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calc-units.el
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;;; calc-units.el --- unit conversion functions for Calc -*- lexical-binding:t -*-
;; Copyright (C) 1990-1993, 2001-2020 Free Software Foundation, Inc.
;; Author: David Gillespie <[email protected]>
;; This file is part of GNU Emacs.
;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(eval-when-compile
(require 'calc-alg))
;;; Units operations.
;;; Units table last updated 9-Jan-91 by Ulrich Mueller ([email protected])
;;; with some additions by Przemek Klosowski ([email protected])
;;; Updated April 2002 by Jochen Küpper
;;; Updated August 2007, using
;;; CODATA (http://physics.nist.gov/cuu/Constants/index.html)
;;; NIST (http://physics.nist.gov/Pubs/SP811/appenB9.html)
;;; ESUWM (Encyclopaedia of Scientific Units, Weights and
;;; Measures, by François Cardarelli)
;;; All conversions are exact unless otherwise noted.
;; CODATA values updated February 2016, using 2014 adjustment
;; http://arxiv.org/pdf/1507.07956.pdf
;; Updated November 2018 for the redefinition of the SI
;; https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
(defvar math-standard-units
'( ;; Length
( m nil "*Meter" )
( in "254*10^(-2) cm" "Inch" nil
"2.54 cm")
( ft "12 in" "Foot")
( yd "3 ft" "Yard" )
( mi "5280 ft" "Mile" )
( au "149597870691. m" "Astronomical Unit" nil
"149597870691 m (*)")
;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
( lyr "c yr" "Light Year" )
( pc "3.0856775854*10^16 m" "Parsec (**)" nil
"3.0856775854 10^16 m (*)") ;; (approx) ESUWM
( nmi "1852 m" "Nautical Mile" )
( fath "6 ft" "Fathom" )
( fur "660 ft" "Furlong")
( mu "1 um" "Micron" )
( mil "(1/1000) in" "Mil" )
( point "(1/72) in" "Point (PostScript convention)" )
( Ang "10^(-10) m" "Angstrom" )
( mfi "mi+ft+in" "Miles + feet + inches" )
;; TeX lengths
( texpt "(100/7227) in" "Point (TeX convention) (**)" )
( texpc "12 texpt" "Pica (TeX convention) (**)" )
( texbp "point" "Big point (TeX convention) (**)" )
( texdd "(1238/1157) texpt" "Didot point (TeX convention) (**)" )
( texcc "12 texdd" "Cicero (TeX convention) (**)" )
( texsp "(1/65536) texpt" "Scaled TeX point (TeX convention) (**)" )
;; Area
( hect "10000 m^2" "*Hectare" )
( a "100 m^2" "Are")
( acre "(1/640) mi^2" "Acre" )
( b "10^(-28) m^2" "Barn" )
;; Volume
( L "10^(-3) m^3" "*Liter" )
( l "L" "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" )
;; ESUWM defines a US gallon as 231 in^3.
;; That gives the following exact value for tsp.
( tsp "492892159375*10^(-11) ml" "Teaspoon" nil
"4.92892159375 ml")
( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" nil
"tsp+tbsp+ozfl+cup+pt+qt+gal")
( galC "galUK" "Canadian Gallon" )
( galUK "454609*10^(-5) L" "UK Gallon" nil
"4.54609 L") ;; NIST
;; 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 "36525*10^(-2) day" "Year (Julian)" nil
"365.25 day")
( Hz "1/s" "Hertz" )
;; Speed
( mph "mi/hr" "*Miles per hour" )
( kph "km/hr" "Kilometers per hour" )
( knot "nmi/hr" "Knot" )
( c "299792458 m/s" "Speed of light" ) ;; SI definition
;; Acceleration
( ga "980665*10^(-5) m/s^2" "*\"g\" acceleration" nil
"9.80665 m / s^2") ;; CODATA
;; Mass
( g nil "*Gram" )
( lb "16 oz" "Pound (mass)" )
( oz "28349523125*10^(-9) g" "Ounce (mass)" nil
"28.349523125 g") ;; ESUWM
( ton "2000 lb" "Ton" )
( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
( t "1000 kg" "Metric ton" )
( tonUK "10160469088*10^(-7) kg" "UK ton" nil
"1016.0469088 kg") ;; ESUWM
( lbt "12 ozt" "Troy pound" )
( ozt "311034768*10^(-7) g" "Troy ounce" nil
"31.10347680 g") ;; ESUWM, 1/12 exact value for lbt
( ct "(2/10) g" "Carat" nil
"0.2 g") ;; ESUWM
( u "1.660539040*10^(-27) kg" "Unified atomic mass" nil
"1.660539040 10^-27 kg (*)");;(approx) CODATA
;; Force
( N "m kg/s^2" "*Newton" )
( dyn "10^(-5) N" "Dyne" )
( gf "ga g" "Gram (force)" )
( lbf "ga lb" "Pound (force)" )
( kip "1000 lbf" "Kilopound (force)" )
( pdl "138254954376*10^(-12) N" "Poundal" nil
"0.138254954376 N") ;; ESUWM
;; Energy
( J "N m" "*Joule" )
( erg "10^(-7) J" "Erg" )
( cal "41868*10^(-4) J" "International Table Calorie" nil
"4.1868 J") ;; NIST
( calth "4184*10^(-3) J" "Thermochemical Calorie" nil
"4.184 J") ;; NIST
( Cal "1000 cal" "Large Calorie")
( Btu "105505585262*10^(-8) J" "International Table Btu" nil
"1055.05585262 J") ;; ESUWM
( 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 hr" "Watt hour")
( Ws "W s" "Watt second")
;; Power
( W "J/s" "*Watt" )
( hp "550 ft lbf/s" "Horsepower") ;;ESUWM
( hpm "75 m kgf/s" "Metric Horsepower") ;;ESUWM
;; 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 "10^5 Pa" "Bar" )
( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA
( Torr "(1/760) atm" "Torr")
( mHg "1000 Torr" "Meter of mercury" )
( inHg "254*10^(-1) mmHg" "Inch of mercury" nil
"25.4 mmHg")
( inH2O "2.490889*10^2 Pa" "Inch of water" nil
"2.490889 10^2 Pa (*)") ;;(approx) NIST
( psi "lbf/in^2" "Pounds per square inch" )
;; Viscosity
( P "(1/10) Pa s" "*Poise" )
( St "10^(-4) m^2/s" "Stokes" )
;; Electromagnetism
( A nil "*Ampere" )
( C "A s" "Coulomb" )
( Fdy "ech Nav" "Faraday" )
( e "ech" "Elementary charge" )
( ech "1.602176634*10^(-19) C" "Elementary charge" nil
"1.602176634 10^-19 C") ;; SI definition
( V "W/A" "Volt" )
( ohm "V/A" "Ohm" )
( Ω "ohm" "Ohm" )
( mho "A/V" "Mho" )
( S "A/V" "Siemens" )
( F "C/V" "Farad" )
( H "Wb/A" "Henry" )
( T "Wb/m^2" "Tesla" )
( Gs "10^(-4) T" "Gauss" )
( Wb "V s" "Weber" )
;; Luminous intensity
( cd nil "*Candela" )
( sb "10000 cd/m^2" "Stilb" )
( lm "cd sr" "Lumen" )
( lx "lm/m^2" "Lux" )
( ph "10000 lx" "Phot" )
( fc "lm/ft^2" "Footcandle") ;; ESUWM
( lam "10000 lm/m^2" "Lambert" )
( flam "(1/pi) cd/ft^2" "Footlambert") ;; ESUWM
;; Radioactivity
( Bq "1/s" "*Becquerel" )
( Ci "37*10^9 Bq" "Curie" ) ;; ESUWM
( Gy "J/kg" "Gray" )
( Sv "Gy" "Sievert" )
( R "258*10^(-6) C/kg" "Roentgen" ) ;; NIST
( rd "(1/100) 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
;; Unless otherwise mentioned, the values are from CODATA,
;; and are approximate.
( h "6.62607015*10^(-34) J s" "*Planck's constant" nil
"6.62607015 10^-34 J s") ;; SI definition
( hbar "h / (2 pi)" "Planck's constant" ) ;; Exact
;; After the 2018 SI redefinition, eps0 and mu0 are measured quantities,
;; and mu0 no longer has the previous exact value of 4 pi 10^(-7) H/m.
( eps0 "ech^2 / (2 alpha h c)" "Permittivity of vacuum" )
( ε0 "eps0" "Permittivity of vacuum" )
( mu0 "1 / (eps0 c^2)" "Permeability of vacuum") ;; Exact
( μ0 "mu0" "Permeability of vacuum") ;; Exact
( G "6.67408*10^(-11) m^3/(kg s^2)" "Gravitational constant" nil
"6.67408 10^-11 m^3/(kg s^2) (*)")
( Nav "6.02214076*10^(23) / mol" "Avogadro's constant" nil
"6.02214076 10^23 / mol") ;; SI definition
( me "9.10938356*10^(-31) kg" "Electron rest mass" nil
"9.10938356 10^-31 kg (*)")
( mp "1.672621898*10^(-27) kg" "Proton rest mass" nil
"1.672621898 10^-27 kg (*)")
( mn "1.674927471*10^(-27) kg" "Neutron rest mass" nil
"1.674927471 10^-27 kg (*)")
( mmu "1.883531594*10^(-28) kg" "Muon rest mass" nil
"1.883531594 10^-28 kg (*)")
( mμ "mmu" "Muon rest mass" nil
"1.883531594 10^-28 kg (*)")
( Ryd "10973731.568508 /m" "Rydberg's constant" nil
"10973731.568508 /m (*)")
( k "1.380649*10^(-23) J/K" "Boltzmann's constant" nil
"1.380649 10^-23 J/K") ;; SI definition
( sigma "2 pi^5 k^4 / (15 h^3 c^2)" "Stefan-Boltzmann constant")
( σ "sigma" "Stefan-Boltzmann constant")
( alpha "7.2973525664*10^(-3)" "Fine structure constant" nil
"7.2973525664 10^-3 (*)")
( α "alpha" "Fine structure constant" nil
"7.2973525664 10^-3 (*)")
( muB "927.4009994*10^(-26) J/T" "Bohr magneton" nil
"927.4009994 10^-26 J/T (*)")
( muN "5.050783699*10^(-27) J/T" "Nuclear magneton" nil
"5.050783699 10^-27 J/T (*)")
( mue "-928.4764620*10^(-26) J/T" "Electron magnetic moment" nil
"-928.4764620 10^-26 J/T (*)")
( mup "1.4106067873*10^(-26) J/T" "Proton magnetic moment" nil
"1.4106067873 10^-26 J/T (*)")
( R0 "Nav k" "Molar gas constant") ;; Exact
( V0 "22.710947*10^(-3) m^3/mol" "Standard volume of ideal gas" nil
"22.710947 10^-3 m^3/mol (*)")
;; Logarithmic units
( Np nil "*Neper")
( dB "(ln(10)/20) Np" "decibel")))
(defvar math-additional-units nil
"Additional units table for user-defined units.
Must be formatted like `math-standard-units'.
If you change this, be sure to set `math-units-table' to nil to ensure
that the combined units table will be rebuilt.")
(defvar math-unit-prefixes
'( ( ?Y (^ 10 24) "Yotta" )
( ?Z (^ 10 21) "Zetta" )
( ?E (^ 10 18) "Exa" )
( ?P (^ 10 15) "Peta" )
( ?T (^ 10 12) "Tera" )
( ?G (^ 10 9) "Giga" )
( ?M (^ 10 6) "Mega" )
( ?k (^ 10 3) "Kilo" )
( ?K (^ 10 3) "Kilo" )
( ?h (^ 10 2) "Hecto" )
( ?H (^ 10 2) "Hecto" )
( ?D (^ 10 1) "Deka" )
( 0 (^ 10 0) nil )
( ?d (^ 10 -1) "Deci" )
( ?c (^ 10 -2) "Centi" )
( ?m (^ 10 -3) "Milli" )
( ?u (^ 10 -6) "Micro" )
( ?μ (^ 10 -6) "Micro" )
( ?n (^ 10 -9) "Nano" )
( ?p (^ 10 -12) "Pico" )
( ?f (^ 10 -15) "Femto" )
( ?a (^ 10 -18) "Atto" )
( ?z (^ 10 -21) "zepto" )
( ?y (^ 10 -24) "yocto" )))
(defvar math-standard-units-systems
'( ( base nil )
( si ( ( g '(/ (var kg var-kg) 1000) ) ) )
( mks ( ( g '(/ (var kg var-kg) 1000) ) ) )
( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
(defvar math-units-table nil
"Internal units table.
Derived from `math-standard-units' and `math-additional-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))))))
(defvar calc-ensure-consistent-units)
(defun calc-quick-units ()
(interactive)
(calc-slow-wrapper
(let* ((num (- last-command-event ?0))
(pos (if (= num 0) 10 num))
(units (calc-var-value 'var-Units))
(expr (calc-top-n 1)))
(unless (and (>= num 0) (<= num 9))
(error "Bad unit number"))
(unless (math-vectorp units)
(error "No \"quick units\" are defined"))
(unless (< pos (length units))
(error "Unit number %d not defined" pos))
(if (math-units-in-expr-p expr nil)
(progn
(if calc-ensure-consistent-units
(math-check-unit-consistency expr (nth pos units)))
(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 math-get-standard-units (expr)
"Return the standard units in EXPR."
(math-simplify-units
(math-extract-units
(math-to-standard-units expr nil))))
(defun math-get-units (expr)
"Return the units in EXPR."
(math-simplify-units
(math-extract-units expr)))
(defun math-make-unit-string (expr)
"Return EXPR in string form.
If EXPR is nil, return nil."
(if expr
(let ((cexpr (math-compose-expr expr 0)))
(replace-regexp-in-string
" / " "/"
(if (stringp cexpr)
cexpr
(math-composition-to-string cexpr))))))
(defvar math-default-units-table
(make-hash-table :test 'equal)
"A table storing previously converted units.")
(defun math-get-default-units (expr)
"Get default units to use when converting the units in EXPR."
(let* ((units (math-get-units expr))
(standard-units (math-get-standard-units expr))
(default-units (gethash
standard-units
math-default-units-table)))
(if (equal units (car default-units))
(math-make-unit-string (cadr default-units))
(math-make-unit-string (car default-units)))))
(defun math-put-default-units (expr &optional comp std)
"Put the units in EXPR in the default units table.
If COMP or STD is non-nil, put that in the units table instead."
(let* ((new-units (or comp std (math-get-units expr)))
(standard-units (math-get-standard-units
(cond
(comp (math-simplify-units expr))
(std expr)
(t new-units))))
(default-units (gethash standard-units math-default-units-table)))
(unless (eq standard-units 1)
(cond
((not default-units)
(puthash standard-units (list new-units) math-default-units-table))
((not (equal new-units (car default-units)))
(puthash standard-units
(list new-units (car default-units))
math-default-units-table))))))
(defvar calc-allow-units-as-numbers t)
(defun calc-convert-units (&optional old-units new-units)
(interactive)
(calc-slow-wrapper
(let ((expr (calc-top-n 1))
(uoldname nil)
(unitscancel nil)
(nouold nil)
units
defunits)
(if (or (not (math-units-in-expr-p expr t))
(setq unitscancel (and
(if (get 'calc-allow-units-as-numbers 'saved-value)
(car (get 'calc-allow-units-as-numbers 'saved-value))
calc-allow-units-as-numbers)
(eq (math-get-standard-units expr) 1))))
(let ((uold (or old-units
(progn
(setq uoldname
(if unitscancel
(read-string
"(The expression is unitless when simplified) Old Units: ")
(read-string "Old units: ")))
(if (equal uoldname "")
(progn
(setq nouold unitscancel)
(setq uoldname "1")
1)
(if (string-match "\\` */" uoldname)
(setq uoldname (concat "1" uoldname)))
(math-read-expr uoldname))))))
(unless (math-units-in-expr-p uold t)
(error "No units specified"))
(when (eq (car-safe uold) 'error)
(error "Bad format in units expression: %s" (nth 1 uold)))
(setq expr (math-mul expr uold))))
(setq defunits (math-get-default-units expr))
(unless new-units
(setq new-units
(read-string (concat
(if (and uoldname (not nouold))
(concat "Old units: "
uoldname
", new units")
"New units")
(if defunits
(concat
" (default "
defunits
"): ")
": "))))
(if (and
(string= new-units "")
defunits)
(setq new-units defunits)))
(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)))
(if calc-ensure-consistent-units
(math-check-unit-consistency expr 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)))
(comp (eq (car-safe units) '+)))
(unless (or unew std)
(error "No units specified"))
(let* ((noold (and uoldname (not (equal uoldname "1"))))
(res
(if std
(math-simplify-units (math-to-standard-units expr (nth 1 std)))
(math-convert-units expr units noold))))
(unless std
(math-put-default-units (if noold units res) (if comp units)))
(calc-enter-result 1 "cvun" res))))))
(defun calc-convert-exact-units ()
(interactive)
(calc-slow-wrapper
(let* ((expr (calc-top-n 1)))
(unless (math-units-in-expr-p expr t)
(error "No units in expression."))
(let* ((old-units (math-extract-units expr))
(defunits (math-get-default-units expr))
units
(new-units
(read-string (concat "New units"
(if defunits
(concat
" (default "
defunits
"): ")
": ")))))
(if (and
(string= new-units "")
defunits)
(setq new-units defunits))
(setq units (math-read-expr new-units))
(when (eq (car-safe units) 'error)
(error "Bad format in units expression: %s" (nth 2 units)))
(math-check-unit-consistency old-units units)
(let ((res
(list '* (math-mul (math-remove-units expr)
(math-simplify-units
(math-to-standard-units (list '/ old-units units) nil)))
units)))
(calc-enter-result 1 "cvxu" res))))))
(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 ((tempunits (delq nil
(mapcar
(lambda (x)
(if (nth 3 x) (car x)))
math-standard-units)))
(expr (calc-top-n 1))
(uold nil)
(uoldname nil)
unew
defunits)
(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 (completing-read
"Old temperature units: "
tempunits)))))))
(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 defunits (math-get-default-units expr))
(setq unew (or new-units
(completing-read
(concat
(if uoldname
(concat "Old temperature units: "
uoldname
", new units")
"New temperature units")
(if defunits
(concat " (default "
defunits
"): ")
": "))
tempunits)))
(setq unew (math-read-expr (if (string= unew "") defunits unew)))
(when (eq (car-safe unew) 'error)
(error "Bad format in units expression: %s" (nth 2 unew)))
(math-put-default-units unew)
(let ((ntemp (calc-normalize
(math-simplify-units
(math-convert-temperature expr uold unew
uoldname)))))
(if (Math-zerop ntemp)
(setq ntemp (list '* ntemp unew)))
(let ((calc-simplify-mode 'none))
(calc-enter-result 1 "cvtm" ntemp))))))
(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 "exun" (math-simplify-units
(math-extract-units (calc-top-n 1))))))
;; The variables calc-num-units and calc-den-units are local to
;; calc-explain-units, but are used by calc-explain-units-rec,
;; which is called by calc-explain-units.
(defvar calc-num-units)
(defvar calc-den-units)
(defun calc-explain-units ()
(interactive)
(calc-wrapper
(let ((calc-num-units nil)
(calc-den-units nil))
(calc-explain-units-rec (calc-top-n 1) 1)
(and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
(setq calc-den-units (concat "(" calc-den-units ")")))
(if calc-num-units
(if calc-den-units
(message "%s per %s" calc-num-units calc-den-units)
(message "%s" calc-num-units))
(if calc-den-units
(message "1 per %s" calc-den-units)
(message "No units in expression"))))))
(defun calc-explain-units-rec (expr pow)
(let ((u (math-check-unit-name expr))
pos)
(if (and u (not (math-zerop pow)))
(let ((name (or (nth 2 u) (symbol-name (car u)))))
(if (eq (aref name 0) ?\*)
(setq name (substring name 1)))
(if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
(if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" 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-Zα-ωΑ-Ω0-9']" 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 calc-num-units (if calc-num-units
(concat calc-num-units " " name)
name))
(setq calc-den-units (if calc-den-units
(concat calc-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 "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
(defun calc-define-unit (uname desc &optional disp)
(interactive "SDefine unit name: \nsDescription: \nP")
(if disp (setq disp (read-string "Display definition: ")))
(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 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))
(if disp
(setcar (cdr (cdr (cdr (cdr unit)))) disp))))
(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
(with-current-buffer buf
(save-excursion
(goto-char (point-min))
(if (looking-at "Calculator Units Table")
(let ((inhibit-read-only t))
(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
(let (expr)
(insert "(setq math-additional-units '(\n")
(dolist (u math-additional-units)
(insert " (" (symbol-name (car u)) " "
(if (setq expr (nth 1 u))
(if (stringp expr)
(prin1-to-string expr)
(prin1-to-string (math-format-flat-expr expr 0)))
"nil")
" "
(prin1-to-string (nth 2 u))
")\n"))
(insert "))\n"))
(insert ";;; (no custom units defined)\n"))
(insert ";;; End of custom units\n")
(save-buffer))))
;; The variable math-cu-unit-list is local to math-build-units-table,
;; but is used by math-compare-unit-names, which is called (indirectly)
;; by math-build-units-table.
;; math-cu-unit-list is also local to math-convert-units, but is used
;; by math-convert-units-rec, which is called by math-convert-units.
(defvar math-cu-unit-list)
(defun math-build-units-table ()
(or math-units-table
(let* ((combined-units (append math-additional-units
math-standard-units))
(math-cu-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)))
(nth 4 x))))
combined-units))
(let ((math-units-table tab))
(mapc #'math-find-base-units tab))
(message "Building units table...done")
(setq math-units-table tab))))
;; The variables math-fbu-base and math-fbu-entry are local to
;; math-find-base-units, but are used by math-find-base-units-rec,
;; which is called by math-find-base-units.
(defvar math-fbu-base)
(defvar math-fbu-entry)
(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 (math-fbu-base
(math-fbu-entry entry))
(setcar (nthcdr 4 entry) 'boom)
(math-find-base-units-rec (nth 1 entry) 1)
'(or math-fbu-base
(error "Dimensionless definition for unit %s" (car entry)))
(while (eq (cdr (car math-fbu-base)) 0)
(setq math-fbu-base (cdr math-fbu-base)))
(let ((b math-fbu-base))
(while (cdr b)
(if (eq (cdr (car (cdr b))) 0)
(setcdr b (cdr (cdr b)))
(setq b (cdr b)))))
(setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
(setcar (nthcdr 4 entry) math-fbu-base)
math-fbu-base)))
(defun math-compare-unit-names (a b)
(memq (car b) (cdr (memq (car a) math-cu-unit-list))))
(defun math-find-base-units-rec (expr pow)
(let ((u (math-check-unit-name expr)))
(cond (u
(dolist (x (math-find-base-units u))
(let ((p (* (cdr x) pow))
(old (assq (car x) math-fbu-base)))
(if old
(setcdr old (+ (cdr old) p))
(setq math-fbu-base
(cons (cons (car x) p) math-fbu-base))))))
((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 math-fbu-entry))))
((equal expr '(calcFunc-ln 10)))
(t (error "Malformed defining expression for unit %s"
(car math-fbu-entry))))))
(defun math-units-in-expr-p (expr sub-exprs)
(and (consp expr)
(if (eq (car expr) 'var)
(math-check-unit-name expr)
(if (eq (car expr) 'neg)
(math-units-in-expr-p (nth 1 expr) sub-exprs)
(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) 'neg)
(math-single-units-in-expr-p (nth 1 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-consistent-units-p (expr newunits)
"Non-nil if EXPR and NEWUNITS have consistent units."
(or
(and (eq (car-safe newunits) 'var)
(assq (nth 1 newunits) math-standard-units-systems))
(math-numberp (math-get-units (math-to-standard-units (list '/ expr newunits) nil)))))
(defun math-check-unit-consistency (expr units)
"Give an error if EXPR and UNITS do not have consistent units."
(unless (math-consistent-units-p expr units)
(error "New units (%s) are inconsistent with current units (%s)"
(math-format-value units)