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;;; calc-units.el --- unit conversion functions for Calc
;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
;; Author: David Gillespie <>
;; Maintainer: Jay Belanger <>
;; 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
;; 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 <>.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(require 'calc-alg))
;;; Units operations.
;;; Units table last updated 9-Jan-91 by Ulrich Mueller (
;;; with some additions by Przemek Klosowski (
;;; Updated April 2002 by Jochen Küpper
;;; Updated August 2007, using
;;; CODATA (
;;; NIST (
;;; ESUWM (Encyclopaedia of Scientific Units, Weights and
;;; Measures, by François Cardarelli)
;;; All conversions are exact unless otherwise noted.
(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 (
( 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
( 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" ) ;;; CODATA
;; 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 "1.660538782*10^(-27) kg" "Unified atomic mass" nil
"1.660538782 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 "1.602176487*10^(-19) C" "Elementary charge" nil
"1.602176487 10^-19 C (*)") ;;(approx) CODATA
( 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
;; The values are from CODATA, and are approximate.
( h "6.62606896*10^(-34) J s" "*Planck's constant" nil
"6.62606896 10^-34 J s (*)")
( hbar "h / (2 pi)" "Planck's constant" ) ;; Exact
( mu0 "4 pi 10^(-7) H/m" "Permeability of vacuum") ;; Exact
( μ0 "mu0" "Permeability of vacuum") ;; Exact
( eps0 "1 / (mu0 c^2)" "Permittivity of vacuum" )
( ε0 "eps0" "Permittivity of vacuum" )
( G "6.67428*10^(-11) m^3/(kg s^2)" "Gravitational constant" nil
"6.67428 10^-11 m^3/(kg s^2) (*)")
( Nav "6.02214179*10^(23) / mol" "Avogadro's constant" nil
"6.02214179 10^23 / mol (*)")
( me "9.10938215*10^(-31) kg" "Electron rest mass" nil
"9.10938215 10^-31 kg (*)")
( mp "1.672621637*10^(-27) kg" "Proton rest mass" nil
"1.672621637 10^-27 kg (*)")
( mn "1.674927211*10^(-27) kg" "Neutron rest mass" nil
"1.674927211 10^-27 kg (*)")
( mmu "1.88353130*10^(-28) kg" "Muon rest mass" nil
"1.88353130 10^-28 kg (*)")
( mμ "mmu" "Muon rest mass" nil
"1.88353130 10^-28 kg (*)")
( Ryd "10973731.568527 /m" "Rydberg's constant" nil
"10973731.568527 /m (*)")
( k "1.3806504*10^(-23) J/K" "Boltzmann's constant" nil
"1.3806504 10^-23 J/K (*)")
( alpha "7.2973525376*10^(-3)" "Fine structure constant" nil
"7.2973525376 10^-3 (*)")
( α "alpha" "Fine structure constant" nil
"7.2973525376 10^-3 (*)")
( muB "927.400915*10^(-26) J/T" "Bohr magneton" nil
"927.400915 10^-26 J/T (*)")
( muN "5.05078324*10^(-27) J/T" "Nuclear magneton" nil
"5.05078324 10^-27 J/T (*)")
( mue "-928.476377*10^(-26) J/T" "Electron magnetic moment" nil
"-928.476377 10^-26 J/T (*)")
( mup "1.410606662*10^(-26) J/T" "Proton magnetic moment" nil
"1.410606662 10^-26 J/T (*)")
( R0 "8.314472 J/(mol K)" "Molar gas constant" nil
"8.314472 J/(mol K) (*)")
( V0 "22.710981*10^(-3) m^3/mol" "Standard volume of ideal gas" nil
"22.710981 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'.
(defvar math-units-table-buffer-valid nil)
;;; Units commands.
(defun calc-base-units ()
(let ((calc-autorange-units nil))
(calc-enter-result 1 "bsun" (math-simplify-units
(math-to-standard-units (calc-top-n 1)
(defvar calc-ensure-consistent-units)
(defun calc-quick-units ()
(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)
(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-mul expr (nth pos units))))))))
(defun math-get-standard-units (expr)
"Return the standard units in EXPR."
(math-to-standard-units expr nil))))
(defun math-get-units (expr)
"Return the units in EXPR."
(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)))
" / " "/"
(if (stringp 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
(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
(comp (math-simplify-units expr))
(std expr)
(t new-units))))
(default-units (gethash standard-units math-default-units-table)))
(unless (eq standard-units 1)
((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))
(defvar calc-allow-units-as-numbers t)
(defun calc-convert-units (&optional old-units new-units)
(let ((expr (calc-top-n 1))
(uoldname nil)
(unitscancel nil)
(nouold nil)
(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))
(eq (math-get-standard-units expr) 1))))
(let ((uold (or old-units
(setq uoldname
(if unitscancel
"(The expression is unitless when simplified) Old Units: ")
(read-string "Old units: ")))
(if (equal uoldname "")
(setq nouold unitscancel)
(setq uoldname "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))))
(setq defunits (math-get-default-units expr))
(unless new-units
(setq new-units
(read-string (concat
(if (and uoldname (not nouold))
(concat "Old units: "
", new units")
"New units")
(if defunits
" (default "
"): ")
": "))))
(if (and
(string= new-units "")
(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"))))
(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-autorange-units (arg)
(interactive "P")
(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)
(let ((expr (calc-top-n 1))
(uold nil)
(uoldname nil)
(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-"
(car units)))))
(error "Not a pure temperature expression"))
(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 defunits (math-get-default-units expr))
(setq unew (or new-units
(if uoldname
(concat "Old temperature units: "
", new units")
"New temperature units")
(if defunits
(concat " (default "
"): ")
": ")))))
(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-convert-temperature expr uold unew
(if (Math-zerop ntemp)
(setq ntemp (list '* ntemp unew)))
(let ((calc-simplify-mode 'none))
(calc-enter-result 1 "cvtm" ntemp))))))
(defun calc-remove-units ()
(calc-enter-result 1 "rmun" (math-simplify-units
(math-remove-units (calc-top-n 1))))))
(defun calc-extract-units ()
(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 ()
(let ((calc-num-units nil)
(calc-den-units nil))
(calc-explain-units-rec (calc-top-n 1) 1)
(and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
(setq calc-den-units (concat "(" calc-den-units ")")))
(if calc-num-units
(if calc-den-units
(message "%s per %s" calc-num-units calc-den-units)
(message "%s" calc-num-units))
(if calc-den-units
(message "1 per %s" calc-den-units)
(message "No units in expression"))))))
(defun calc-explain-units-rec (expr pow)
(let ((u (math-check-unit-name expr))
(if (and u (not (math-zerop pow)))
(let ((name (or (nth 2 u) (symbol-name (car u)))))
(if (eq (aref name 0) ?\*)
(setq name (substring name 1)))
(if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
(if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" 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)
(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"))))
(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)
(setq calc-den-units (if calc-den-units
(concat calc-den-units " " 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 ()
(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
(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: ")))
(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-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 ""))
(if disp
(setcar (cdr (cdr (cdr (cdr unit)))) disp))))
(defun calc-undefine-unit (uname)
(interactive "SUndefine unit name: ")
(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)))
(defun calc-invalidate-units-table ()
(setq math-units-table nil)
(let ((buf (get-buffer "*Units Table*")))
(and buf
(with-current-buffer buf
(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: ")
(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)
(calc-enter-result 0 "ugdf" (nth 1 unit))
(message "Derived unit: %s" msg))
(calc-enter-result 0 "ugdf" (list 'var uname
(concat "var-"
(symbol-name uname)))))
(message "Base unit: %s" msg))))))
(defun calc-permanent-units ()
(let (pos)
(set-buffer (find-file-noselect (substitute-in-file-name
(goto-char (point-min))
(if (and (search-forward ";;; Custom units stored by Calc" nil t)
(setq pos (point))
(search-forward "\n;;; End of custom units" nil t)))
(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
(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)))
" "
(prin1-to-string (nth 2 (car list)))
(setq list (cdr list))))
(insert "))\n"))
(insert ";;; (no custom units defined)\n"))
(insert ";;; End of custom units\n")
;; 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-cu-unit-list (mapcar 'car combined-units))
(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))
(nth 1 x)))
(nth 2 x)
(nth 3 x)
(and (not (nth 1 x))
(list (cons (car x) 1)))
(nth 4 x))))
(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 (math-fbu-entry)
(if (eq (nth 4 math-fbu-entry) 'boom)
(error "Circular definition involving unit %s" (car math-fbu-entry)))
(or (nth 4 math-fbu-entry)
(let (math-fbu-base)
(setcar (nthcdr 4 math-fbu-entry) 'boom)
(math-find-base-units-rec (nth 1 math-fbu-entry) 1)
'(or math-fbu-base
(error "Dimensionless definition for unit %s" (car math-fbu-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 math-fbu-entry) 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
(let ((ulist (math-find-base-units u)))
(while ulist
(let ((p (* (cdr (car ulist)) pow))
(old (assq (car (car ulist)) math-fbu-base)))
(if old
(setcdr old (+ (cdr old) p))
(setq math-fbu-base
(cons (cons (car (car ulist)) p) math-fbu-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 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)
((eq (car expr) '/)
(if (math-units-in-expr-p (nth 2 expr) nil)
(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."
(and (eq (car-safe newunits) 'var)
(assq (nth 1 newunits) math-standard-units-systems))
(math-numberp (math-get-units (list '/ expr newunits)))))
(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)
(math-format-value (math-get-units expr)))))
(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))
;; The variable math-which-standard is local to math-to-standard-units,
;; but is used by math-to-standard-rec, which is called by
;; math-to-standard-units.
(defvar math-which-standard)
(defun math-to-standard-units (expr math-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
(if (nth 1 u)
(setq expr (math-to-standard-rec (nth 1 u)))
(let ((st (assq (car u) math-which-standard)))
(if st
(setq expr (nth 1 st))
(setq expr (list 'var (car u)
(intern (concat "var-"
(car u)))))))))
(or (null u)
(eq base (car u))
(setq expr (list '*
(nth 1 (assq (aref (symbol-name base) 0)
(if (eq base 'pi)
(if (or
(Math-primp expr)
(and (eq (car-safe expr) 'calcFunc-subscr)
(eq (car-safe (nth 1 expr)) 'var)))
(cons (car expr)
(mapcar 'math-to-standard-rec (cdr expr))))))
(defun math-apply-units (expr units ulist &optional pure)
(setq expr (math-simplify-units expr))
(if ulist
(let ((new 0)
(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)))))
(if pure
(math-simplify-units (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))
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
(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))
;; The variable math-fcu-u is local to math-find-compatible-unit,
;; but is used by math-find-compatible-rec which is called by
;; math-find-compatible-unit.
(defvar math-fcu-u)
(defun math-find-compatible-unit (expr unit)
(let ((math-fcu-u (math-check-unit-name unit)))
(if math-fcu-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))))
((eq (car-safe expr) 'neg)
(math-find-compatible-unit-rec (nth 1 expr) pow))
((and (eq (car-safe expr) '^)
(integerp (nth 2 expr)))
(math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
(let ((u2 (math-check-unit-name expr)))
(if (equal (nth 4 math-fcu-u) (nth 4 u2))
(cons expr pow))))))
;; The variables math-cu-new-units and math-cu-pure are local to
;; math-convert-units, but are used by math-convert-units-rec,
;; which is called by math-convert-units.
(defvar math-cu-new-units)
(defvar math-cu-pure)
(defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
(if (eq (car-safe math-cu-new-units) 'var)
(let ((unew (assq (nth 1 math-cu-new-units)
(if (eq (car-safe (nth 1 unew)) '+)
(setq math-cu-new-units (nth 1 unew)))))
(math-with-extra-prec 2
(let ((compat (and (not math-cu-pure)
(math-find-compatible-unit expr math-cu-new-units)))
(math-cu-unit-list nil)
(math-combining-units nil))
(if compat
(math-mul (math-mul (math-simplify-units
(math-div expr (math-pow (car compat)
(cdr compat))))
(math-pow math-cu-new-units (cdr compat)))
(math-pow (math-div (car compat) math-cu-new-units)
(cdr compat))
(when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
(setq math-cu-new-units (nth 2 (car math-cu-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 math-cu-new-units) nil)
math-cu-new-units math-cu-unit-list math-cu-pure))))))
(defun math-convert-units-rec (expr)
(if (math-units-in-expr-p expr nil)
(math-apply-units (math-to-standard-units
(list '/ expr math-cu-new-units) nil)
math-cu-new-units math-cu-unit-list math-cu-pure)
(if (Math-primp 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"))
(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 '(/ 27315 100)))
(if (eq (nth 3 unew) 'F)
(setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
((eq (nth 3 uold) 'C)
(if (eq (nth 3 unew) 'F)
(setq expr (list '+ (list '* expr '(/ 9 5)) 32))
(setq expr (list '+ expr '(/ 27315 100)))))
(setq expr (list '* (list '- expr 32) '(/ 5 9)))
(if (eq (nth 3 unew) 'K)
(setq expr (list '+ expr '(/ 27315 100)))))))
(if pure
(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)
;; The function created by math-defsimplify uses the variable
;; math-simplify-expr, and so is used by functions in math-defsimplify
(defvar math-simplify-expr)
(math-defsimplify (+ -)
(and math-simplifying-units
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
(let* ((units (math-extract-units (nth 1 math-simplify-expr)))
(ratio (math-simplify (math-to-standard-units
(list '/ (nth 2 math-simplify-expr) units) nil))))
(if (math-units-in-expr-p ratio nil)
(calc-record-why "*Inconsistent units" math-simplify-expr)
(list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
(if (eq (car math-simplify-expr) '-)
(math-neg ratio) ratio))
(math-defsimplify *
(defun math-simplify-units-prod ()
(and math-simplifying-units
(Math-realp (nth 1 math-simplify-expr))
(let* ((num (math-float (nth 1 math-simplify-expr)))
(xpon (calcFunc-xpon num))
(unitp (cdr (cdr math-simplify-expr)))
(unit (car unitp))
(pow (if (eq (car math-simplify-expr) '*) 1 -1))
(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)
(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)
(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)))
(setq pname (math-build-var-name
(if (eq (car (car p)) 0)
(car u)
(concat (char-to-string
(car (car p)))
(car u))))))
(and (/= (car (car p)) 0)
(assq (nth 1 pname)
(setq p (cdr p)))
(and p
(/= pxpon uxpon)
(or (not (eq p pref))
(< xpon (+ pxpon (* (math-abs pow) 3))))
(setcar (cdr math-simplify-expr)
(let ((calc-prefer-frac nil))
(calcFunc-scf (nth 1 math-simplify-expr)
(- uxpon pxpon))))
(setcar unitp pname)
(defvar math-try-cancel-units)
(math-defsimplify /
(and math-simplifying-units
(let ((np (cdr math-simplify-expr))
(math-try-cancel-units 0)
n nn)
(setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
(cdr (nth 2 math-simplify-expr))
(nthcdr 2 math-simplify-expr)))
(if (math-realp (car n))
(setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-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 math-simplify-expr)))
(setq np (cdr (cdr n))))
(math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
(if (eq math-try-cancel-units 0)
(let* ((math-simplifying-units nil)
(base (math-simplify
(math-to-standard-units math-simplify-expr nil))))
(if (Math-numberp base)
(setq math-simplify-expr base))))
(if (eq (car-safe math-simplify-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))
(if (eq pow1 1)
(math-to-standard-units (list '/ n d) nil)
(list '^ (math-to-standard-units (list '/ n d) nil) pow1))
(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 math-try-cancel-units
(+ math-try-cancel-units
(- (* (cdr (car un)) pow1)
(* (cdr (car ud)) pow2)))))
(setq ud1 (cdr ud1)))
(setq un (cdr un)))
(math-defsimplify ^
(and math-simplifying-units
(math-realp (nth 2 math-simplify-expr))
(if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
(list (car (nth 1 math-simplify-expr))
(list '^ (nth 1 (nth 1 math-simplify-expr))
(nth 2 math-simplify-expr))
(list '^ (nth 2 (nth 1 math-simplify-expr))
(nth 2 math-simplify-expr)))
(math-simplify-units-pow (nth 1 math-simplify-expr)
(nth 2 math-simplify-expr)))))
(math-defsimplify calcFunc-sqrt
(and math-simplifying-units
(if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
(list (car (nth 1 math-simplify-expr))
(list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
(list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
(math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
(math-defsimplify (calcFunc-floor
(and math-simplifying-units
(= (length math-simplify-expr) 2)
(if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
(nth 1 math-simplify-expr)
(if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
(or (math-only-units-in-expr-p
(nth 1 (nth 1 math-simplify-expr)))
(nth 2 (nth 1 math-simplify-expr)))))
(list (car (nth 1 math-simplify-expr))
(cons (car math-simplify-expr)
(cons (nth 1 (nth 1 math-simplify-expr))
(cdr (cdr math-simplify-expr))))
(cons (car math-simplify-expr)
(cons (nth 2 (nth 1 math-simplify-expr))
(cdr (cdr math-simplify-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 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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))))))
(math-defsimplify calcFunc-sec
(and math-simplifying-units
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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-sec (nth 1 rad))))))
(math-defsimplify calcFunc-csc
(and math-simplifying-units
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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-csc (nth 1 rad))))))
(math-defsimplify calcFunc-cot
(and math-simplifying-units
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
(let ((rad (math-simplify-units
(math-to-standard-units (nth 1 math-simplify-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-cot (nth 1 rad))))))
(defun math-remove-units (expr)
(if (math-check-unit-name expr)
(if (Math-primp expr)
(cons (car expr)
(mapcar 'math-remove-units (cdr expr))))))
(defun math-extract-units (expr)
((memq (car-safe expr) '(* /))
(cons (car expr)
(mapcar 'math-extract-units (cdr expr))))
((eq (car-safe expr) 'neg)
(math-extract-units (nth 1 expr)))
((eq (car-safe expr) '^)
(list '^ (math-extract-units (nth 1 expr)) (nth 2 expr)))
((math-check-unit-name expr) expr)
(t 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-twos-complement-mode nil)
(calc-point-char ".")
(std nil)
u name shadowed)
(message "Formatting units table...")
(set-buffer buf)
(let ((inhibit-read-only t))
(insert "Calculator Units Table:\n\n")
(insert "(All definitions are exact unless marked with an asterisk (*).)\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)
(indent-to 10)
(insert (symbol-name (nth 3 u))))
(or std
(indent-to 10)
(insert "U"))))
(indent-to 14)
(and shadowed (insert "("))
(if (nth 5 u)
(insert (nth 5 u))
(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\n")
(insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
"names will not use the `tex' prefix; the unit name for a\n"
"TeX point will be `pt' instead of `texpt', for example.\n"
"To avoid conflicts, the unit names for pint and parsec will\n"
"be `pint' and `parsec' instead of `pt' and `pc'."))
(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*")))))
;;; Logarithmic units functions
(defvar math-logunits '((var dB var-dB)
(var Np var-Np)))
(defun math-conditional-apply (fn &rest args)
"Evaluate f(args) unless in symbolic mode.
In symbolic mode, return the list (fn args)."
(if calc-symbolic-mode
(cons fn args)
(apply fn args)))
(defun math-conditional-pow (a b)
"Evaluate a^b unless in symbolic mode.
In symbolic mode, return the list (^ a b)."
(if calc-symbolic-mode
(list '^ a b)
(math-pow a b)))
(defun math-extract-logunits (expr)
(if (memq (car-safe expr) '(* /))
(cons (car expr)
(mapcar 'math-extract-logunits (cdr expr)))
(if (memq (car-safe expr) '(^))
(list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
(if (member expr math-logunits) expr 1))))
(defun math-logunits-add (a b neg power)
(let ((aunit (math-simplify (math-extract-logunits a))))
(if (not (eq (car-safe aunit) 'var))
(calc-record-why "*Improper logarithmic unit" aunit)
(let* ((units (math-extract-units a))
(acoeff (math-simplify (math-remove-units a)))
(bcoeff (math-simplify (math-to-standard-units
(list '/ b units) nil))))
(if (math-units-in-expr-p bcoeff nil)
(calc-record-why "*Inconsistent units" nil)
(if (and neg
(or (math-lessp acoeff bcoeff)
(math-equal acoeff bcoeff)))
(calc-record-why "*Improper coefficients" nil)
(if (equal aunit '(var dB var-dB))
(let ((coef (if power 10 20)))
(math-mul coef
(math-conditional-apply 'calcFunc-log10
(if neg
(math-conditional-pow 10 (math-div acoeff coef))
(math-conditional-pow 10 (math-div bcoeff coef)))
(math-conditional-pow 10 (math-div acoeff coef))
(math-conditional-pow 10 (math-div bcoeff coef)))))))
(let ((coef (if power 2 1)))
(math-conditional-apply 'calcFunc-ln
(if neg
(math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
(math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
(math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
(math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
(defun calcFunc-lufadd (a b)
(math-logunits-add a b nil nil))
(defun calcFunc-lupadd (a b)
(math-logunits-add a b nil t))
(defun calcFunc-lufsub (a b)
(math-logunits-add a b t nil))
(defun calcFunc-lupsub (a b)
(math-logunits-add a b t t))
(defun calc-lu-plus (arg)
(interactive "P")
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
(calc-binary-op "lu-" 'calcFunc-lufsub arg)
(calc-binary-op "lu-" 'calcFunc-lupsub arg))
(if (calc-is-hyperbolic)
(calc-binary-op "lu+" 'calcFunc-lufadd arg)
(calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
(defun calc-lu-minus (arg)
(interactive "P")
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
(calc-binary-op "lu+" 'calcFunc-lufadd arg)
(calc-binary-op "lu+" 'calcFunc-lupadd arg))
(if (calc-is-hyperbolic)
(calc-binary-op "lu-" 'calcFunc-lufsub arg)
(calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
(defun math-logunits-mul (a b power)
(let (logunit coef units number)
(setq logunit (math-simplify (math-extract-logunits a)))
(eq (car-safe logunit) 'var)
(eq (math-simplify (math-extract-units b)) 1))
(setq coef (math-simplify (math-remove-units a))
units (math-extract-units a)
number b))
(setq logunit (math-simplify (math-extract-logunits b)))
(eq (car-safe logunit) 'var)
(eq (math-simplify (math-extract-units a)) 1))
(setq coef (math-simplify (math-remove-units b))
units (math-extract-units b)
number a))
(t (setq logunit nil)))
(if logunit
((equal logunit '(var dB var-dB))
(math-mul (if power 10 20)
(math-conditional-apply 'calcFunc-log10 number)))
(math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
(calc-record-why "*Improper units" nil))))
(defun math-logunits-divide (a b power)
(let ((logunit (math-simplify (math-extract-logunits a))))
(if (not (eq (car-safe logunit) 'var))
(calc-record-why "*Improper logarithmic unit" logunit)
(if (math-units-in-expr-p b nil)
(calc-record-why "*Improper units quantity" b)
(let* ((units (math-extract-units a))
(coef (math-simplify (math-remove-units a))))
((equal logunit '(var dB var-dB))
(math-mul (if power 10 20)
(math-conditional-apply 'calcFunc-log10 b)))
(math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
(defun calcFunc-lufmul (a b)
(math-logunits-mul a b nil))
(defun calcFunc-lupmul (a b)
(math-logunits-mul a b t))
(defun calc-lu-times (arg)
(interactive "P")
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
(calc-binary-op "lu/" 'calcFunc-lufdiv arg)
(calc-binary-op "lu/" 'calcFunc-lupdiv arg))
(if (calc-is-hyperbolic)
(calc-binary-op "lu*" 'calcFunc-lufmul arg)
(calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
(defun calcFunc-lufdiv (a b)
(math-logunits-divide a b nil))
(defun calcFunc-lupdiv (a b)
(math-logunits-divide a b t))
(defun calc-lu-divide (arg)
(interactive "P")
(if (calc-is-inverse)
(if (calc-is-hyperbolic)
(calc-binary-op "lu*" 'calcFunc-lufmul arg)
(calc-binary-op "lu*" 'calcFunc-lupmul arg))
(if (calc-is-hyperbolic)
(calc-binary-op "lu/" 'calcFunc-lufdiv arg)
(calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
(defun math-logunits-quant (val ref power)
(let* ((units (math-simplify (math-extract-units val)))
(lunit (math-simplify (math-extract-logunits units))))
(if (not (eq (car-safe lunit) 'var))
(calc-record-why "*Improper logarithmic unit" lunit)
(let ((runits (math-simplify (math-div units lunit)))
(coeff (math-simplify (math-div val units))))
(if (equal lunit '(var dB var-dB))
(if power 10 20))))
(math-conditional-apply 'calcFunc-exp
(if power
(math-mul 2 coeff)
(defvar calc-lu-field-reference)
(defvar calc-lu-power-reference)
(defun calcFunc-lufquant (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-quant val ref nil))
(defun calcFunc-lupquant (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-quant val ref t))
(defun calc-lu-quant (arg)
(interactive "P")
(if (calc-is-hyperbolic)
(if (calc-is-option)
(calc-binary-op "lupq" 'calcFunc-lufquant arg)
(calc-unary-op "lupq" 'calcFunc-lufquant arg))
(if (calc-is-option)
(calc-binary-op "lufq" 'calcFunc-lupquant arg)
(calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
(defun math-logunits-level (val ref db power)
"Compute the value of VAL in decibels or nepers."
(let* ((ratio (math-simplify-units (math-div val ref)))
(ratiou (math-simplify-units (math-remove-units ratio)))
(units (math-simplify (math-extract-units ratio))))
(if db
(math-mul (if power 10 20)
(math-conditional-apply 'calcFunc-log10 ratiou))
'(var dB var-dB))
(math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
'(var Np var-Np)))
(defun calcFunc-dbfield (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-level val ref t nil))
(defun calcFunc-dbpower (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-level val ref t t))
(defun calcFunc-npfield (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-field-reference)))
(math-logunits-level val ref nil nil))
(defun calcFunc-nppower (val &optional ref)
(unless ref
(setq ref (math-read-expr calc-lu-power-reference)))
(math-logunits-level val ref nil t))
(defun calc-db (arg)
(interactive "P")
(if (calc-is-hyperbolic)
(if (calc-is-option)
(calc-binary-op "ludb" 'calcFunc-dbfield arg)
(calc-unary-op "ludb" 'calcFunc-dbfield arg))
(if (calc-is-option)
(calc-binary-op "ludb" 'calcFunc-dbpower arg)
(calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
(defun calc-np (arg)
(interactive "P")
(if (calc-is-hyperbolic)
(if (calc-is-option)
(calc-binary-op "lunp" 'calcFunc-npfield arg)
(calc-unary-op "lunp" 'calcFunc-npfield arg))
(if (calc-is-option)
(calc-binary-op "lunp" 'calcFunc-nppower arg)
(calc-unary-op "lunp" 'calcFunc-nppower arg)))))
;;; Musical notes
(defvar calc-note-threshold)
(defun math-midi-round (num)
"Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
(let* ((n (math-round num))
(diff (math-abs
(math-sub num n))))
(if (< (math-compare diff
(math-div (math-read-expr calc-note-threshold) 100)) 0)
(defconst math-notes
'(((var C var-C) . 0)
((var Csharp var-Csharp) . 1)
; ((var C♯ var-C♯) . 1)
((var Dflat var-Dflat) . 1)
; ((var D♭ var-D♭) . 1)
((var D var-D) . 2)
((var Dsharp var-Dsharp) . 3)
; ((var D♯ var-D♯) . 3)
((var E var-E) . 4)
((var F var-F) . 5)
((var Fsharp var-Fsharp) . 6)
; ((var F♯ var-F♯) . 6)
((var Gflat var-Gflat) . 6)
; ((var G♭ var-G♭) . 6)
((var G var-G) . 7)
((var Gsharp var-Gsharp) . 8)
; ((var G♯ var-G♯) . 8)
((var A var-A) . 9)
((var Asharp var-Asharp) . 10)
; ((var A♯ var-A♯) . 10)
((var Bflat var-Bflat) . 10)
; ((var B♭ var-B♭) . 10)
((var B var-B) . 11))
"An alist of notes with their number of semitones above C.")
(defun math-freqp (freq)
"Non-nil if FREQ is a positive number times the unit Hz.
If non-nil, return the coefficient of Hz."
(let ((freqcoef (math-simplify-units
(math-div freq '(var Hz var-Hz)))))
(if (Math-posp freqcoef) freqcoef)))
(defun math-midip (num)
"Non-nil if NUM is a possible MIDI note number.
If non-nil, return NUM."
(if (Math-numberp num) num))
(defun math-spnp (spn)
"Non-nil if NUM is a scientific pitch note (note + cents).
If non-nil, return a list consisting of the note and the cents coefficient."
(let (note cents rnote rcents)
(if (eq (car-safe spn) '+)
(setq note (nth 1 spn)
cents (nth 2 spn))
(setq note spn
cents nil))
((and ;; NOTE is a note, CENTS is nil or cents.
(eq (car-safe note) 'calcFunc-subscr)
(assoc (nth 1 note) math-notes)
(integerp (nth 2 note))
(setq rnote note)
(not cents)
(Math-numberp (setq rcents
(math-div cents '(var cents var-cents)))))))
(list rnote rcents))
((and ;; CENTS is a note, NOTE is cents.
(eq (car-safe cents) 'calcFunc-subscr)
(assoc (nth 1 cents) math-notes)
(integerp (nth 2 cents))
(setq rnote cents)
(not note)
(Math-numberp (setq rcents
(math-div note '(var cents var-cents)))))))
(list rnote rcents)))))
(defun math-freq-to-midi (freq)
"Return the midi note number corresponding to FREQ Hz."
(let ((midi (math-add
(math-div freq 440)
(math-midi-round midi)))
(defun math-spn-to-midi (spn)
"Return the MIDI number corresponding to SPN."
(let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
(octave (math-add (nth 2 (car spn)) 1))
(cents (nth 1 spn))
(midi (math-add
(math-mul 12 octave)
(if cents
(math-add midi (math-div cents 100))
(defun math-midi-to-spn (midi)
"Return the scientific pitch notation corresponding to midi number MIDI."
(let (midin cents)
(if (math-integerp midi)
(setq midin midi
cents nil)
(setq midin (math-floor midi)
cents (math-mul 100 (math-sub midi midin))))
(let* ((nr ;; This should be (math-idivmod midin 12), but with
;; better behavior for negative midin.
(if (Math-negp midin)
(let ((dm (math-idivmod (math-neg midin) 12)))
(if (= (cdr dm) 0)
(cons (math-neg (car dm)) 0)
(math-sub (math-neg (car dm)) 1)
(math-sub 12 (cdr dm)))))
(math-idivmod midin 12)))
(n (math-sub (car nr) 1))
(note (car (rassoc (cdr nr) math-notes))))
(if cents
(list '+ (list 'calcFunc-subscr note n)
(list '* cents '(var cents var-cents)))
(list 'calcFunc-subscr note n)))))
(defun math-freq-to-spn (freq)
"Return the scientific pitch notation corresponding to FREQ Hz."
(math-with-extra-prec 3
(math-midi-to-spn (math-freq-to-midi freq))))
(defun math-midi-to-freq (midi)
"Return the frequency of the note with midi number MIDI."
(list '*
'(var Hz var-Hz)))
(defun math-spn-to-freq (spn)
"Return the frequency of the note with scientific pitch notation SPN."
(math-midi-to-freq (math-spn-to-midi spn)))
(defun calcFunc-spn (expr)
"Return EXPR written as scientific pitch notation + cents."
;; Get the coefficient of Hz
(let (note)
((setq note (math-freqp expr))
(math-freq-to-spn note))
((setq note (math-midip expr))
(math-midi-to-spn note))
((math-spnp expr)
(math-reject-arg expr "*Improper expression")))))
(defun calcFunc-midi (expr)
"Return EXPR written as a MIDI number."
(let (note)
((setq note (math-freqp expr))
(math-freq-to-midi note))
((setq note (math-spnp expr))
(math-spn-to-midi note))
((math-midip expr)
(math-reject-arg expr "*Improper expression")))))
(defun calcFunc-freq (expr)
"Return the frequency corresponding to EXPR."
(let (note)
((setq note (math-midip expr))
(math-midi-to-freq note))
((setq note (math-spnp expr))
(math-spn-to-freq note))
((math-freqp expr)
(math-reject-arg expr "*Improper expression")))))
(defun calc-freq (arg)
"Return the frequency corresponding to the expression on the stack."
(interactive "P")
(calc-unary-op "freq" 'calcFunc-freq arg)))
(defun calc-midi (arg)
"Return the MIDI number corresponding to the expression on the stack."
(interactive "P")
(calc-unary-op "midi" 'calcFunc-midi arg)))
(defun calc-spn (arg)
"Return the scientific pitch notation corresponding to the expression on the stack."
(interactive "P")
(calc-unary-op "spn" 'calcFunc-spn arg)))
(provide 'calc-units)
;; Local variables:
;; coding: utf-8
;; End:
;;; calc-units.el ends here
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