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1502 lines
52 KiB
EmacsLisp
1502 lines
52 KiB
EmacsLisp
;;; calc-units.el --- unit conversion functions for Calc
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;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
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;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; Maintainer: Jay Belanger <jay.p.belanger@gmail.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, or (at your option)
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;; 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; see the file COPYING. If not, write to the
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;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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;; Boston, MA 02110-1301, USA.
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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 (http://physics.nist.gov/cuu/Constants/index.html)
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;;; NIST (http://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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(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" )
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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" )
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;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
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( lyr "c yr" "Light Year" )
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( pc "3.0856775854e16 m" "Parsec" ) ;; (approx) ESUWM
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( nmi "1852 m" "Nautical Mile" )
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( fath "6 ft" "Fathom" )
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( mu "1 um" "Micron" )
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( mil "in/1000" "Mil" )
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( point "in/72" "Point (1/72 inch)" )
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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 conventions)" )
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( texpc "12 texpt" "Pica" )
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( texbp "point" "Big point (TeX conventions)" )
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( texdd "(1238/1157) texpt" "Didot point" )
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( texcc "12 texdd" "Cicero" )
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( texsp "(1/65536) texpt" "Scaled TeX point" )
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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 "mi^2 / 640" "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" )
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( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" )
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( galC "galUK" "Canadian Gallon" )
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( galUK "454609*10^(-5) L" "UK Gallon" ) ;; 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 "365.25 day" "Year" ) ;; (approx, but keep)
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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" ) ;;; CODATA
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;; Acceleration
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( ga "980665*10^(-5) m/s^2" "*\"g\" acceleration" ) ;; 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)" ) ;; 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" ) ;; ESUWM
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( lbt "12 ozt" "Troy pound" )
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( ozt "31.10347680 g" "Troy ounce" ) ;; (approx) ESUWM
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( ct "(2/10) g" "Carat" ) ;; ESUWM
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( u "1.660538782e-27 kg" "Unified atomic mass" );;(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" ) ;; 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 "4.18674 J" "International Table Calorie" );;(approx) ESUWM
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( Btu "105505585262*10^(-8) J" "International Table Btu" ) ;; 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 "745.699871581 W" "Horsepower" ) ;;(approx) 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 "1.333224e2 Pa" "Torr" ) ;;(approx) NIST
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( mHg "1000 Torr" "Meter of mercury" )
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( inHg "254*10^(-1) mmHg" "Inch of mercury" )
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( inH2O "2.490889e2 Pa" "Inch of water" ) ;;(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 "1.602176487e-19 C" "Elementary charge" ) ;;(approx) CODATA
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( V "W/A" "Volt" )
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( ohm "V/A" "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 "10.76391 lx" "Footcandle" ) ;;(approx) NIST
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( lam "10000 lm/m^2" "Lambert" )
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( flam "3.426259 cd/m^2" "Footlambert" ) ;;(approx) NIST
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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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;; The values are from CODATA, and are approximate.
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( h "6.62606896e-34 J s" "*Planck's constant" )
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( hbar "h / (2 pi)" "Planck's constant" )
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( mu0 "4 pi 10^(-7) H/m" "Permeability of vacuum" )
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( G "6.67428e-11 m^3/(kg s^2)" "Gravitational constant" )
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( Nav "6.02214179e23 / mol" "Avagadro's constant" )
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( me "9.10938215e-31 kg" "Electron rest mass" )
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( mp "1.672621637e-27 kg" "Proton rest mass" )
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( mn "1.674927211e-27 kg" "Neutron rest mass" )
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( mmu "1.88353130e-28 kg" "Muon rest mass" )
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( Ryd "10973731.568527 /m" "Rydberg's constant" )
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( k "1.3806504e-23 J/K" "Boltzmann's constant" )
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( alpha "7.2973525376e-3" "Fine structure constant" )
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( muB "927.400915e-26 J/T" "Bohr magneton" )
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( muN "5.05078324e-27 J/T" "Nuclear magneton" )
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( mue "-928.476377e-26 J/T" "Electron magnetic moment" )
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( mup "1.410606662e-26 J/T" "Proton magnetic moment" )
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( R0 "8.314472 J/(mol K)" "Molar gas constant" )
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( V0 "22.710981e-3 m^3/mol" "Standard volume of ideal gas" )))
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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 this is changed, 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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( ?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 derived from math-defined-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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(defun calc-quick-units ()
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(interactive)
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(calc-slow-wrapper
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(let* ((num (- last-command-char ?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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(calc-enter-result 1 (format "cun%d" num)
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(math-convert-units expr (nth pos units)))
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(calc-enter-result 1 (format "*un%d" num)
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(math-simplify-units
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(math-mul expr (nth pos units))))))))
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(defun math-get-standard-units (expr)
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"Return the standard units in EXPR."
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(math-simplify-units
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(math-extract-units
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(math-to-standard-units expr nil))))
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(defun math-get-units (expr)
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"Return the units in EXPR."
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(math-simplify-units
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(math-extract-units expr)))
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(defun math-make-unit-string (expr)
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"Return EXPR in string form.
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If EXPR is nil, return nil."
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(if expr
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(let ((cexpr (math-compose-expr expr 0)))
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(replace-regexp-in-string
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" / " "/"
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(if (stringp cexpr)
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cexpr
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(math-composition-to-string cexpr))))))
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(defvar math-default-units-table
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(make-hash-table :test 'equal)
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"A table storing previously converted units.")
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(defun math-get-default-units (expr)
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"Get default units to use when converting the units in EXPR."
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(let* ((units (math-get-units expr))
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(standard-units (math-get-standard-units expr))
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(default-units (gethash
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standard-units
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math-default-units-table)))
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(if (equal units (car default-units))
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(math-make-unit-string (cadr default-units))
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(math-make-unit-string (car default-units)))))
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(defun math-put-default-units (expr)
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"Put the units in EXPR in the default units table."
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(let* ((units (math-get-units expr))
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(standard-units (math-get-standard-units expr))
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(default-units (gethash
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standard-units
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math-default-units-table)))
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(cond
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((not default-units)
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(puthash standard-units (list units) math-default-units-table))
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((not (equal units (car default-units)))
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(puthash standard-units
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(list units (car default-units))
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math-default-units-table)))))
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(defun calc-convert-units (&optional old-units new-units)
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(interactive)
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(calc-slow-wrapper
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(let ((expr (calc-top-n 1))
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(uoldname nil)
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unew
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units
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defunits)
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(unless (math-units-in-expr-p expr t)
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(let ((uold (or old-units
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(progn
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(setq uoldname (read-string "Old units: "))
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(if (equal uoldname "")
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(progn
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(setq uoldname "1")
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1)
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(if (string-match "\\` */" uoldname)
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(setq uoldname (concat "1" uoldname)))
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(math-read-expr uoldname))))))
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(when (eq (car-safe uold) 'error)
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(error "Bad format in units expression: %s" (nth 1 uold)))
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(setq expr (math-mul expr uold))))
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(unless new-units
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(setq defunits (math-get-default-units expr))
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(setq new-units
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(read-string (concat
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(if uoldname
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(concat "Old units: "
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uoldname
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", new units")
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"New units")
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(if defunits
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(concat
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" (default "
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defunits
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"): ")
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": "))))
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(if (and
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(string= new-units "")
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defunits)
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(setq new-units defunits)))
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(when (string-match "\\` */" new-units)
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(setq new-units (concat "1" new-units)))
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(setq units (math-read-expr new-units))
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(when (eq (car-safe units) 'error)
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(error "Bad format in units expression: %s" (nth 2 units)))
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(math-put-default-units units)
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(let ((unew (math-units-in-expr-p units t))
|
|
(std (and (eq (car-safe units) 'var)
|
|
(assq (nth 1 units) math-standard-units-systems))))
|
|
(if std
|
|
(calc-enter-result 1 "cvun" (math-simplify-units
|
|
(math-to-standard-units expr
|
|
(nth 1 std))))
|
|
(unless unew
|
|
(error "No units specified"))
|
|
(calc-enter-result 1 "cvun"
|
|
(math-convert-units
|
|
expr units
|
|
(and uoldname (not (equal uoldname "1"))))))))))
|
|
|
|
(defun calc-autorange-units (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-change-mode 'calc-autorange-units arg nil t)
|
|
(message (if calc-autorange-units
|
|
"Adjusting target unit prefix automatically"
|
|
"Using target units exactly"))))
|
|
|
|
(defun calc-convert-temperature (&optional old-units new-units)
|
|
(interactive)
|
|
(calc-slow-wrapper
|
|
(let ((expr (calc-top-n 1))
|
|
(uold nil)
|
|
(uoldname nil)
|
|
unew
|
|
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 (read-string
|
|
"Old temperature units: ")))))))
|
|
(when (eq (car-safe uold) 'error)
|
|
(error "Bad format in units expression: %s" (nth 2 uold)))
|
|
(or (math-units-in-expr-p expr nil)
|
|
(setq expr (math-mul expr uold)))
|
|
(setq defunits (math-get-default-units expr))
|
|
(setq unew (or new-units
|
|
(math-read-expr
|
|
(read-string
|
|
(concat
|
|
(if uoldname
|
|
(concat "Old temperature units: "
|
|
uoldname
|
|
", new units")
|
|
"New temperature units")
|
|
(if defunits
|
|
(concat " (default "
|
|
defunits
|
|
"): ")
|
|
": "))))))
|
|
(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 "rmun" (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 "^[^(].* .*[^)]$" calc-den-units)
|
|
(setq calc-den-units (concat "(" calc-den-units ")")))
|
|
(if calc-num-units
|
|
(if calc-den-units
|
|
(message "%s per %s" calc-num-units calc-den-units)
|
|
(message "%s" calc-num-units))
|
|
(if calc-den-units
|
|
(message "1 per %s" calc-den-units)
|
|
(message "No units in expression"))))))
|
|
|
|
(defun calc-explain-units-rec (expr pow)
|
|
(let ((u (math-check-unit-name expr))
|
|
pos)
|
|
(if (and u (not (math-zerop pow)))
|
|
(let ((name (or (nth 2 u) (symbol-name (car u)))))
|
|
(if (eq (aref name 0) ?\*)
|
|
(setq name (substring name 1)))
|
|
(if (string-match "[^a-zA-Z0-9']" name)
|
|
(if (string-match "^[a-zA-Z0-9' ()]*$" name)
|
|
(while (setq pos (string-match "[ ()]" name))
|
|
(setq name (concat (substring name 0 pos)
|
|
(if (eq (aref name pos) 32) "-" "")
|
|
(substring name (1+ pos)))))
|
|
(setq name (concat "(" name ")"))))
|
|
(or (eq (nth 1 expr) (car u))
|
|
(setq name (concat (nth 2 (assq (aref (symbol-name
|
|
(nth 1 expr)) 0)
|
|
math-unit-prefixes))
|
|
(if (and (string-match "[^a-zA-Z0-9']" name)
|
|
(not (memq (car u) '(mHg gf))))
|
|
(concat "-" name)
|
|
(downcase name)))))
|
|
(cond ((or (math-equal-int pow 1)
|
|
(math-equal-int pow -1)))
|
|
((or (math-equal-int pow 2)
|
|
(math-equal-int pow -2))
|
|
(if (equal (nth 4 u) '((m . 1)))
|
|
(setq name (concat "Square-" name))
|
|
(setq name (concat name "-squared"))))
|
|
((or (math-equal-int pow 3)
|
|
(math-equal-int pow -3))
|
|
(if (equal (nth 4 u) '((m . 1)))
|
|
(setq name (concat "Cubic-" name))
|
|
(setq name (concat name "-cubed"))))
|
|
(t
|
|
(setq name (concat name "^"
|
|
(math-format-number (math-abs pow))))))
|
|
(if (math-posp pow)
|
|
(setq 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)
|
|
(interactive "SDefine unit name: \nsDescription: ")
|
|
(calc-wrapper
|
|
(let ((form (calc-top-n 1))
|
|
(unit (assq uname math-additional-units)))
|
|
(or unit
|
|
(setq math-additional-units
|
|
(cons (setq unit (list uname nil nil))
|
|
math-additional-units)
|
|
math-units-table nil))
|
|
(setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
|
|
(eq (nth 1 form) uname)))
|
|
(not (math-equal-int form 1))
|
|
(math-format-flat-expr form 0)))
|
|
(setcar (cdr (cdr unit)) (and (not (equal desc ""))
|
|
desc))))
|
|
(calc-invalidate-units-table))
|
|
|
|
(defun calc-undefine-unit (uname)
|
|
(interactive "SUndefine unit name: ")
|
|
(calc-wrapper
|
|
(let ((unit (assq uname math-additional-units)))
|
|
(or unit
|
|
(if (assq uname math-standard-units)
|
|
(error "\"%s\" is a predefined unit name" uname)
|
|
(error "Unit name \"%s\" not found" uname)))
|
|
(setq math-additional-units (delq unit math-additional-units)
|
|
math-units-table nil)))
|
|
(calc-invalidate-units-table))
|
|
|
|
(defun calc-invalidate-units-table ()
|
|
(setq math-units-table nil)
|
|
(let ((buf (get-buffer "*Units Table*")))
|
|
(and buf
|
|
(save-excursion
|
|
(set-buffer buf)
|
|
(save-excursion
|
|
(goto-char (point-min))
|
|
(if (looking-at "Calculator Units Table")
|
|
(let ((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
|
|
(progn
|
|
(insert "(setq math-additional-units '(\n")
|
|
(let ((list math-additional-units))
|
|
(while list
|
|
(insert " (" (symbol-name (car (car list))) " "
|
|
(if (nth 1 (car list))
|
|
(if (stringp (nth 1 (car list)))
|
|
(prin1-to-string (nth 1 (car list)))
|
|
(prin1-to-string (math-format-flat-expr
|
|
(nth 1 (car list)) 0)))
|
|
"nil")
|
|
" "
|
|
(prin1-to-string (nth 2 (car list)))
|
|
")\n")
|
|
(setq list (cdr list))))
|
|
(insert "))\n"))
|
|
(insert ";;; (no custom units defined)\n"))
|
|
(insert ";;; End of custom units\n")
|
|
(save-buffer))))
|
|
|
|
|
|
;; The variable math-cu-unit-list is local to math-build-units-table,
|
|
;; but is used by math-compare-unit-names, which is called (indirectly)
|
|
;; by math-build-units-table.
|
|
;; math-cu-unit-list is also local to math-convert-units, but is used
|
|
;; by math-convert-units-rec, which is called by math-convert-units.
|
|
(defvar math-cu-unit-list)
|
|
|
|
(defun math-build-units-table ()
|
|
(or math-units-table
|
|
(let* ((combined-units (append math-additional-units
|
|
math-standard-units))
|
|
(math-cu-unit-list (mapcar 'car combined-units))
|
|
tab)
|
|
(message "Building units table...")
|
|
(setq math-units-table-buffer-valid nil)
|
|
(setq tab (mapcar (function
|
|
(lambda (x)
|
|
(list (car x)
|
|
(and (nth 1 x)
|
|
(if (stringp (nth 1 x))
|
|
(let ((exp (math-read-plain-expr
|
|
(nth 1 x))))
|
|
(if (eq (car-safe exp) 'error)
|
|
(error "Format error in definition of %s in units table: %s"
|
|
(car x) (nth 2 exp))
|
|
exp))
|
|
(nth 1 x)))
|
|
(nth 2 x)
|
|
(nth 3 x)
|
|
(and (not (nth 1 x))
|
|
(list (cons (car x) 1))))))
|
|
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 (math-fbu-entry)
|
|
(if (eq (nth 4 math-fbu-entry) 'boom)
|
|
(error "Circular definition involving unit %s" (car math-fbu-entry)))
|
|
(or (nth 4 math-fbu-entry)
|
|
(let (math-fbu-base)
|
|
(setcar (nthcdr 4 math-fbu-entry) 'boom)
|
|
(math-find-base-units-rec (nth 1 math-fbu-entry) 1)
|
|
'(or math-fbu-base
|
|
(error "Dimensionless definition for unit %s" (car math-fbu-entry)))
|
|
(while (eq (cdr (car math-fbu-base)) 0)
|
|
(setq math-fbu-base (cdr math-fbu-base)))
|
|
(let ((b math-fbu-base))
|
|
(while (cdr b)
|
|
(if (eq (cdr (car (cdr b))) 0)
|
|
(setcdr b (cdr (cdr b)))
|
|
(setq b (cdr b)))))
|
|
(setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
|
|
(setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
|
|
math-fbu-base)))
|
|
|
|
(defun math-compare-unit-names (a b)
|
|
(memq (car b) (cdr (memq (car a) math-cu-unit-list))))
|
|
|
|
(defun math-find-base-units-rec (expr pow)
|
|
(let ((u (math-check-unit-name expr)))
|
|
(cond (u
|
|
(let ((ulist (math-find-base-units u)))
|
|
(while ulist
|
|
(let ((p (* (cdr (car ulist)) pow))
|
|
(old (assq (car (car ulist)) math-fbu-base)))
|
|
(if old
|
|
(setcdr old (+ (cdr old) p))
|
|
(setq math-fbu-base
|
|
(cons (cons (car (car ulist)) p) math-fbu-base))))
|
|
(setq ulist (cdr ulist)))))
|
|
((math-scalarp expr))
|
|
((and (eq (car expr) '^)
|
|
(integerp (nth 2 expr)))
|
|
(math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
|
|
((eq (car expr) '*)
|
|
(math-find-base-units-rec (nth 1 expr) pow)
|
|
(math-find-base-units-rec (nth 2 expr) pow))
|
|
((eq (car expr) '/)
|
|
(math-find-base-units-rec (nth 1 expr) pow)
|
|
(math-find-base-units-rec (nth 2 expr) (- pow)))
|
|
((eq (car expr) 'neg)
|
|
(math-find-base-units-rec (nth 1 expr) pow))
|
|
((eq (car expr) '+)
|
|
(math-find-base-units-rec (nth 1 expr) pow))
|
|
((eq (car expr) 'var)
|
|
(or (eq (nth 1 expr) 'pi)
|
|
(error "Unknown name %s in defining expression for unit %s"
|
|
(nth 1 expr) (car math-fbu-entry))))
|
|
(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)
|
|
(and (or sub-exprs
|
|
(memq (car expr) '(* / ^)))
|
|
(or (math-units-in-expr-p (nth 1 expr) sub-exprs)
|
|
(math-units-in-expr-p (nth 2 expr) sub-exprs))))))
|
|
|
|
(defun math-only-units-in-expr-p (expr)
|
|
(and (consp expr)
|
|
(if (eq (car expr) 'var)
|
|
(math-check-unit-name expr)
|
|
(if (memq (car expr) '(* /))
|
|
(and (math-only-units-in-expr-p (nth 1 expr))
|
|
(math-only-units-in-expr-p (nth 2 expr)))
|
|
(and (eq (car expr) '^)
|
|
(and (math-only-units-in-expr-p (nth 1 expr))
|
|
(math-realp (nth 2 expr))))))))
|
|
|
|
(defun math-single-units-in-expr-p (expr)
|
|
(cond ((math-scalarp expr) nil)
|
|
((eq (car expr) 'var)
|
|
(math-check-unit-name expr))
|
|
((eq (car expr) '*)
|
|
(let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
|
|
(u2 (math-single-units-in-expr-p (nth 2 expr))))
|
|
(or (and u1 u2 'wrong)
|
|
u1
|
|
u2)))
|
|
((eq (car expr) '/)
|
|
(if (math-units-in-expr-p (nth 2 expr) nil)
|
|
'wrong
|
|
(math-single-units-in-expr-p (nth 1 expr))))
|
|
(t 'wrong)))
|
|
|
|
(defun math-check-unit-name (v)
|
|
(and (eq (car-safe v) 'var)
|
|
(or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
|
|
(let ((name (symbol-name (nth 1 v))))
|
|
(and (> (length name) 1)
|
|
(assq (aref name 0) math-unit-prefixes)
|
|
(or (assq (intern (substring name 1)) math-units-table)
|
|
(and (eq (aref name 0) ?M)
|
|
(> (length name) 3)
|
|
(eq (aref name 1) ?e)
|
|
(eq (aref name 2) ?g)
|
|
(assq (intern (substring name 3))
|
|
math-units-table))))))))
|
|
|
|
;; The variable math-which-standard is local to math-to-standard-units,
|
|
;; but is used by math-to-standard-rec, which is called by
|
|
;; math-to-standard-units.
|
|
(defvar math-which-standard)
|
|
|
|
(defun math-to-standard-units (expr math-which-standard)
|
|
(math-to-standard-rec expr))
|
|
|
|
(defun math-to-standard-rec (expr)
|
|
(if (eq (car-safe expr) 'var)
|
|
(let ((u (math-check-unit-name expr))
|
|
(base (nth 1 expr)))
|
|
(if u
|
|
(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 (Math-primp expr)
|
|
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)
|
|
qty unit)
|
|
(while (eq (car-safe utemp) '+)
|
|
(setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
|
|
ulist)
|
|
utemp (nth 1 utemp)))
|
|
(setq ulist (cons (math-decompose-unit-part utemp) ulist)
|
|
utemp ulist)
|
|
(while (setq utemp (cdr utemp))
|
|
(unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
|
|
(error "Inconsistent units in sum")))
|
|
(setq math-decompose-units-cache
|
|
(cons entry
|
|
(sort ulist
|
|
(function
|
|
(lambda (x y)
|
|
(not (Math-lessp (nth 1 x)
|
|
(nth 1 y))))))))))
|
|
(cdr math-decompose-units-cache))))
|
|
|
|
(defun math-decompose-unit-part (unit)
|
|
(cons unit
|
|
(math-is-multiple (math-simplify-units (math-to-standard-units
|
|
unit nil))
|
|
t)))
|
|
|
|
;; 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))))
|
|
((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 math-cu-new-units &optional math-cu-pure)
|
|
(if (eq (car-safe math-cu-new-units) 'var)
|
|
(let ((unew (assq (nth 1 math-cu-new-units)
|
|
(math-build-units-table))))
|
|
(if (eq (car-safe (nth 1 unew)) '+)
|
|
(setq math-cu-new-units (nth 1 unew)))))
|
|
(math-with-extra-prec 2
|
|
(let ((compat (and (not math-cu-pure)
|
|
(math-find-compatible-unit expr math-cu-new-units)))
|
|
(math-cu-unit-list nil)
|
|
(math-combining-units nil))
|
|
(if compat
|
|
(math-simplify-units
|
|
(math-mul (math-mul (math-simplify-units
|
|
(math-div expr (math-pow (car compat)
|
|
(cdr compat))))
|
|
(math-pow math-cu-new-units (cdr compat)))
|
|
(math-simplify-units
|
|
(math-to-standard-units
|
|
(math-pow (math-div (car compat) math-cu-new-units)
|
|
(cdr compat))
|
|
nil))))
|
|
(when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
|
|
(setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
|
|
(when (eq (car-safe expr) '+)
|
|
(setq expr (math-simplify-units expr)))
|
|
(if (math-units-in-expr-p expr t)
|
|
(math-convert-units-rec expr)
|
|
(math-apply-units (math-to-standard-units
|
|
(list '/ expr math-cu-new-units) nil)
|
|
math-cu-new-units math-cu-unit-list math-cu-pure))))))
|
|
|
|
(defun math-convert-units-rec (expr)
|
|
(if (math-units-in-expr-p expr nil)
|
|
(math-apply-units (math-to-standard-units
|
|
(list '/ expr math-cu-new-units) nil)
|
|
math-cu-new-units math-cu-unit-list math-cu-pure)
|
|
(if (Math-primp expr)
|
|
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
|
|
;; math-simplify-expr, and so is used by functions in math-defsimplify
|
|
(defvar math-simplify-expr)
|
|
|
|
(math-defsimplify (+ -)
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let* ((units (math-extract-units (nth 1 math-simplify-expr)))
|
|
(ratio (math-simplify (math-to-standard-units
|
|
(list '/ (nth 2 math-simplify-expr) units) nil))))
|
|
(if (math-units-in-expr-p ratio nil)
|
|
(progn
|
|
(calc-record-why "*Inconsistent units" math-simplify-expr)
|
|
math-simplify-expr)
|
|
(list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
|
|
(if (eq (car math-simplify-expr) '-)
|
|
(math-neg ratio) ratio))
|
|
units)))))
|
|
|
|
(math-defsimplify *
|
|
(math-simplify-units-prod))
|
|
|
|
(defun math-simplify-units-prod ()
|
|
(and math-simplifying-units
|
|
calc-autorange-units
|
|
(Math-realp (nth 1 math-simplify-expr))
|
|
(let* ((num (math-float (nth 1 math-simplify-expr)))
|
|
(xpon (calcFunc-xpon num))
|
|
(unitp (cdr (cdr math-simplify-expr)))
|
|
(unit (car unitp))
|
|
(pow (if (eq (car math-simplify-expr) '*) 1 -1))
|
|
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 math-simplify-expr)
|
|
(let ((calc-prefer-frac nil))
|
|
(calcFunc-scf (nth 1 math-simplify-expr)
|
|
(- uxpon pxpon))))
|
|
(setcar unitp pname)
|
|
math-simplify-expr)))))))
|
|
|
|
(defvar math-try-cancel-units)
|
|
|
|
(math-defsimplify /
|
|
(and math-simplifying-units
|
|
(let ((np (cdr math-simplify-expr))
|
|
(math-try-cancel-units 0)
|
|
n nn)
|
|
(setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
|
|
(cdr (nth 2 math-simplify-expr))
|
|
(nthcdr 2 math-simplify-expr)))
|
|
(if (math-realp (car n))
|
|
(progn
|
|
(setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
|
|
(let ((calc-prefer-frac nil))
|
|
(math-div 1 (car n)))))
|
|
(setcar n 1)))
|
|
(while (eq (car-safe (setq n (car np))) '*)
|
|
(math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
|
|
(setq np (cdr (cdr n))))
|
|
(math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
|
|
(if (eq math-try-cancel-units 0)
|
|
(let* ((math-simplifying-units nil)
|
|
(base (math-simplify
|
|
(math-to-standard-units math-simplify-expr nil))))
|
|
(if (Math-numberp base)
|
|
(setq math-simplify-expr base))))
|
|
(if (eq (car-safe math-simplify-expr) '/)
|
|
(math-simplify-units-prod))
|
|
math-simplify-expr)))
|
|
|
|
(defun math-simplify-units-divisor (np dp)
|
|
(let ((n (car np))
|
|
d dd temp)
|
|
(while (eq (car-safe (setq d (car dp))) '*)
|
|
(when (setq temp (math-simplify-units-quotient n (nth 1 d)))
|
|
(setcar np (setq n temp))
|
|
(setcar (cdr d) 1))
|
|
(setq dp (cdr (cdr d))))
|
|
(when (setq temp (math-simplify-units-quotient n d))
|
|
(setcar np (setq n temp))
|
|
(setcar dp 1))))
|
|
|
|
;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
|
|
(defun math-simplify-units-quotient (n d)
|
|
(let ((pow1 1)
|
|
(pow2 1))
|
|
(when (and (eq (car-safe n) '^)
|
|
(integerp (nth 2 n)))
|
|
(setq pow1 (nth 2 n) n (nth 1 n)))
|
|
(when (and (eq (car-safe d) '^)
|
|
(integerp (nth 2 d)))
|
|
(setq pow2 (nth 2 d) d (nth 1 d)))
|
|
(let ((un (math-check-unit-name n))
|
|
(ud (math-check-unit-name d)))
|
|
(and un ud
|
|
(if (and (equal (nth 4 un) (nth 4 ud))
|
|
(eq pow1 pow2))
|
|
(if (eq pow1 1)
|
|
(math-to-standard-units (list '/ n d) nil)
|
|
(list '^ (math-to-standard-units (list '/ n d) nil) pow1))
|
|
(let (ud1)
|
|
(setq un (nth 4 un)
|
|
ud (nth 4 ud))
|
|
(while un
|
|
(setq ud1 ud)
|
|
(while ud1
|
|
(and (eq (car (car un)) (car (car ud1)))
|
|
(setq math-try-cancel-units
|
|
(+ math-try-cancel-units
|
|
(- (* (cdr (car un)) pow1)
|
|
(* (cdr (car ud)) pow2)))))
|
|
(setq ud1 (cdr ud1)))
|
|
(setq un (cdr un)))
|
|
nil))))))
|
|
|
|
(math-defsimplify ^
|
|
(and math-simplifying-units
|
|
(math-realp (nth 2 math-simplify-expr))
|
|
(if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
|
|
(list (car (nth 1 math-simplify-expr))
|
|
(list '^ (nth 1 (nth 1 math-simplify-expr))
|
|
(nth 2 math-simplify-expr))
|
|
(list '^ (nth 2 (nth 1 math-simplify-expr))
|
|
(nth 2 math-simplify-expr)))
|
|
(math-simplify-units-pow (nth 1 math-simplify-expr)
|
|
(nth 2 math-simplify-expr)))))
|
|
|
|
(math-defsimplify calcFunc-sqrt
|
|
(and math-simplifying-units
|
|
(if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
|
|
(list (car (nth 1 math-simplify-expr))
|
|
(list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
|
|
(list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
|
|
(math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
|
|
|
|
(math-defsimplify (calcFunc-floor
|
|
calcFunc-ceil
|
|
calcFunc-round
|
|
calcFunc-rounde
|
|
calcFunc-roundu
|
|
calcFunc-trunc
|
|
calcFunc-float
|
|
calcFunc-frac
|
|
calcFunc-abs
|
|
calcFunc-clean)
|
|
(and math-simplifying-units
|
|
(= (length math-simplify-expr) 2)
|
|
(if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
|
|
(nth 1 math-simplify-expr)
|
|
(if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
|
|
(or (math-only-units-in-expr-p
|
|
(nth 1 (nth 1 math-simplify-expr)))
|
|
(math-only-units-in-expr-p
|
|
(nth 2 (nth 1 math-simplify-expr)))))
|
|
(list (car (nth 1 math-simplify-expr))
|
|
(cons (car math-simplify-expr)
|
|
(cons (nth 1 (nth 1 math-simplify-expr))
|
|
(cdr (cdr math-simplify-expr))))
|
|
(cons (car math-simplify-expr)
|
|
(cons (nth 2 (nth 1 math-simplify-expr))
|
|
(cdr (cdr math-simplify-expr)))))))))
|
|
|
|
(defun math-simplify-units-pow (a pow)
|
|
(if (and (eq (car-safe a) '^)
|
|
(math-check-unit-name (nth 1 a))
|
|
(math-realp (nth 2 a)))
|
|
(list '^ (nth 1 a) (math-mul pow (nth 2 a)))
|
|
(let* ((u (math-check-unit-name a))
|
|
(pf (math-to-simple-fraction pow))
|
|
(d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
|
|
(and u d
|
|
(math-units-are-multiple u d)
|
|
(list '^ (math-to-standard-units a nil) pow)))))
|
|
|
|
|
|
(defun math-units-are-multiple (u n)
|
|
(setq u (nth 4 u))
|
|
(while (and u (= (% (cdr (car u)) n) 0))
|
|
(setq u (cdr u)))
|
|
(null u))
|
|
|
|
(math-defsimplify calcFunc-sin
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-sin (nth 1 rad))))))
|
|
|
|
(math-defsimplify calcFunc-cos
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-cos (nth 1 rad))))))
|
|
|
|
(math-defsimplify calcFunc-tan
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-tan (nth 1 rad))))))
|
|
|
|
(math-defsimplify calcFunc-sec
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-sec (nth 1 rad))))))
|
|
|
|
(math-defsimplify calcFunc-csc
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-csc (nth 1 rad))))))
|
|
|
|
(math-defsimplify calcFunc-cot
|
|
(and math-simplifying-units
|
|
(math-units-in-expr-p (nth 1 math-simplify-expr) nil)
|
|
(let ((rad (math-simplify-units
|
|
(math-evaluate-expr
|
|
(math-to-standard-units (nth 1 math-simplify-expr) nil))))
|
|
(calc-angle-mode 'rad))
|
|
(and (eq (car-safe rad) '*)
|
|
(math-realp (nth 1 rad))
|
|
(eq (car-safe (nth 2 rad)) 'var)
|
|
(eq (nth 1 (nth 2 rad)) 'rad)
|
|
(list 'calcFunc-cot (nth 1 rad))))))
|
|
|
|
|
|
(defun math-remove-units (expr)
|
|
(if (math-check-unit-name expr)
|
|
1
|
|
(if (Math-primp expr)
|
|
expr
|
|
(cons (car expr)
|
|
(mapcar 'math-remove-units (cdr expr))))))
|
|
|
|
(defun math-extract-units (expr)
|
|
(if (memq (car-safe expr) '(* /))
|
|
(cons (car expr)
|
|
(mapcar 'math-extract-units (cdr expr)))
|
|
(if (math-check-unit-name expr) expr 1)))
|
|
|
|
(defun math-build-units-table-buffer (enter-buffer)
|
|
(if (not (and math-units-table math-units-table-buffer-valid
|
|
(get-buffer "*Units Table*")))
|
|
(let ((buf (get-buffer-create "*Units Table*"))
|
|
(uptr (math-build-units-table))
|
|
(calc-language (if (eq calc-language 'big) nil calc-language))
|
|
(calc-float-format '(float 0))
|
|
(calc-group-digits nil)
|
|
(calc-number-radix 10)
|
|
(calc-point-char ".")
|
|
(std nil)
|
|
u name shadowed)
|
|
(save-excursion
|
|
(message "Formatting units table...")
|
|
(set-buffer buf)
|
|
(let ((inhibit-read-only t))
|
|
(erase-buffer)
|
|
(insert "Calculator Units Table:\n\n")
|
|
(insert "Unit Type Definition Description\n\n")
|
|
(while uptr
|
|
(setq u (car uptr)
|
|
name (nth 2 u))
|
|
(when (eq (car u) 'm)
|
|
(setq std t))
|
|
(setq shadowed (and std (assq (car u) math-additional-units)))
|
|
(when (and name
|
|
(> (length name) 1)
|
|
(eq (aref name 0) ?\*))
|
|
(unless (eq uptr math-units-table)
|
|
(insert "\n"))
|
|
(setq name (substring name 1)))
|
|
(insert " ")
|
|
(and shadowed (insert "("))
|
|
(insert (symbol-name (car u)))
|
|
(and shadowed (insert ")"))
|
|
(if (nth 3 u)
|
|
(progn
|
|
(indent-to 10)
|
|
(insert (symbol-name (nth 3 u))))
|
|
(or std
|
|
(progn
|
|
(indent-to 10)
|
|
(insert "U"))))
|
|
(indent-to 14)
|
|
(and shadowed (insert "("))
|
|
(if (nth 1 u)
|
|
(insert (math-format-value (nth 1 u) 80))
|
|
(insert (symbol-name (car u))))
|
|
(and shadowed (insert ")"))
|
|
(indent-to 41)
|
|
(insert " ")
|
|
(when name
|
|
(insert name))
|
|
(if shadowed
|
|
(insert " (redefined above)")
|
|
(unless (nth 1 u)
|
|
(insert " (base unit)")))
|
|
(insert "\n")
|
|
(setq uptr (cdr uptr)))
|
|
(insert "\n\nUnit Prefix Table:\n\n")
|
|
(setq uptr math-unit-prefixes)
|
|
(while uptr
|
|
(setq u (car uptr))
|
|
(insert " " (char-to-string (car u)))
|
|
(if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
|
|
(insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
|
|
" ")
|
|
(insert " "))
|
|
(insert "10^" (int-to-string (nth 2 (nth 1 u))))
|
|
(indent-to 15)
|
|
(insert " " (nth 2 u) "\n")
|
|
(while (eq (car (car (setq uptr (cdr uptr)))) 0)))
|
|
(insert "\n"))
|
|
(view-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*")))))
|
|
|
|
(provide 'calc-units)
|
|
|
|
;; Local Variables:
|
|
;; coding: iso-latin-1
|
|
;; End:
|
|
|
|
;;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
|
|
;;; calc-units.el ends here
|