;;; calc-units.el --- unit conversion functions for Calc -*- lexical-binding:t -*- ;; Copyright (C) 1990-1993, 2001-2021 Free Software Foundation, Inc. ;; Author: David Gillespie ;; 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 . ;;; 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 (ulm@vsnhd1.cern.ch) ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov) ;;; Updated April 2002 by Jochen Küpper ;;; Updated August 2007, using ;;; CODATA (https://physics.nist.gov/cuu/Constants/index.html) ;;; NIST (https://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 ;; https://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 (https://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))) (string-replace " / " "/" (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 (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) (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)) math-units-table)))))))) ;; 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 which-standard) (let ((math-which-standard 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) math-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 (or (Math-primp expr) (and (eq (car-safe expr) 'calcFunc-subscr) (eq (car-safe (nth 1 expr)) 'var))) expr (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) value) (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 expr (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)) (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 (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))) ;; 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)))) (t (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 new-units &optional pure) (if (eq (car-safe new-units) 'var) (let ((unew (assq (nth 1 new-units) (math-build-units-table)))) (if (eq (car-safe (nth 1 unew)) '+) (setq new-units (nth 1 unew))))) (math-with-extra-prec 2 (let ((compat (and (not pure) (math-find-compatible-unit expr new-units))) (math-cu-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 math-cu-unit-list (math-decompose-units new-units)) (setq 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) (let ((math-cu-new-units new-units) (math-cu-pure pure)) (math-convert-units-rec expr)) (math-apply-units (math-to-standard-units (list '/ expr new-units) nil) new-units math-cu-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 math-cu-new-units) nil) math-cu-new-units math-cu-unit-list math-cu-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 '(/ 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))))) (t (setq expr (list '* (list '- expr 32) '(/ 5 9))) (if (eq (nth 3 unew) 'K) (setq expr (list '+ expr '(/ 27315 100))))))) (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) ;; The function created by math-defsimplify uses the variable `expr'. (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 expr)) (defun math-simplify-units-prod (expr) (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))))))) (defvar math-try-cancel-units) (math-defsimplify / (and math-simplifying-units (let ((np (cdr expr)) (math-try-cancel-units 0) n) (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 math-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)) expr))) (defun math-simplify-units-divisor (np dp) (let ((n (car np)) d 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)) (setq un (nth 4 un) ud (nth 4 ud)) (dolist (x un) (dolist (y ud) (when (eq (car x) (car y)) (setq math-try-cancel-units (+ math-try-cancel-units (- (* (cdr x) pow1) (* (cdr (car ud)) pow2)))))))))))) (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)))))) (math-defsimplify calcFunc-sec (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-sec (nth 1 rad)))))) (math-defsimplify calcFunc-csc (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-csc (nth 1 rad)))))) (math-defsimplify calcFunc-cot (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-cot (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) (cond ((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) (save-excursion (message "Formatting units table...") (set-buffer buf) (let ((inhibit-read-only t)) (erase-buffer) (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") (dolist (u uptr) (setq 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 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")) (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 (format-message (concat "(**) 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'.")))) (special-mode) (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) (math-mul (if (equal aunit '(var dB var-dB)) (let ((coef (if power 10 20))) (math-mul coef (math-conditional-apply 'calcFunc-log10 (if neg (math-sub (math-conditional-pow 10 (math-div acoeff coef)) (math-conditional-pow 10 (math-div bcoeff coef))) (math-add (math-conditional-pow 10 (math-div acoeff coef)) (math-conditional-pow 10 (math-div bcoeff coef))))))) (let ((coef (if power 2 1))) (math-div (math-conditional-apply 'calcFunc-ln (if neg (math-sub (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff)) (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff))) (math-add (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff)) (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff))))) coef))) units))))))) (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") (calc-slow-wrapper (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") (calc-slow-wrapper (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) (cond ((and (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)) ((and (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 (cond ((equal logunit '(var dB var-dB)) (math-simplify (math-mul (math-add coef (math-mul (if power 10 20) (math-conditional-apply 'calcFunc-log10 number))) units))) (t (math-simplify (math-mul (math-add coef (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1))) units)))) (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)))) (cond ((equal logunit '(var dB var-dB)) (math-simplify (math-mul (math-sub coef (math-mul (if power 10 20) (math-conditional-apply 'calcFunc-log10 b))) units))) (t (math-simplify (math-mul (math-sub coef (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1))) units))))))))) (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") (calc-slow-wrapper (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") (calc-slow-wrapper (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)))) (math-mul (if (equal lunit '(var dB var-dB)) (math-mul ref (math-conditional-pow 10 (math-div coeff (if power 10 20)))) (math-mul ref (math-conditional-apply 'calcFunc-exp (if power (math-mul 2 coeff) coeff)))) runits))))) (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") (calc-slow-wrapper (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)))) (math-mul (if db (math-mul (math-mul (if power 10 20) (math-conditional-apply 'calcFunc-log10 ratiou)) '(var dB var-dB)) (math-mul (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1)) '(var Np var-Np))) units))) (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") (calc-slow-wrapper (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") (calc-slow-wrapper (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) n num))) (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)) (cond ((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) (or (not cents) (Math-numberp (setq rcents (math-simplify (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) (or (not note) (Math-numberp (setq rcents (math-simplify (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 69 (math-mul 12 (calcFunc-log (math-div freq 440) 2))))) (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) note))) (if cents (math-add midi (math-div cents 100)) midi))) (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) (cons (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 '* (math-mul 440 (math-pow 2 (math-div (math-sub midi 69) 12))) '(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) (cond ((setq note (math-freqp expr)) (math-freq-to-spn note)) ((setq note (math-midip expr)) (math-midi-to-spn note)) ((math-spnp expr) expr) (t (math-reject-arg expr "*Improper expression"))))) (defun calcFunc-midi (expr) "Return EXPR written as a MIDI number." (let (note) (cond ((setq note (math-freqp expr)) (math-freq-to-midi note)) ((setq note (math-spnp expr)) (math-spn-to-midi note)) ((math-midip expr) expr) (t (math-reject-arg expr "*Improper expression"))))) (defun calcFunc-freq (expr) "Return the frequency corresponding to EXPR." (let (note) (cond ((setq note (math-midip expr)) (math-midi-to-freq note)) ((setq note (math-spnp expr)) (math-spn-to-freq note)) ((math-freqp expr) expr) (t (math-reject-arg expr "*Improper expression"))))) (defun calc-freq (arg) "Return the frequency corresponding to the expression on the stack." (interactive "P") (calc-slow-wrapper (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-slow-wrapper (calc-unary-op "midi" 'calcFunc-midi arg))) (defun calc-spn (arg) "Return scientific pitch notation corresponding to the expression on the stack." (interactive "P") (calc-slow-wrapper (calc-unary-op "spn" 'calcFunc-spn arg))) (provide 'calc-units) ;;; calc-units.el ends here