")) 1384 (insert "10^" (int-to-string (nth 2 (nth 1 u)))) 1385 (indent-to 15) 1386 (insert " " (nth 2 u) "\n") 1387 (while (eq (car (car (setq uptr (cdr uptr)))) 0))) 1388 (insert "\n")) 1389 (view-mode) 1390 (message "Formatting units table...done")) 1391 (setq math-units-table-buffer-valid t) 1392 (let ((oldbuf (current-buffer))) 1393 (set-buffer buf) 1394 (goto-char (point-min)) 1395 (set-buffer oldbuf)) 1396 (if enter-buffer 1397 (pop-to-buffer buf) 1398 (display-buffer buf))) 1399 (if enter-buffer 1400 (pop-to-buffer (get-buffer "*Units Table*")) 1401 (display-buffer (get-buffer "*Units Table*"))))) 1402 1403(provide 'calc-units) 1404 1405;; Local Variables: 1406;; coding: iso-latin-1 1407;; End: 1408 1409;;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4 1410;;; calc-units.el ends here 1411