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2152 lines
76 KiB
EmacsLisp
2152 lines
76 KiB
EmacsLisp
;;; calc-units.el --- unit conversion functions for Calc -*- lexical-binding:t -*-
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;; Copyright (C) 1990-1993, 2001-2022 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software: you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation, either version 3 of the License, or
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;; (at your option) any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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(eval-when-compile
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(require 'calc-alg))
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;;; Units operations.
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;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
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;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)
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;;; Updated April 2002 by Jochen Küpper
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;;; Updated August 2007, using
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;;; CODATA (https://physics.nist.gov/cuu/Constants/index.html)
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;;; NIST (https://physics.nist.gov/Pubs/SP811/appenB9.html)
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;;; ESUWM (Encyclopaedia of Scientific Units, Weights and
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;;; Measures, by François Cardarelli)
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;;; All conversions are exact unless otherwise noted.
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;; CODATA values updated February 2016, using 2014 adjustment
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;; https://arxiv.org/pdf/1507.07956.pdf
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;; Updated November 2018 for the redefinition of the SI
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;; https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
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(defvar math-standard-units
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'( ;; Length
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( m nil "*Meter" )
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( in "254*10^(-2) cm" "Inch" nil
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"2.54 cm")
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( ft "12 in" "Foot")
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( yd "3 ft" "Yard" )
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( mi "5280 ft" "Mile" )
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( au "149597870691. m" "Astronomical Unit" nil
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"149597870691 m (*)")
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;; (approx) NASA JPL (https://neo.jpl.nasa.gov/glossary/au.html)
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( lyr "c yr" "Light Year" )
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( pc "3.0856775854*10^16 m" "Parsec (**)" nil
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"3.0856775854 10^16 m (*)") ;; (approx) ESUWM
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( nmi "1852 m" "Nautical Mile" )
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( fath "6 ft" "Fathom" )
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( fur "660 ft" "Furlong")
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( mu "1 um" "Micron" )
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( mil "(1/1000) in" "Mil" )
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( point "(1/72) in" "Point (PostScript convention)" )
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( Ang "10^(-10) m" "Angstrom" )
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( mfi "mi+ft+in" "Miles + feet + inches" )
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;; TeX lengths
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( texpt "(100/7227) in" "Point (TeX convention) (**)" )
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( texpc "12 texpt" "Pica (TeX convention) (**)" )
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( texbp "point" "Big point (TeX convention) (**)" )
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( texdd "(1238/1157) texpt" "Didot point (TeX convention) (**)" )
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( texcc "12 texdd" "Cicero (TeX convention) (**)" )
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( texsp "(1/65536) texpt" "Scaled TeX point (TeX convention) (**)" )
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;; Area
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( hect "10000 m^2" "*Hectare" )
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( a "100 m^2" "Are")
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( acre "(1/640) mi^2" "Acre" )
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( b "10^(-28) m^2" "Barn" )
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;; Volume
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( L "10^(-3) m^3" "*Liter" )
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( l "L" "Liter" )
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( gal "4 qt" "US Gallon" )
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( qt "2 pt" "Quart" )
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( pt "2 cup" "Pint (**)" )
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( cup "8 ozfl" "Cup" )
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( ozfl "2 tbsp" "Fluid Ounce" )
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( floz "2 tbsp" "Fluid Ounce" )
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( tbsp "3 tsp" "Tablespoon" )
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;; ESUWM defines a US gallon as 231 in^3.
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;; That gives the following exact value for tsp.
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( tsp "492892159375*10^(-11) ml" "Teaspoon" nil
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"4.92892159375 ml")
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( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" nil
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"tsp+tbsp+ozfl+cup+pt+qt+gal")
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( galC "galUK" "Canadian Gallon" )
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( galUK "454609*10^(-5) L" "UK Gallon" nil
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"4.54609 L") ;; NIST
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;; Time
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( s nil "*Second" )
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( sec "s" "Second" )
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( min "60 s" "Minute" )
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( hr "60 min" "Hour" )
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( day "24 hr" "Day" )
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( wk "7 day" "Week" )
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( hms "wk+day+hr+min+s" "Hours, minutes, seconds" )
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( yr "36525*10^(-2) day" "Year (Julian)" nil
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"365.25 day")
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( Hz "1/s" "Hertz" )
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;; Speed
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( mph "mi/hr" "*Miles per hour" )
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( kph "km/hr" "Kilometers per hour" )
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( knot "nmi/hr" "Knot" )
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( c "299792458 m/s" "Speed of light" ) ;; SI definition
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;; Acceleration
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( ga "980665*10^(-5) m/s^2" "*\"g\" acceleration" nil
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"9.80665 m / s^2") ;; CODATA
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;; Mass
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( g nil "*Gram" )
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( lb "16 oz" "Pound (mass)" )
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( oz "28349523125*10^(-9) g" "Ounce (mass)" nil
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"28.349523125 g") ;; ESUWM
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( ton "2000 lb" "Ton" )
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( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" )
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( t "1000 kg" "Metric ton" )
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( tonUK "10160469088*10^(-7) kg" "UK ton" nil
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"1016.0469088 kg") ;; ESUWM
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( lbt "12 ozt" "Troy pound" )
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( ozt "311034768*10^(-7) g" "Troy ounce" nil
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"31.10347680 g") ;; ESUWM, 1/12 exact value for lbt
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( ct "(2/10) g" "Carat" nil
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"0.2 g") ;; ESUWM
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( u "1.660539040*10^(-27) kg" "Unified atomic mass" nil
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"1.660539040 10^-27 kg (*)");;(approx) CODATA
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;; Force
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( N "m kg/s^2" "*Newton" )
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( dyn "10^(-5) N" "Dyne" )
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( gf "ga g" "Gram (force)" )
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( lbf "ga lb" "Pound (force)" )
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( kip "1000 lbf" "Kilopound (force)" )
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( pdl "138254954376*10^(-12) N" "Poundal" nil
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"0.138254954376 N") ;; ESUWM
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;; Energy
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( J "N m" "*Joule" )
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( erg "10^(-7) J" "Erg" )
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( cal "41868*10^(-4) J" "International Table Calorie" nil
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"4.1868 J") ;; NIST
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( calth "4184*10^(-3) J" "Thermochemical Calorie" nil
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"4.184 J") ;; NIST
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( Cal "1000 cal" "Large Calorie")
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( Btu "105505585262*10^(-8) J" "International Table Btu" nil
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"1055.05585262 J") ;; ESUWM
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( eV "ech V" "Electron volt" )
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( ev "eV" "Electron volt" )
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( therm "105506000 J" "EEC therm" )
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( invcm "h c/cm" "Energy in inverse centimeters" )
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( Kayser "invcm" "Kayser (inverse centimeter energy)" )
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( men "100/invcm" "Inverse energy in meters" )
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( Hzen "h Hz" "Energy in Hertz")
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( Ken "k K" "Energy in Kelvins")
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( Wh "W hr" "Watt hour")
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( Ws "W s" "Watt second")
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;; Power
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( W "J/s" "*Watt" )
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( hp "550 ft lbf/s" "Horsepower") ;;ESUWM
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( hpm "75 m kgf/s" "Metric Horsepower") ;;ESUWM
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;; Temperature
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( K nil "*Degree Kelvin" K )
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( dK "K" "Degree Kelvin" K )
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( degK "K" "Degree Kelvin" K )
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( dC "K" "Degree Celsius" C )
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( degC "K" "Degree Celsius" C )
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( dF "(5/9) K" "Degree Fahrenheit" F )
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( degF "(5/9) K" "Degree Fahrenheit" F )
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;; Pressure
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( Pa "N/m^2" "*Pascal" )
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( bar "10^5 Pa" "Bar" )
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( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA
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( Torr "(1/760) atm" "Torr")
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( mHg "1000 Torr" "Meter of mercury" )
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( inHg "254*10^(-1) mmHg" "Inch of mercury" nil
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"25.4 mmHg")
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( inH2O "2.490889*10^2 Pa" "Inch of water" nil
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"2.490889 10^2 Pa (*)") ;;(approx) NIST
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( psi "lbf/in^2" "Pounds per square inch" )
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;; Viscosity
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( P "(1/10) Pa s" "*Poise" )
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( St "10^(-4) m^2/s" "Stokes" )
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;; Electromagnetism
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( A nil "*Ampere" )
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( C "A s" "Coulomb" )
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( Fdy "ech Nav" "Faraday" )
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( e "ech" "Elementary charge" )
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( ech "1.602176634*10^(-19) C" "Elementary charge" nil
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"1.602176634 10^-19 C") ;; SI definition
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( V "W/A" "Volt" )
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( ohm "V/A" "Ohm" )
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( Ω "ohm" "Ohm" )
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( mho "A/V" "Mho" )
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( S "A/V" "Siemens" )
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( F "C/V" "Farad" )
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( H "Wb/A" "Henry" )
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( T "Wb/m^2" "Tesla" )
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( Gs "10^(-4) T" "Gauss" )
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( Wb "V s" "Weber" )
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;; Luminous intensity
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( cd nil "*Candela" )
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( sb "10000 cd/m^2" "Stilb" )
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( lm "cd sr" "Lumen" )
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( lx "lm/m^2" "Lux" )
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( ph "10000 lx" "Phot" )
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( fc "lm/ft^2" "Footcandle") ;; ESUWM
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( lam "10000 lm/m^2" "Lambert" )
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( flam "(1/pi) cd/ft^2" "Footlambert") ;; ESUWM
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;; Radioactivity
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( Bq "1/s" "*Becquerel" )
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( Ci "37*10^9 Bq" "Curie" ) ;; ESUWM
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( Gy "J/kg" "Gray" )
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( Sv "Gy" "Sievert" )
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( R "258*10^(-6) C/kg" "Roentgen" ) ;; NIST
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( rd "(1/100) Gy" "Rad" )
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( rem "rd" "Rem" )
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;; Amount of substance
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( mol nil "*Mole" )
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;; Plane angle
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( rad nil "*Radian" )
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( circ "2 pi rad" "Full circle" )
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( rev "circ" "Full revolution" )
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( deg "circ/360" "Degree" )
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( arcmin "deg/60" "Arc minute" )
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( arcsec "arcmin/60" "Arc second" )
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( grad "circ/400" "Grade" )
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( rpm "rev/min" "Revolutions per minute" )
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;; Solid angle
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( sr nil "*Steradian" )
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;; Other physical quantities
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;; Unless otherwise mentioned, the values are from CODATA,
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;; and are approximate.
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( h "6.62607015*10^(-34) J s" "*Planck's constant" nil
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"6.62607015 10^-34 J s") ;; SI definition
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( hbar "h / (2 pi)" "Planck's constant" ) ;; Exact
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;; After the 2018 SI redefinition, eps0 and mu0 are measured quantities,
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;; and mu0 no longer has the previous exact value of 4 pi 10^(-7) H/m.
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( eps0 "ech^2 / (2 alpha h c)" "Permittivity of vacuum" )
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( ε0 "eps0" "Permittivity of vacuum" )
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( mu0 "1 / (eps0 c^2)" "Permeability of vacuum") ;; Exact
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( μ0 "mu0" "Permeability of vacuum") ;; Exact
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( G "6.67408*10^(-11) m^3/(kg s^2)" "Gravitational constant" nil
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"6.67408 10^-11 m^3/(kg s^2) (*)")
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( Nav "6.02214076*10^(23) / mol" "Avogadro's constant" nil
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"6.02214076 10^23 / mol") ;; SI definition
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( me "9.10938356*10^(-31) kg" "Electron rest mass" nil
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"9.10938356 10^-31 kg (*)")
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( mp "1.672621898*10^(-27) kg" "Proton rest mass" nil
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"1.672621898 10^-27 kg (*)")
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( mn "1.674927471*10^(-27) kg" "Neutron rest mass" nil
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"1.674927471 10^-27 kg (*)")
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( mmu "1.883531594*10^(-28) kg" "Muon rest mass" nil
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"1.883531594 10^-28 kg (*)")
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( mμ "mmu" "Muon rest mass" nil
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"1.883531594 10^-28 kg (*)")
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( Ryd "10973731.568508 /m" "Rydberg's constant" nil
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"10973731.568508 /m (*)")
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( k "1.380649*10^(-23) J/K" "Boltzmann's constant" nil
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"1.380649 10^-23 J/K") ;; SI definition
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( sigma "2 pi^5 k^4 / (15 h^3 c^2)" "Stefan-Boltzmann constant")
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( σ "sigma" "Stefan-Boltzmann constant")
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( alpha "7.2973525664*10^(-3)" "Fine structure constant" nil
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"7.2973525664 10^-3 (*)")
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( α "alpha" "Fine structure constant" nil
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"7.2973525664 10^-3 (*)")
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( muB "927.4009994*10^(-26) J/T" "Bohr magneton" nil
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"927.4009994 10^-26 J/T (*)")
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( muN "5.050783699*10^(-27) J/T" "Nuclear magneton" nil
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"5.050783699 10^-27 J/T (*)")
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( mue "-928.4764620*10^(-26) J/T" "Electron magnetic moment" nil
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"-928.4764620 10^-26 J/T (*)")
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( mup "1.4106067873*10^(-26) J/T" "Proton magnetic moment" nil
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"1.4106067873 10^-26 J/T (*)")
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( R0 "Nav k" "Molar gas constant") ;; Exact
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( V0 "22.710947*10^(-3) m^3/mol" "Standard volume of ideal gas" nil
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"22.710947 10^-3 m^3/mol (*)")
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;; Logarithmic units
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( Np nil "*Neper")
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( dB "(ln(10)/20) Np" "decibel")))
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(defvar math-additional-units nil
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"Additional units table for user-defined units.
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Must be formatted like `math-standard-units'.
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If you change this, be sure to set `math-units-table' to nil to ensure
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that the combined units table will be rebuilt.")
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(defvar math-unit-prefixes
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'( ( ?Y (^ 10 24) "Yotta" )
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( ?Z (^ 10 21) "Zetta" )
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( ?E (^ 10 18) "Exa" )
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( ?P (^ 10 15) "Peta" )
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( ?T (^ 10 12) "Tera" )
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( ?G (^ 10 9) "Giga" )
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( ?M (^ 10 6) "Mega" )
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( ?k (^ 10 3) "Kilo" )
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( ?K (^ 10 3) "Kilo" )
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( ?h (^ 10 2) "Hecto" )
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( ?H (^ 10 2) "Hecto" )
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( ?D (^ 10 1) "Deka" )
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( 0 (^ 10 0) nil )
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( ?d (^ 10 -1) "Deci" )
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( ?c (^ 10 -2) "Centi" )
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( ?m (^ 10 -3) "Milli" )
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( ?u (^ 10 -6) "Micro" )
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( ?μ (^ 10 -6) "Micro" )
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( ?n (^ 10 -9) "Nano" )
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( ?p (^ 10 -12) "Pico" )
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( ?f (^ 10 -15) "Femto" )
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( ?a (^ 10 -18) "Atto" )
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( ?z (^ 10 -21) "zepto" )
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( ?y (^ 10 -24) "yocto" )))
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(defvar math-standard-units-systems
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'( ( base nil )
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( si ( ( g '(/ (var kg var-kg) 1000) ) ) )
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( mks ( ( g '(/ (var kg var-kg) 1000) ) ) )
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( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) )))
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(defvar math-units-table nil
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"Internal units table.
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Derived from `math-standard-units' and `math-additional-units'.
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Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
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(defvar math-units-table-buffer-valid nil)
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;;; Units commands.
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(defun calc-base-units ()
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(interactive)
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(calc-slow-wrapper
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(let ((calc-autorange-units nil))
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(calc-enter-result 1 "bsun" (math-simplify-units
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(math-to-standard-units (calc-top-n 1)
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nil))))))
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(defvar calc-ensure-consistent-units)
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(defun calc-quick-units ()
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(interactive)
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(calc-slow-wrapper
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(let* ((num (- last-command-event ?0))
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(pos (if (= num 0) 10 num))
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(units (calc-var-value 'var-Units))
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(expr (calc-top-n 1)))
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(unless (and (>= num 0) (<= num 9))
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(error "Bad unit number"))
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(unless (math-vectorp units)
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(error "No \"quick units\" are defined"))
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(unless (< pos (length units))
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(error "Unit number %d not defined" pos))
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(if (math-units-in-expr-p expr nil)
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(progn
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(if calc-ensure-consistent-units
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(math-check-unit-consistency expr (nth pos units)))
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(calc-enter-result 1 (format "cun%d" num)
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(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 (format-prompt
|
||
(if (and uoldname (not nouold))
|
||
(concat "Old units: "
|
||
uoldname
|
||
", new units")
|
||
"New units")
|
||
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 (format-prompt "New units" 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 (format-prompt
|
||
(if uoldname
|
||
(concat "Old temperature units: "
|
||
uoldname
|
||
", new units")
|
||
"New temperature units")
|
||
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
|