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emacs/lisp/calc/calc-units.el
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;;; calc-units.el --- unit conversion functions for Calc
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainers: D. Goel <deego@gnufans.org>
;; Colin Walters <walters@debian.org>
;; 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.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(defun calc-Need-calc-units () nil)
;;; 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 April 2002 by Jochen Küpper
;;; 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 "*Meter" )
( 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" "*Liter" )
( L "1e-3 m^3" "Liter" )
( 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" "Kilometers 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 ton" )
( 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 centimeters" )
( Kayser "invcm" "Kayser (inverse centimeter energy)" )
( men "100/invcm" "Inverse energy in meters" )
( 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 " 1.333224e2 Pa" "Torr" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
( mHg "1000 torr" "Meter 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 "3.426259 cd/m^2" "Footlambert" ) ;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
;; 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)
;;; 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)))
(unless (and (>= num 0) (<= num 9))
(errunless "Bad unit number"))
(unless (math-vectorp units)
(errunless "No \"quick units\" are defined"))
(unless (< pos (length units))
(errunless "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)
(unless (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))))))
(when (eq (car-safe uold) 'error)
(error "Bad format in units expression: %s" (nth 1 uold)))
(setq expr (math-mul expr uold))))
(unless new-units
(setq new-units (read-string (if uoldname
(concat "Old units: "
uoldname
", new units: ")
"New units: "))))
(when (string-match "\\` */" new-units)
(setq new-units (concat "1" new-units)))
(setq units (math-read-expr new-units))
(when (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))))
(unless 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: ")))))))
(when (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: ")))))
(when (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))))
(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)))))
(defvar math-decompose-units-cache nil)
(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))
(unless (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))))
(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))))
(when (setq unit-list (math-decompose-units new-units))
(setq new-units (nth 2 (car unit-list))))
(when (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)))
(unless (and (consp unew) (nth 3 unew))
(error "Not a valid temperature unit"))
(unless (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)))
(defalias 'calcFunc-usimplify '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))) '*)
(when (setq temp (math-simplify-units-quotient n (nth 1 d)))
(setcar np (setq n temp))
(setcar (cdr d) 1))
(setq dp (cdr (cdr d))))
(when (setq temp (math-simplify-units-quotient n d))
(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))
(when (and (eq (car-safe n) '^)
(integerp (nth 2 n)))
(setq pow1 (nth 2 n) n (nth 1 n)))
(when (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))
(when (eq (car u) 'm)
(setq std t))
(setq shadowed (and std (assq (car u) math-additional-units)))
(when (and name
(> (length name) 1)
(eq (aref name 0) ?\*))
(unless (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 " ")
(when name
(insert name))
(if shadowed
(insert " (redefined above)")
(unless (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*")))))
;; Local Variables:
;; coding: iso-latin-1
;; End:
;;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
;;; calc-units.el ends here
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