;; Calculator for GNU Emacs, part II [calc-units.el] ;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc. ;; Written by Dave Gillespie, daveg@synaptics.com. ;; This file is part of GNU Emacs. ;; GNU Emacs is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY. No author or distributor ;; accepts responsibility to anyone for the consequences of using it ;; or for whether it serves any particular purpose or works at all, ;; unless he says so in writing. Refer to the GNU Emacs General Public ;; License for full details. ;; Everyone is granted permission to copy, modify and redistribute ;; GNU Emacs, but only under the conditions described in the ;; GNU Emacs General Public License. A copy of this license is ;; supposed to have been given to you along with GNU Emacs so you ;; can know your rights and responsibilities. It should be in a ;; file named COPYING. Among other things, the copyright notice ;; and this notice must be preserved on all copies. ;; This file is autoloaded from calc-ext.el. (require 'calc-ext) (require 'calc-macs) (defun calc-Need-calc-units () nil) ;;; Units commands. (defun calc-base-units () (interactive) (calc-slow-wrapper (let ((calc-autorange-units nil)) (calc-enter-result 1 "bsun" (math-simplify-units (math-to-standard-units (calc-top-n 1) nil))))) ) (defun calc-quick-units () (interactive) (calc-slow-wrapper (let* ((num (- last-command-char ?0)) (pos (if (= num 0) 10 num)) (units (calc-var-value 'var-Units)) (expr (calc-top-n 1))) (or (and (>= num 0) (<= num 9)) (error "Bad unit number")) (or (math-vectorp units) (error "No \"quick units\" are defined")) (or (< pos (length units)) (error "Unit number %d not defined" pos)) (if (math-units-in-expr-p expr nil) (calc-enter-result 1 (format "cun%d" num) (math-convert-units expr (nth pos units))) (calc-enter-result 1 (format "*un%d" num) (math-simplify-units (math-mul expr (nth pos units))))))) ) (defun calc-convert-units (&optional old-units new-units) (interactive) (calc-slow-wrapper (let ((expr (calc-top-n 1)) (uoldname nil) unew) (or (math-units-in-expr-p expr t) (let ((uold (or old-units (progn (setq uoldname (read-string "Old units: ")) (if (equal uoldname "") (progn (setq uoldname "1") 1) (if (string-match "\\` */" uoldname) (setq uoldname (concat "1" uoldname))) (math-read-expr uoldname)))))) (if (eq (car-safe uold) 'error) (error "Bad format in units expression: %s" (nth 1 uold))) (setq expr (math-mul expr uold)))) (or new-units (setq new-units (read-string (if uoldname (concat "Old units: " uoldname ", new units: ") "New units: ")))) (if (string-match "\\` */" new-units) (setq new-units (concat "1" new-units))) (setq units (math-read-expr new-units)) (if (eq (car-safe units) 'error) (error "Bad format in units expression: %s" (nth 2 units))) (let ((unew (math-units-in-expr-p units t)) (std (and (eq (car-safe units) 'var) (assq (nth 1 units) math-standard-units-systems)))) (if std (calc-enter-result 1 "cvun" (math-simplify-units (math-to-standard-units expr (nth 1 std)))) (or unew (error "No units specified")) (calc-enter-result 1 "cvun" (math-convert-units expr units (and uoldname (not (equal uoldname "1"))))))))) ) (defun calc-autorange-units (arg) (interactive "P") (calc-wrapper (calc-change-mode 'calc-autorange-units arg nil t) (message (if calc-autorange-units "Adjusting target unit prefix automatically." "Using target units exactly."))) ) (defun calc-convert-temperature (&optional old-units new-units) (interactive) (calc-slow-wrapper (let ((expr (calc-top-n 1)) (uold nil) (uoldname nil) unew) (setq uold (or old-units (let ((units (math-single-units-in-expr-p expr))) (if units (if (consp units) (list 'var (car units) (intern (concat "var-" (symbol-name (car units))))) (error "Not a pure temperature expression")) (math-read-expr (setq uoldname (read-string "Old temperature units: "))))))) (if (eq (car-safe uold) 'error) (error "Bad format in units expression: %s" (nth 2 uold))) (or (math-units-in-expr-p expr nil) (setq expr (math-mul expr uold))) (setq unew (or new-units (math-read-expr (read-string (if uoldname (concat "Old temperature units: " uoldname ", new units: ") "New temperature units: "))))) (if (eq (car-safe unew) 'error) (error "Bad format in units expression: %s" (nth 2 unew))) (calc-enter-result 1 "cvtm" (math-simplify-units (math-convert-temperature expr uold unew uoldname))))) ) (defun calc-remove-units () (interactive) (calc-slow-wrapper (calc-enter-result 1 "rmun" (math-simplify-units (math-remove-units (calc-top-n 1))))) ) (defun calc-extract-units () (interactive) (calc-slow-wrapper (calc-enter-result 1 "rmun" (math-simplify-units (math-extract-units (calc-top-n 1))))) ) (defun calc-explain-units () (interactive) (calc-wrapper (let ((num-units nil) (den-units nil)) (calc-explain-units-rec (calc-top-n 1) 1) (and den-units (string-match "^[^(].* .*[^)]$" den-units) (setq den-units (concat "(" den-units ")"))) (if num-units (if den-units (message "%s per %s" num-units den-units) (message "%s" num-units)) (if den-units (message "1 per %s" den-units) (message "No units in expression"))))) ) (defun calc-explain-units-rec (expr pow) (let ((u (math-check-unit-name expr)) pos) (if (and u (not (math-zerop pow))) (let ((name (or (nth 2 u) (symbol-name (car u))))) (if (eq (aref name 0) ?\*) (setq name (substring name 1))) (if (string-match "[^a-zA-Z0-9']" name) (if (string-match "^[a-zA-Z0-9' ()]*$" name) (while (setq pos (string-match "[ ()]" name)) (setq name (concat (substring name 0 pos) (if (eq (aref name pos) 32) "-" "") (substring name (1+ pos))))) (setq name (concat "(" name ")")))) (or (eq (nth 1 expr) (car u)) (setq name (concat (nth 2 (assq (aref (symbol-name (nth 1 expr)) 0) math-unit-prefixes)) (if (and (string-match "[^a-zA-Z0-9']" name) (not (memq (car u) '(mHg gf)))) (concat "-" name) (downcase name))))) (cond ((or (math-equal-int pow 1) (math-equal-int pow -1))) ((or (math-equal-int pow 2) (math-equal-int pow -2)) (if (equal (nth 4 u) '((m . 1))) (setq name (concat "Square-" name)) (setq name (concat name "-squared")))) ((or (math-equal-int pow 3) (math-equal-int pow -3)) (if (equal (nth 4 u) '((m . 1))) (setq name (concat "Cubic-" name)) (setq name (concat name "-cubed")))) (t (setq name (concat name "^" (math-format-number (math-abs pow)))))) (if (math-posp pow) (setq num-units (if num-units (concat num-units " " name) name)) (setq den-units (if den-units (concat den-units " " name) name)))) (cond ((eq (car-safe expr) '*) (calc-explain-units-rec (nth 1 expr) pow) (calc-explain-units-rec (nth 2 expr) pow)) ((eq (car-safe expr) '/) (calc-explain-units-rec (nth 1 expr) pow) (calc-explain-units-rec (nth 2 expr) (- pow))) ((memq (car-safe expr) '(neg + -)) (calc-explain-units-rec (nth 1 expr) pow)) ((and (eq (car-safe expr) '^) (math-realp (nth 2 expr))) (calc-explain-units-rec (nth 1 expr) (math-mul pow (nth 2 expr))))))) ) (defun calc-simplify-units () (interactive) (calc-slow-wrapper (calc-with-default-simplification (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))) ) (defun calc-view-units-table (n) (interactive "P") (and n (setq math-units-table-buffer-valid nil)) (let ((win (get-buffer-window "*Units Table*"))) (if (and win math-units-table math-units-table-buffer-valid) (progn (bury-buffer (window-buffer win)) (let ((curwin (selected-window))) (select-window win) (switch-to-buffer nil) (select-window curwin))) (math-build-units-table-buffer nil))) ) (defun calc-enter-units-table (n) (interactive "P") (and n (setq math-units-table-buffer-valid nil)) (math-build-units-table-buffer t) (message (substitute-command-keys "Type \\[calc] to return to the Calculator.")) ) (defun calc-define-unit (uname desc) (interactive "SDefine unit name: \nsDescription: ") (calc-wrapper (let ((form (calc-top-n 1)) (unit (assq uname math-additional-units))) (or unit (setq math-additional-units (cons (setq unit (list uname nil nil)) math-additional-units) math-units-table nil)) (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var) (eq (nth 1 form) uname))) (not (math-equal-int form 1)) (math-format-flat-expr form 0))) (setcar (cdr (cdr unit)) (and (not (equal desc "")) desc)))) (calc-invalidate-units-table) ) (defun calc-undefine-unit (uname) (interactive "SUndefine unit name: ") (calc-wrapper (let ((unit (assq uname math-additional-units))) (or unit (if (assq uname math-standard-units) (error "\"%s\" is a predefined unit name" uname) (error "Unit name \"%s\" not found" uname))) (setq math-additional-units (delq unit math-additional-units) math-units-table nil))) (calc-invalidate-units-table) ) (defun calc-invalidate-units-table () (setq math-units-table nil) (let ((buf (get-buffer "*Units Table*"))) (and buf (save-excursion (set-buffer buf) (save-excursion (goto-char (point-min)) (if (looking-at "Calculator Units Table") (let ((buffer-read-only nil)) (insert "(Obsolete) "))))))) ) (defun calc-get-unit-definition (uname) (interactive "SGet definition for unit: ") (calc-wrapper (math-build-units-table) (let ((unit (assq uname math-units-table))) (or unit (error "Unit name \"%s\" not found" uname)) (let ((msg (nth 2 unit))) (if (stringp msg) (if (string-match "^\\*" msg) (setq msg (substring msg 1))) (setq msg (symbol-name uname))) (if (nth 1 unit) (progn (calc-enter-result 0 "ugdf" (nth 1 unit)) (message "Derived unit: %s" msg)) (calc-enter-result 0 "ugdf" (list 'var uname (intern (concat "var-" (symbol-name uname))))) (message "Base unit: %s" msg))))) ) (defun calc-permanent-units () (interactive) (calc-wrapper (let (pos) (set-buffer (find-file-noselect (substitute-in-file-name calc-settings-file))) (goto-char (point-min)) (if (and (search-forward ";;; Custom units stored by Calc" nil t) (progn (beginning-of-line) (setq pos (point)) (search-forward "\n;;; End of custom units" nil t))) (progn (beginning-of-line) (forward-line 1) (delete-region pos (point))) (goto-char (point-max)) (insert "\n\n") (forward-char -1)) (insert ";;; Custom units stored by Calc on " (current-time-string) "\n") (if math-additional-units (progn (insert "(setq math-additional-units '(\n") (let ((list math-additional-units)) (while list (insert " (" (symbol-name (car (car list))) " " (if (nth 1 (car list)) (if (stringp (nth 1 (car list))) (prin1-to-string (nth 1 (car list))) (prin1-to-string (math-format-flat-expr (nth 1 (car list)) 0))) "nil") " " (prin1-to-string (nth 2 (car list))) ")\n") (setq list (cdr list)))) (insert "))\n")) (insert ";;; (no custom units defined)\n")) (insert ";;; End of custom units\n") (save-buffer))) ) ;;; Units operations. ;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch) ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov) ;;; Updated 2002-04-09 to include CODATA (1998) entries. ;;; for CODATA 1998 see one of ;;; - Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999. ;;; - Reviews of Modern Physics, 72(2), 351-495, 2000. ;;; - http://physics.nist.gov/cuu/Constants/index.html (defvar math-standard-units '( ;; Length ( m nil "*Metre" ) ( in "2.54 cm" "Inch" ) ( ft "12 in" "Foot" ) ( yd "3 ft" "Yard" ) ( mi "5280 ft" "Mile" ) ( au "149597870691. m" "Astronomical Unit" ) ;; NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html) ( lyr "9460536207068016 m" "Light Year" ) ( pc "206264.80625 au" "Parsec" ) ( nmi "1852 m" "Nautical Mile" ) ( fath "6 ft" "Fathom" ) ( u "1 um" "Micron" ) ( mil "in/1000" "Mil" ) ( point "in/72" "Point (1/72 inch)" ) ( tpt "in/72.27" "Point (TeX conventions)" ) ( Ang "1e-10 m" "Angstrom" ) ( mfi "mi+ft+in" "Miles + feet + inches" ) ;; Area ( hect "10000 m^2" "*Hectare" ) ( acre "mi^2 / 640" "Acre" ) ( b "1e-28 m^2" "Barn" ) ;; Volume ( l "1e-3 m^3" "*Litre" ) ( L "1e-3 m^3" "Litre" ) ( gal "4 qt" "US Gallon" ) ( qt "2 pt" "Quart" ) ( pt "2 cup" "Pint" ) ( cup "8 ozfl" "Cup" ) ( ozfl "2 tbsp" "Fluid Ounce" ) ( floz "2 tbsp" "Fluid Ounce" ) ( tbsp "3 tsp" "Tablespoon" ) ( tsp "4.92892159375 ml" "Teaspoon" ) ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" ) ( galC "4.54609 l" "Canadian Gallon" ) ( galUK "4.546092 l" "UK Gallon" ) ;; Time ( s nil "*Second" ) ( sec "s" "Second" ) ( min "60 s" "Minute" ) ( hr "60 min" "Hour" ) ( day "24 hr" "Day" ) ( wk "7 day" "Week" ) ( hms "wk+day+hr+min+s" "Hours, minutes, seconds" ) ( yr "365.25 day" "Year" ) ( Hz "1/s" "Hertz" ) ;; Speed ( mph "mi/hr" "*Miles per hour" ) ( kph "km/hr" "Kilometres per hour" ) ( knot "nmi/hr" "Knot" ) ( c "2.99792458e8 m/s" "Speed of light" ) ;; Acceleration ( ga "9.80665 m/s^2" "*\"g\" acceleration" ) ;; Mass ( g nil "*Gram" ) ( lb "16 oz" "Pound (mass)" ) ( oz "28.349523125 g" "Ounce (mass)" ) ( ton "2000 lb" "Ton" ) ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" ) ( t "1000 kg" "Metric tonne" ) ( tonUK "1016.0469088 kg" "UK ton" ) ( lbt "12 ozt" "Troy pound" ) ( ozt "31.103475 g" "Troy ounce" ) ( ct ".2 g" "Carat" ) ( amu "1.66053873e-27 kg" "Unified atomic mass" ) ;; CODATA 1998 ;; Force ( N "m kg/s^2" "*Newton" ) ( dyn "1e-5 N" "Dyne" ) ( gf "ga g" "Gram (force)" ) ( lbf "4.44822161526 N" "Pound (force)" ) ( kip "1000 lbf" "Kilopound (force)" ) ( pdl "0.138255 N" "Poundal" ) ;; Energy ( J "N m" "*Joule" ) ( erg "1e-7 J" "Erg" ) ( cal "4.1868 J" "International Table Calorie" ) ( Btu "1055.05585262 J" "International Table Btu" ) ( eV "ech V" "Electron volt" ) ( ev "eV" "Electron volt" ) ( therm "105506000 J" "EEC therm" ) ( invcm "h c/cm" "Energy in inverse centimetres" ) ( Kayser "invcm" "Kayser (inverse centimetre energy)" ) ( men "100/invcm" "Inverse energy in metres" ) ( Hzen "h Hz" "Energy in Hertz") ( Ken "k K" "Energy in Kelvins") ( Wh "W h" "Watt hour") ( Ws "W s" "Watt second") ;; Power ( W "J/s" "*Watt" ) ( hp "745.7 W" "Horsepower" ) ;; Temperature ( K nil "*Degree Kelvin" K ) ( dK "K" "Degree Kelvin" K ) ( degK "K" "Degree Kelvin" K ) ( dC "K" "Degree Celsius" C ) ( degC "K" "Degree Celsius" C ) ( dF "(5/9) K" "Degree Fahrenheit" F ) ( degF "(5/9) K" "Degree Fahrenheit" F ) ;; Pressure ( Pa "N/m^2" "*Pascal" ) ( bar "1e5 Pa" "Bar" ) ( atm "101325 Pa" "Standard atmosphere" ) ( torr "atm/760" "Torr" ) ( mHg "1000 torr" "Metre of mercury" ) ( inHg "25.4 mmHg" "Inch of mercury" ) ( inH2O "2.490889e2 Pa" "Inch of water" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) ( psi "6894.75729317 Pa" "Pound per square inch" ) ;; Viscosity ( P "0.1 Pa s" "*Poise" ) ( St "1e-4 m^2/s" "Stokes" ) ;; Electromagnetism ( A nil "*Ampere" ) ( C "A s" "Coulomb" ) ( Fdy "ech Nav" "Faraday" ) ( e "1.602176462e-19 C" "Elementary charge" ) ;; CODATA 1998 ( ech "1.602176462e-19 C" "Elementary charge" ) ;; CODATA 1998 ( V "W/A" "Volt" ) ( ohm "V/A" "Ohm" ) ( mho "A/V" "Mho" ) ( S "A/V" "Siemens" ) ( F "C/V" "Farad" ) ( H "Wb/A" "Henry" ) ( T "Wb/m^2" "Tesla" ) ( G "1e-4 T" "Gauss" ) ( Wb "V s" "Weber" ) ;; Luminous intensity ( cd nil "*Candela" ) ( sb "1e4 cd/m^2" "Stilb" ) ( lm "cd sr" "Lumen" ) ( lx "lm/m^2" "Lux" ) ( ph "1e4 lx" "Phot" ) ( fc "10.76391 lx" "Footcandle" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html) ( lam "1e4 lm/m^2" "Lambert" ) ( flam "1.07639104e-3 lam" "Footlambert" ) ;; Radioactivity ( Bq "1/s" "*Becquerel" ) ( Ci "3.7e10 Bq" "Curie" ) ( Gy "J/kg" "Gray" ) ( Sv "Gy" "Sievert" ) ( R "2.58e-4 C/kg" "Roentgen" ) ( rd ".01 Gy" "Rad" ) ( rem "rd" "Rem" ) ;; Amount of substance ( mol nil "*Mole" ) ;; Plane angle ( rad nil "*Radian" ) ( circ "2 pi rad" "Full circle" ) ( rev "circ" "Full revolution" ) ( deg "circ/360" "Degree" ) ( arcmin "deg/60" "Arc minute" ) ( arcsec "arcmin/60" "Arc second" ) ( grad "circ/400" "Grade" ) ( rpm "rev/min" "Revolutions per minute" ) ;; Solid angle ( sr nil "*Steradian" ) ;; other physical quantities (CODATA 1998) ( h "6.62606876e-34 J s" "*Planck's constant" ) ( hbar "h / 2 pi" "Planck's constant" ) ( mu0 "4 pi 1e-7 H/m" "Permeability of vacuum" ) ( Grav "6.673e-11 m^3/kg^1/s^2" "Gravitational constant" ) ( Nav "6.02214199e23 / mol" "Avagadro's constant" ) ( me "9.10938188e-31 kg" "Electron rest mass" ) ( mp "1.67262158e-27 kg" "Proton rest mass" ) ( mn "1.67492716e-27 kg" "Neutron rest mass" ) ( mu "1.88353109e-28 kg" "Muon rest mass" ) ( Ryd "10973731.568549 /m" "Rydberg's constant" ) ( k "1.3806503e-23 J/K" "Boltzmann's constant" ) ( fsc "7.297352533e-3" "Fine structure constant" ) ( muB "927.400899e-26 J/T" "Bohr magneton" ) ( muN "5.05078317e-27 J/T" "Nuclear magneton" ) ( mue "-928.476362e-26 J/T" "Electron magnetic moment" ) ( mup "1.410606633e-26 J/T" "Proton magnetic moment" ) ( R0 "8.314472 J/mol/K" "Molar gas constant" ) ( V0 "22.710981e-3 m^3/mol" "Standard volume of ideal gas" ) )) (defvar math-additional-units nil "*Additional units table for user-defined units. Must be formatted like math-standard-units. If this is changed, be sure to set math-units-table to nil to ensure that the combined units table will be rebuilt.") (defvar math-unit-prefixes '( ( ?E (float 1 18) "Exa" ) ( ?P (float 1 15) "Peta" ) ( ?T (float 1 12) "Tera" ) ( ?G (float 1 9) "Giga" ) ( ?M (float 1 6) "Mega" ) ( ?k (float 1 3) "Kilo" ) ( ?K (float 1 3) "Kilo" ) ( ?h (float 1 2) "Hecto" ) ( ?H (float 1 2) "Hecto" ) ( ?D (float 1 1) "Deka" ) ( 0 (float 1 0) nil ) ( ?d (float 1 -1) "Deci" ) ( ?c (float 1 -2) "Centi" ) ( ?m (float 1 -3) "Milli" ) ( ?u (float 1 -6) "Micro" ) ( ?n (float 1 -9) "Nano" ) ( ?p (float 1 -12) "Pico" ) ( ?f (float 1 -15) "Femto" ) ( ?a (float 1 -18) "Atto" ) )) (defvar math-standard-units-systems '( ( base nil ) ( si ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) ) ( mks ( ( g '(* (var kg var-kg) (float 1 -3)) ) ) ) ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) ) )) (defvar math-units-table nil "Internal units table derived from math-defined-units. Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).") (defvar math-units-table-buffer-valid nil) (defun math-build-units-table () (or math-units-table (let* ((combined-units (append math-additional-units math-standard-units)) (unit-list (mapcar 'car combined-units)) tab) (message "Building units table...") (setq math-units-table-buffer-valid nil) (setq tab (mapcar (function (lambda (x) (list (car x) (and (nth 1 x) (if (stringp (nth 1 x)) (let ((exp (math-read-plain-expr (nth 1 x)))) (if (eq (car-safe exp) 'error) (error "Format error in definition of %s in units table: %s" (car x) (nth 2 exp)) exp)) (nth 1 x))) (nth 2 x) (nth 3 x) (and (not (nth 1 x)) (list (cons (car x) 1)))))) combined-units)) (let ((math-units-table tab)) (mapcar 'math-find-base-units tab)) (message "Building units table...done") (setq math-units-table tab))) ) (defun math-find-base-units (entry) (if (eq (nth 4 entry) 'boom) (error "Circular definition involving unit %s" (car entry))) (or (nth 4 entry) (let (base) (setcar (nthcdr 4 entry) 'boom) (math-find-base-units-rec (nth 1 entry) 1) '(or base (error "Dimensionless definition for unit %s" (car entry))) (while (eq (cdr (car base)) 0) (setq base (cdr base))) (let ((b base)) (while (cdr b) (if (eq (cdr (car (cdr b))) 0) (setcdr b (cdr (cdr b))) (setq b (cdr b))))) (setq base (sort base 'math-compare-unit-names)) (setcar (nthcdr 4 entry) base) base)) ) (defun math-compare-unit-names (a b) (memq (car b) (cdr (memq (car a) unit-list))) ) (defun math-find-base-units-rec (expr pow) (let ((u (math-check-unit-name expr))) (cond (u (let ((ulist (math-find-base-units u))) (while ulist (let ((p (* (cdr (car ulist)) pow)) (old (assq (car (car ulist)) base))) (if old (setcdr old (+ (cdr old) p)) (setq base (cons (cons (car (car ulist)) p) base)))) (setq ulist (cdr ulist))))) ((math-scalarp expr)) ((and (eq (car expr) '^) (integerp (nth 2 expr))) (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr)))) ((eq (car expr) '*) (math-find-base-units-rec (nth 1 expr) pow) (math-find-base-units-rec (nth 2 expr) pow)) ((eq (car expr) '/) (math-find-base-units-rec (nth 1 expr) pow) (math-find-base-units-rec (nth 2 expr) (- pow))) ((eq (car expr) 'neg) (math-find-base-units-rec (nth 1 expr) pow)) ((eq (car expr) '+) (math-find-base-units-rec (nth 1 expr) pow)) ((eq (car expr) 'var) (or (eq (nth 1 expr) 'pi) (error "Unknown name %s in defining expression for unit %s" (nth 1 expr) (car entry)))) (t (error "Malformed defining expression for unit %s" (car entry))))) ) (defun math-units-in-expr-p (expr sub-exprs) (and (consp expr) (if (eq (car expr) 'var) (math-check-unit-name expr) (and (or sub-exprs (memq (car expr) '(* / ^))) (or (math-units-in-expr-p (nth 1 expr) sub-exprs) (math-units-in-expr-p (nth 2 expr) sub-exprs))))) ) (defun math-only-units-in-expr-p (expr) (and (consp expr) (if (eq (car expr) 'var) (math-check-unit-name expr) (if (memq (car expr) '(* /)) (and (math-only-units-in-expr-p (nth 1 expr)) (math-only-units-in-expr-p (nth 2 expr))) (and (eq (car expr) '^) (and (math-only-units-in-expr-p (nth 1 expr)) (math-realp (nth 2 expr))))))) ) (defun math-single-units-in-expr-p (expr) (cond ((math-scalarp expr) nil) ((eq (car expr) 'var) (math-check-unit-name expr)) ((eq (car expr) '*) (let ((u1 (math-single-units-in-expr-p (nth 1 expr))) (u2 (math-single-units-in-expr-p (nth 2 expr)))) (or (and u1 u2 'wrong) u1 u2))) ((eq (car expr) '/) (if (math-units-in-expr-p (nth 2 expr) nil) 'wrong (math-single-units-in-expr-p (nth 1 expr)))) (t 'wrong)) ) (defun math-check-unit-name (v) (and (eq (car-safe v) 'var) (or (assq (nth 1 v) (or math-units-table (math-build-units-table))) (let ((name (symbol-name (nth 1 v)))) (and (> (length name) 1) (assq (aref name 0) math-unit-prefixes) (or (assq (intern (substring name 1)) math-units-table) (and (eq (aref name 0) ?M) (> (length name) 3) (eq (aref name 1) ?e) (eq (aref name 2) ?g) (assq (intern (substring name 3)) math-units-table))))))) ) (defun math-to-standard-units (expr which-standard) (math-to-standard-rec expr) ) (defun math-to-standard-rec (expr) (if (eq (car-safe expr) 'var) (let ((u (math-check-unit-name expr)) (base (nth 1 expr))) (if u (progn (if (nth 1 u) (setq expr (math-to-standard-rec (nth 1 u))) (let ((st (assq (car u) which-standard))) (if st (setq expr (nth 1 st)) (setq expr (list 'var (car u) (intern (concat "var-" (symbol-name (car u))))))))) (or (null u) (eq base (car u)) (setq expr (list '* (nth 1 (assq (aref (symbol-name base) 0) math-unit-prefixes)) expr))) expr) (if (eq base 'pi) (math-pi) expr))) (if (Math-primp expr) expr (cons (car expr) (mapcar 'math-to-standard-rec (cdr expr))))) ) (defun math-apply-units (expr units ulist &optional pure) (if ulist (let ((new 0) value) (setq expr (math-simplify-units expr)) (or (math-numberp expr) (error "Incompatible units")) (while (cdr ulist) (setq value (math-div expr (nth 1 (car ulist))) value (math-floor (let ((calc-internal-prec (1- calc-internal-prec))) (math-normalize value))) new (math-add new (math-mul value (car (car ulist)))) expr (math-sub expr (math-mul value (nth 1 (car ulist)))) ulist (cdr ulist))) (math-add new (math-mul (math-div expr (nth 1 (car ulist))) (car (car ulist))))) (math-simplify-units (if pure expr (list '* expr units)))) ) (defun math-decompose-units (units) (let ((u (math-check-unit-name units))) (and u (eq (car-safe (nth 1 u)) '+) (setq units (nth 1 u)))) (setq units (calcFunc-expand units)) (and (eq (car-safe units) '+) (let ((entry (list units calc-internal-prec calc-prefer-frac))) (or (equal entry (car math-decompose-units-cache)) (let ((ulist nil) (utemp units) qty unit) (while (eq (car-safe utemp) '+) (setq ulist (cons (math-decompose-unit-part (nth 2 utemp)) ulist) utemp (nth 1 utemp))) (setq ulist (cons (math-decompose-unit-part utemp) ulist) utemp ulist) (while (setq utemp (cdr utemp)) (or (equal (nth 2 (car utemp)) (nth 2 (car ulist))) (error "Inconsistent units in sum"))) (setq math-decompose-units-cache (cons entry (sort ulist (function (lambda (x y) (not (Math-lessp (nth 1 x) (nth 1 y)))))))))) (cdr math-decompose-units-cache))) ) (setq math-decompose-units-cache nil) (defun math-decompose-unit-part (unit) (cons unit (math-is-multiple (math-simplify-units (math-to-standard-units unit nil)) t)) ) (defun math-find-compatible-unit (expr unit) (let ((u (math-check-unit-name unit))) (if u (math-find-compatible-unit-rec expr 1))) ) (defun math-find-compatible-unit-rec (expr pow) (cond ((eq (car-safe expr) '*) (or (math-find-compatible-unit-rec (nth 1 expr) pow) (math-find-compatible-unit-rec (nth 2 expr) pow))) ((eq (car-safe expr) '/) (or (math-find-compatible-unit-rec (nth 1 expr) pow) (math-find-compatible-unit-rec (nth 2 expr) (- pow)))) ((and (eq (car-safe expr) '^) (integerp (nth 2 expr))) (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr)))) (t (let ((u2 (math-check-unit-name expr))) (if (equal (nth 4 u) (nth 4 u2)) (cons expr pow))))) ) (defun math-convert-units (expr new-units &optional pure) (math-with-extra-prec 2 (let ((compat (and (not pure) (math-find-compatible-unit expr new-units))) (unit-list nil) (math-combining-units nil)) (if compat (math-simplify-units (math-mul (math-mul (math-simplify-units (math-div expr (math-pow (car compat) (cdr compat)))) (math-pow new-units (cdr compat))) (math-simplify-units (math-to-standard-units (math-pow (math-div (car compat) new-units) (cdr compat)) nil)))) (if (setq unit-list (math-decompose-units new-units)) (setq new-units (nth 2 (car unit-list)))) (if (eq (car-safe expr) '+) (setq expr (math-simplify-units expr))) (if (math-units-in-expr-p expr t) (math-convert-units-rec expr) (math-apply-units (math-to-standard-units (list '/ expr new-units) nil) new-units unit-list pure))))) ) (defun math-convert-units-rec (expr) (if (math-units-in-expr-p expr nil) (math-apply-units (math-to-standard-units (list '/ expr new-units) nil) new-units unit-list pure) (if (Math-primp expr) expr (cons (car expr) (mapcar 'math-convert-units-rec (cdr expr))))) ) (defun math-convert-temperature (expr old new &optional pure) (let* ((units (math-single-units-in-expr-p expr)) (uold (if old (if (or (null units) (equal (nth 1 old) (car units))) (math-check-unit-name old) (error "Inconsistent temperature units")) units)) (unew (math-check-unit-name new))) (or (and (consp unew) (nth 3 unew)) (error "Not a valid temperature unit")) (or (and (consp uold) (nth 3 uold)) (error "Not a pure temperature expression")) (let ((v (car uold))) (setq expr (list '/ expr (list 'var v (intern (concat "var-" (symbol-name v))))))) (or (eq (nth 3 uold) (nth 3 unew)) (cond ((eq (nth 3 uold) 'K) (setq expr (list '- expr '(float 27315 -2))) (if (eq (nth 3 unew) 'F) (setq expr (list '+ (list '* expr '(frac 9 5)) 32)))) ((eq (nth 3 uold) 'C) (if (eq (nth 3 unew) 'F) (setq expr (list '+ (list '* expr '(frac 9 5)) 32)) (setq expr (list '+ expr '(float 27315 -2))))) (t (setq expr (list '* (list '- expr 32) '(frac 5 9))) (if (eq (nth 3 unew) 'K) (setq expr (list '+ expr '(float 27315 -2))))))) (if pure expr (list '* expr new))) ) (defun math-simplify-units (a) (let ((math-simplifying-units t) (calc-matrix-mode 'scalar)) (math-simplify a)) ) (fset 'calcFunc-usimplify (symbol-function 'math-simplify-units)) (math-defsimplify (+ -) (and math-simplifying-units (math-units-in-expr-p (nth 1 expr) nil) (let* ((units (math-extract-units (nth 1 expr))) (ratio (math-simplify (math-to-standard-units (list '/ (nth 2 expr) units) nil)))) (if (math-units-in-expr-p ratio nil) (progn (calc-record-why "*Inconsistent units" expr) expr) (list '* (math-add (math-remove-units (nth 1 expr)) (if (eq (car expr) '-) (math-neg ratio) ratio)) units)))) ) (math-defsimplify * (math-simplify-units-prod) ) (defun math-simplify-units-prod () (and math-simplifying-units calc-autorange-units (Math-realp (nth 1 expr)) (let* ((num (math-float (nth 1 expr))) (xpon (calcFunc-xpon num)) (unitp (cdr (cdr expr))) (unit (car unitp)) (pow (if (eq (car expr) '*) 1 -1)) u) (and (eq (car-safe unit) '*) (setq unitp (cdr unit) unit (car unitp))) (and (eq (car-safe unit) '^) (integerp (nth 2 unit)) (setq pow (* pow (nth 2 unit)) unitp (cdr unit) unit (car unitp))) (and (setq u (math-check-unit-name unit)) (integerp xpon) (or (< xpon 0) (>= xpon (if (eq (car u) 'm) 1 3))) (let* ((uxpon 0) (pref (if (< pow 0) (reverse math-unit-prefixes) math-unit-prefixes)) (p pref) pxpon pname) (or (eq (car u) (nth 1 unit)) (setq uxpon (* pow (nth 2 (nth 1 (assq (aref (symbol-name (nth 1 unit)) 0) math-unit-prefixes)))))) (setq xpon (+ xpon uxpon)) (while (and p (or (memq (car (car p)) '(?d ?D ?h ?H)) (and (eq (car (car p)) ?c) (not (eq (car u) 'm))) (< xpon (setq pxpon (* (nth 2 (nth 1 (car p))) pow))) (progn (setq pname (math-build-var-name (if (eq (car (car p)) 0) (car u) (concat (char-to-string (car (car p))) (symbol-name (car u)))))) (and (/= (car (car p)) 0) (assq (nth 1 pname) math-units-table))))) (setq p (cdr p))) (and p (/= pxpon uxpon) (or (not (eq p pref)) (< xpon (+ pxpon (* (math-abs pow) 3)))) (progn (setcar (cdr expr) (let ((calc-prefer-frac nil)) (calcFunc-scf (nth 1 expr) (- uxpon pxpon)))) (setcar unitp pname) expr)))))) ) (math-defsimplify / (and math-simplifying-units (let ((np (cdr expr)) (try-cancel-units 0) n nn) (setq n (if (eq (car-safe (nth 2 expr)) '*) (cdr (nth 2 expr)) (nthcdr 2 expr))) (if (math-realp (car n)) (progn (setcar (cdr expr) (math-mul (nth 1 expr) (let ((calc-prefer-frac nil)) (math-div 1 (car n))))) (setcar n 1))) (while (eq (car-safe (setq n (car np))) '*) (math-simplify-units-divisor (cdr n) (cdr (cdr expr))) (setq np (cdr (cdr n)))) (math-simplify-units-divisor np (cdr (cdr expr))) (if (eq try-cancel-units 0) (let* ((math-simplifying-units nil) (base (math-simplify (math-to-standard-units expr nil)))) (if (Math-numberp base) (setq expr base)))) (if (eq (car-safe expr) '/) (math-simplify-units-prod)) expr)) ) (defun math-simplify-units-divisor (np dp) (let ((n (car np)) d dd temp) (while (eq (car-safe (setq d (car dp))) '*) (if (setq temp (math-simplify-units-quotient n (nth 1 d))) (progn (setcar np (setq n temp)) (setcar (cdr d) 1))) (setq dp (cdr (cdr d)))) (if (setq temp (math-simplify-units-quotient n d)) (progn (setcar np (setq n temp)) (setcar dp 1)))) ) ;; Simplify, e.g., "in / cm" to "2.54" in a units expression. (defun math-simplify-units-quotient (n d) (let ((pow1 1) (pow2 1)) (and (eq (car-safe n) '^) (integerp (nth 2 n)) (setq pow1 (nth 2 n) n (nth 1 n))) (and (eq (car-safe d) '^) (integerp (nth 2 d)) (setq pow2 (nth 2 d) d (nth 1 d))) (let ((un (math-check-unit-name n)) (ud (math-check-unit-name d))) (and un ud (if (and (equal (nth 4 un) (nth 4 ud)) (eq pow1 pow2)) (math-to-standard-units (list '/ n d) nil) (let (ud1) (setq un (nth 4 un) ud (nth 4 ud)) (while un (setq ud1 ud) (while ud1 (and (eq (car (car un)) (car (car ud1))) (setq try-cancel-units (+ try-cancel-units (- (* (cdr (car un)) pow1) (* (cdr (car ud)) pow2))))) (setq ud1 (cdr ud1))) (setq un (cdr un))) nil))))) ) (math-defsimplify ^ (and math-simplifying-units (math-realp (nth 2 expr)) (if (memq (car-safe (nth 1 expr)) '(* /)) (list (car (nth 1 expr)) (list '^ (nth 1 (nth 1 expr)) (nth 2 expr)) (list '^ (nth 2 (nth 1 expr)) (nth 2 expr))) (math-simplify-units-pow (nth 1 expr) (nth 2 expr)))) ) (math-defsimplify calcFunc-sqrt (and math-simplifying-units (if (memq (car-safe (nth 1 expr)) '(* /)) (list (car (nth 1 expr)) (list 'calcFunc-sqrt (nth 1 (nth 1 expr))) (list 'calcFunc-sqrt (nth 2 (nth 1 expr)))) (math-simplify-units-pow (nth 1 expr) '(frac 1 2)))) ) (math-defsimplify (calcFunc-floor calcFunc-ceil calcFunc-round calcFunc-rounde calcFunc-roundu calcFunc-trunc calcFunc-float calcFunc-frac calcFunc-abs calcFunc-clean) (and math-simplifying-units (= (length expr) 2) (if (math-only-units-in-expr-p (nth 1 expr)) (nth 1 expr) (if (and (memq (car-safe (nth 1 expr)) '(* /)) (or (math-only-units-in-expr-p (nth 1 (nth 1 expr))) (math-only-units-in-expr-p (nth 2 (nth 1 expr))))) (list (car (nth 1 expr)) (cons (car expr) (cons (nth 1 (nth 1 expr)) (cdr (cdr expr)))) (cons (car expr) (cons (nth 2 (nth 1 expr)) (cdr (cdr expr))))))))) (defun math-simplify-units-pow (a pow) (if (and (eq (car-safe a) '^) (math-check-unit-name (nth 1 a)) (math-realp (nth 2 a))) (list '^ (nth 1 a) (math-mul pow (nth 2 a))) (let* ((u (math-check-unit-name a)) (pf (math-to-simple-fraction pow)) (d (and (eq (car-safe pf) 'frac) (nth 2 pf)))) (and u d (math-units-are-multiple u d) (list '^ (math-to-standard-units a nil) pow)))) ) (defun math-units-are-multiple (u n) (setq u (nth 4 u)) (while (and u (= (% (cdr (car u)) n) 0)) (setq u (cdr u))) (null u) ) (math-defsimplify calcFunc-sin (and math-simplifying-units (math-units-in-expr-p (nth 1 expr) nil) (let ((rad (math-simplify-units (math-evaluate-expr (math-to-standard-units (nth 1 expr) nil)))) (calc-angle-mode 'rad)) (and (eq (car-safe rad) '*) (math-realp (nth 1 rad)) (eq (car-safe (nth 2 rad)) 'var) (eq (nth 1 (nth 2 rad)) 'rad) (list 'calcFunc-sin (nth 1 rad))))) ) (math-defsimplify calcFunc-cos (and math-simplifying-units (math-units-in-expr-p (nth 1 expr) nil) (let ((rad (math-simplify-units (math-evaluate-expr (math-to-standard-units (nth 1 expr) nil)))) (calc-angle-mode 'rad)) (and (eq (car-safe rad) '*) (math-realp (nth 1 rad)) (eq (car-safe (nth 2 rad)) 'var) (eq (nth 1 (nth 2 rad)) 'rad) (list 'calcFunc-cos (nth 1 rad))))) ) (math-defsimplify calcFunc-tan (and math-simplifying-units (math-units-in-expr-p (nth 1 expr) nil) (let ((rad (math-simplify-units (math-evaluate-expr (math-to-standard-units (nth 1 expr) nil)))) (calc-angle-mode 'rad)) (and (eq (car-safe rad) '*) (math-realp (nth 1 rad)) (eq (car-safe (nth 2 rad)) 'var) (eq (nth 1 (nth 2 rad)) 'rad) (list 'calcFunc-tan (nth 1 rad))))) ) (defun math-remove-units (expr) (if (math-check-unit-name expr) 1 (if (Math-primp expr) expr (cons (car expr) (mapcar 'math-remove-units (cdr expr))))) ) (defun math-extract-units (expr) (if (memq (car-safe expr) '(* /)) (cons (car expr) (mapcar 'math-extract-units (cdr expr))) (if (math-check-unit-name expr) expr 1)) ) (defun math-build-units-table-buffer (enter-buffer) (if (not (and math-units-table math-units-table-buffer-valid (get-buffer "*Units Table*"))) (let ((buf (get-buffer-create "*Units Table*")) (uptr (math-build-units-table)) (calc-language (if (eq calc-language 'big) nil calc-language)) (calc-float-format '(float 0)) (calc-group-digits nil) (calc-number-radix 10) (calc-point-char ".") (std nil) u name shadowed) (save-excursion (message "Formatting units table...") (set-buffer buf) (setq buffer-read-only nil) (erase-buffer) (insert "Calculator Units Table:\n\n") (insert "Unit Type Definition Description\n\n") (while uptr (setq u (car uptr) name (nth 2 u)) (if (eq (car u) 'm) (setq std t)) (setq shadowed (and std (assq (car u) math-additional-units))) (if (and name (> (length name) 1) (eq (aref name 0) ?\*)) (progn (or (eq uptr math-units-table) (insert "\n")) (setq name (substring name 1)))) (insert " ") (and shadowed (insert "(")) (insert (symbol-name (car u))) (and shadowed (insert ")")) (if (nth 3 u) (progn (indent-to 10) (insert (symbol-name (nth 3 u)))) (or std (progn (indent-to 10) (insert "U")))) (indent-to 14) (and shadowed (insert "(")) (if (nth 1 u) (insert (math-format-value (nth 1 u) 80)) (insert (symbol-name (car u)))) (and shadowed (insert ")")) (indent-to 41) (insert " ") (if name (insert name)) (if shadowed (insert " (redefined above)") (or (nth 1 u) (insert " (base unit)"))) (insert "\n") (setq uptr (cdr uptr))) (insert "\n\nUnit Prefix Table:\n\n") (setq uptr math-unit-prefixes) (while uptr (setq u (car uptr)) (insert " " (char-to-string (car u))) (if (equal (nth 1 u) (nth 1 (nth 1 uptr))) (insert " " (char-to-string (car (car (setq uptr (cdr uptr))))) " ") (insert " ")) (insert "10^" (int-to-string (nth 2 (nth 1 u)))) (indent-to 15) (insert " " (nth 2 u) "\n") (while (eq (car (car (setq uptr (cdr uptr)))) 0))) (insert "\n") (setq buffer-read-only t) (message "Formatting units table...done")) (setq math-units-table-buffer-valid t) (let ((oldbuf (current-buffer))) (set-buffer buf) (goto-char (point-min)) (set-buffer oldbuf)) (if enter-buffer (pop-to-buffer buf) (display-buffer buf))) (if enter-buffer (pop-to-buffer (get-buffer "*Units Table*")) (display-buffer (get-buffer "*Units Table*")))) )