lisp/calc/calc-units.el

   1 ;;; calc-units.el --- unit conversion functions for Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
   4
   5 ;; Author: David Gillespie <daveg@synaptics.com>
   6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
   7
   8 ;; This file is part of GNU Emacs.
   9
  10 ;; GNU Emacs is free software: you can redistribute it and/or modify
  11 ;; it under the terms of the GNU General Public License as published by
  12 ;; the Free Software Foundation, either version 3 of the License, or
  13 ;; (at your option) any later version.
  14
  15 ;; GNU Emacs is distributed in the hope that it will be useful,
  16 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
  17 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18 ;; GNU General Public License for more details.
  19
  20 ;; You should have received a copy of the GNU General Public License
  21 ;; along with GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
  22
  23 ;;; Commentary:
  24
  25 ;;; Code:
  26
  27 ;; This file is autoloaded from calc-ext.el.
  28
  29 (require 'calc-ext)
  30 (require 'calc-macs)
  31 (eval-when-compile
  32   (require 'calc-alg))
  33
  34 ;;; Units operations.
  35
  36 ;;; Units table last updated 9-Jan-91 by Ulrich Mueller (ulm@vsnhd1.cern.ch)
  37 ;;; with some additions by Przemek Klosowski (przemek@rrdstrad.nist.gov)
  38 ;;; Updated April 2002 by Jochen Küpper
  39
  40 ;;; Updated August 2007, using
  41 ;;;     CODATA (http://physics.nist.gov/cuu/Constants/index.html)
  42 ;;;     NIST   (http://physics.nist.gov/Pubs/SP811/appenB9.html)
  43 ;;;     ESUWM  (Encyclopaedia of Scientific Units, Weights and
  44 ;;;             Measures, by François Cardarelli)
  45 ;;; All conversions are exact unless otherwise noted.
  46
  47 (defvar math-standard-units
  48   '( ;; Length
  49     ( m       nil                    "*Meter" )
  50     ( in      "254*10^(-2) cm"       "Inch"  nil
  51               "2.54 cm")
  52     ( ft      "12 in"                "Foot")
  53     ( yd      "3 ft"                 "Yard" )
  54     ( mi      "5280 ft"              "Mile" )
  55     ( au      "149597870691. m"      "Astronomical Unit" nil
  56               "149597870691 m (*)")
  57               ;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
  58     ( lyr     "c yr"                 "Light Year" )
  59     ( pc      "3.0856775854*10^16 m" "Parsec  (**)" nil
  60               "3.0856775854 10^16 m (*)") ;; (approx) ESUWM
  61     ( nmi     "1852 m"               "Nautical Mile" )
  62     ( fath    "6 ft"                 "Fathom" )
  63     ( fur     "660 ft"               "Furlong")
  64     ( mu      "1 um"                 "Micron" )
  65     ( mil     "(1/1000) in"          "Mil" )
  66     ( point   "(1/72) in"            "Point  (PostScript convention)" )
  67     ( Ang     "10^(-10) m"           "Angstrom" )
  68     ( mfi     "mi+ft+in"             "Miles + feet + inches" )
  69     ;; TeX lengths
  70     ( texpt   "(100/7227) in"        "Point  (TeX convention) (**)" )
  71     ( texpc   "12 texpt"             "Pica  (TeX convention) (**)" )
  72     ( texbp   "point"                "Big point  (TeX convention) (**)" )
  73     ( texdd   "(1238/1157) texpt"    "Didot point  (TeX convention) (**)" )
  74     ( texcc   "12 texdd"             "Cicero  (TeX convention) (**)" )
  75     ( texsp   "(1/65536) texpt"      "Scaled TeX point (TeX convention) (**)" )
  76
  77     ;; Area
  78     ( hect    "10000 m^2"            "*Hectare" )
  79     ( a       "100 m^2"              "Are")
  80     ( acre    "(1/640) mi^2"         "Acre" )
  81     ( b       "10^(-28) m^2"         "Barn" )
  82
  83     ;; Volume
  84     ( L       "10^(-3) m^3"          "*Liter" )
  85     ( l       "L"                    "Liter" )
  86     ( gal     "4 qt"                 "US Gallon" )
  87     ( qt      "2 pt"                 "Quart" )
  88     ( pt      "2 cup"                "Pint (**)" )
  89     ( cup     "8 ozfl"               "Cup" )
  90     ( ozfl    "2 tbsp"               "Fluid Ounce" )
  91     ( floz    "2 tbsp"               "Fluid Ounce" )
  92     ( tbsp    "3 tsp"                "Tablespoon" )
  93     ;; ESUWM defines a US gallon as 231 in^3.
  94     ;; That gives the following exact value for tsp.
  95     ( tsp     "492892159375*10^(-11) ml" "Teaspoon" nil
  96               "4.92892159375 ml")
  97     ( vol     "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" nil
  98               "tsp+tbsp+ozfl+cup+pt+qt+gal")
  99     ( galC    "galUK"                "Canadian Gallon" )
 100     ( galUK   "454609*10^(-5) L"     "UK Gallon" nil
 101               "4.54609 L") ;; NIST
 102
 103     ;; Time
 104     ( s       nil                    "*Second" )
 105     ( sec     "s"                    "Second" )
 106     ( min     "60 s"                 "Minute" )
 107     ( hr      "60 min"               "Hour" )
 108     ( day     "24 hr"                "Day" )
 109     ( wk      "7 day"                "Week" )
 110     ( hms     "wk+day+hr+min+s"      "Hours, minutes, seconds" )
 111     ( yr      "36525*10^(-2) day"    "Year (Julian)" nil
 112               "365.25 day")
 113     ( Hz      "1/s"                  "Hertz" )
 114
 115     ;; Speed
 116     ( mph     "mi/hr"                "*Miles per hour" )
 117     ( kph     "km/hr"                "Kilometers per hour" )
 118     ( knot    "nmi/hr"               "Knot" )
 119     ( c       "299792458 m/s"        "Speed of light" ) ;;; CODATA
 120
 121     ;; Acceleration
 122     ( ga      "980665*10^(-5) m/s^2" "*\"g\" acceleration" nil
 123               "9.80665 m / s^2") ;; CODATA
 124
 125     ;; Mass
 126     ( g       nil                    "*Gram" )
 127     ( lb      "16 oz"                "Pound (mass)" )
 128     ( oz      "28349523125*10^(-9) g" "Ounce (mass)" nil
 129               "28.349523125 g") ;; ESUWM
 130     ( ton     "2000 lb"              "Ton" )
 131     ( tpo     "ton+lb+oz"            "Tons + pounds + ounces (mass)" )
 132     ( t       "1000 kg"              "Metric ton" )
 133     ( tonUK   "10160469088*10^(-7) kg" "UK ton" nil
 134               "1016.0469088 kg") ;; ESUWM
 135     ( lbt     "12 ozt"               "Troy pound" )
 136     ( ozt     "311034768*10^(-7) g"        "Troy ounce" nil
 137               "31.10347680 g") ;; ESUWM, 1/12 exact value for lbt
 138     ( ct      "(2/10) g"             "Carat" nil
 139               "0.2 g") ;; ESUWM
 140     ( u       "1.660538782*10^(-27) kg"    "Unified atomic mass" nil
 141               "1.660538782 10^-27 kg (*)");;(approx) CODATA
 142
 143     ;; Force
 144     ( N       "m kg/s^2"             "*Newton" )
 145     ( dyn     "10^(-5) N"            "Dyne" )
 146     ( gf      "ga g"                 "Gram (force)" )
 147     ( lbf     "ga lb"                "Pound (force)" )
 148     ( kip     "1000 lbf"             "Kilopound (force)" )
 149     ( pdl     "138254954376*10^(-12) N" "Poundal" nil
 150               "0.138254954376 N") ;; ESUWM
 151
 152     ;; Energy
 153     ( J       "N m"                  "*Joule" )
 154     ( erg     "10^(-7) J"            "Erg" )
 155     ( cal     "41868*10^(-4) J"      "International Table Calorie" nil
 156               "4.1868 J") ;; NIST
 157     ( calth   "4184*10^(-3) J"       "Thermochemical Calorie" nil
 158               "4.184 J") ;; NIST
 159     ( Cal     "1000 cal"             "Large Calorie")
 160     ( Btu     "105505585262*10^(-8) J" "International Table Btu" nil
 161               "1055.05585262 J") ;; ESUWM
 162     ( eV      "ech V"                "Electron volt" )
 163     ( ev      "eV"                   "Electron volt" )
 164     ( therm   "105506000 J"          "EEC therm" )
 165     ( invcm   "h c/cm"               "Energy in inverse centimeters" )
 166     ( Kayser  "invcm"                "Kayser (inverse centimeter energy)" )
 167     ( men     "100/invcm"            "Inverse energy in meters" )
 168     ( Hzen    "h Hz"                 "Energy in Hertz")
 169     ( Ken     "k K"                  "Energy in Kelvins")
 170     ( Wh      "W hr"                 "Watt hour")
 171     ( Ws      "W s"                  "Watt second")
 172
 173     ;; Power
 174     ( W       "J/s"                  "*Watt" )
 175     ( hp      "550 ft lbf/s"         "Horsepower") ;;ESUWM
 176     ( hpm     "75 m kgf/s"           "Metric Horsepower") ;;ESUWM
 177
 178     ;; Temperature
 179     ( K       nil                    "*Degree Kelvin"     K )
 180     ( dK      "K"                    "Degree Kelvin"      K )
 181     ( degK    "K"                    "Degree Kelvin"      K )
 182     ( dC      "K"                    "Degree Celsius"     C )
 183     ( degC    "K"                    "Degree Celsius"     C )
 184     ( dF      "(5/9) K"              "Degree Fahrenheit"  F )
 185     ( degF    "(5/9) K"              "Degree Fahrenheit"  F )
 186
 187     ;; Pressure
 188     ( Pa      "N/m^2"                "*Pascal" )
 189     ( bar     "10^5 Pa"              "Bar" )
 190     ( atm     "101325 Pa"            "Standard atmosphere" ) ;; CODATA
 191     ( Torr    "(1/760) atm"          "Torr")
 192     ( mHg     "1000 Torr"            "Meter of mercury" )
 193     ( inHg    "254*10^(-1) mmHg"     "Inch of mercury" nil
 194               "25.4 mmHg")
 195     ( inH2O   "2.490889*10^2 Pa"        "Inch of water" nil
 196               "2.490889 10^2 Pa (*)") ;;(approx) NIST
 197     ( psi     "lbf/in^2"             "Pounds per square inch" )
 198
 199     ;; Viscosity
 200     ( P       "(1/10) Pa s"           "*Poise" )
 201     ( St      "10^(-4) m^2/s"         "Stokes" )
 202
 203     ;; Electromagnetism
 204     ( A       nil                     "*Ampere" )
 205     ( C       "A s"                   "Coulomb" )
 206     ( Fdy     "ech Nav"               "Faraday" )
 207     ( e       "ech"                   "Elementary charge" )
 208     ( ech     "1.602176487*10^(-19) C"     "Elementary charge" nil
 209               "1.602176487 10^-19 C (*)") ;;(approx) CODATA
 210     ( V       "W/A"                   "Volt" )
 211     ( ohm     "V/A"                   "Ohm" )
 212     ( Ω       "ohm"                   "Ohm" )
 213     ( mho     "A/V"                   "Mho" )
 214     ( S       "A/V"                   "Siemens" )
 215     ( F       "C/V"                   "Farad" )
 216     ( H       "Wb/A"                  "Henry" )
 217     ( T       "Wb/m^2"                "Tesla" )
 218     ( Gs      "10^(-4) T"             "Gauss" )
 219     ( Wb      "V s"                   "Weber" )
 220
 221     ;; Luminous intensity
 222     ( cd      nil                     "*Candela" )
 223     ( sb      "10000 cd/m^2"          "Stilb" )
 224     ( lm      "cd sr"                 "Lumen" )
 225     ( lx      "lm/m^2"                "Lux" )
 226     ( ph      "10000 lx"              "Phot" )
 227     ( fc      "lm/ft^2"               "Footcandle") ;; ESUWM
 228     ( lam     "10000 lm/m^2"          "Lambert" )
 229     ( flam    "(1/pi) cd/ft^2"        "Footlambert") ;; ESUWM
 230
 231     ;; Radioactivity
 232     ( Bq      "1/s"                    "*Becquerel" )
 233     ( Ci      "37*10^9 Bq"             "Curie" ) ;; ESUWM
 234     ( Gy      "J/kg"                   "Gray" )
 235     ( Sv      "Gy"                     "Sievert" )
 236     ( R       "258*10^(-6) C/kg"       "Roentgen" ) ;; NIST
 237     ( rd      "(1/100) Gy"             "Rad" )
 238     ( rem     "rd"                     "Rem" )
 239
 240     ;; Amount of substance
 241     ( mol     nil                      "*Mole" )
 242
 243     ;; Plane angle
 244     ( rad     nil                      "*Radian" )
 245     ( circ    "2 pi rad"               "Full circle" )
 246     ( rev     "circ"                   "Full revolution" )
 247     ( deg     "circ/360"               "Degree" )
 248     ( arcmin  "deg/60"                 "Arc minute" )
 249     ( arcsec  "arcmin/60"              "Arc second" )
 250     ( grad    "circ/400"               "Grade" )
 251     ( rpm     "rev/min"                "Revolutions per minute" )
 252
 253     ;; Solid angle
 254     ( sr      nil                      "*Steradian" )
 255
 256     ;; Other physical quantities
 257     ;; The values are from CODATA, and are approximate.
 258     ( h       "6.62606896*10^(-34) J s"     "*Planck's constant" nil
 259               "6.62606896 10^-34 J s (*)")
 260     ( hbar    "h / (2 pi)"                  "Planck's constant" ) ;; Exact
 261     ( mu0     "4 pi 10^(-7) H/m"            "Permeability of vacuum") ;; Exact
 262     ( μ0      "mu0"                         "Permeability of vacuum") ;; Exact
 263     ( eps0    "1 / (mu0 c^2)"               "Permittivity of vacuum" )
 264     ( ε0      "eps0"                        "Permittivity of vacuum" )
 265     ( G       "6.67428*10^(-11) m^3/(kg s^2)"    "Gravitational constant" nil
 266               "6.67428 10^-11 m^3/(kg s^2) (*)")
 267     ( Nav     "6.02214179*10^(23) / mol"    "Avogadro's constant" nil
 268               "6.02214179 10^23 / mol (*)")
 269     ( me      "9.10938215*10^(-31) kg"      "Electron rest mass" nil
 270               "9.10938215 10^-31 kg (*)")
 271     ( mp      "1.672621637*10^(-27) kg"     "Proton rest mass" nil
 272               "1.672621637 10^-27 kg (*)")
 273     ( mn      "1.674927211*10^(-27) kg"     "Neutron rest mass" nil
 274               "1.674927211 10^-27 kg (*)")
 275     ( mmu     "1.88353130*10^(-28) kg"      "Muon rest mass" nil
 276               "1.88353130 10^-28 kg (*)")
 277     ( mμ      "mmu"                         "Muon rest mass" nil
 278               "1.88353130 10^-28 kg (*)")
 279     ( Ryd     "10973731.568527 /m"          "Rydberg's constant" nil
 280               "10973731.568527 /m (*)")
 281     ( k       "1.3806504*10^(-23) J/K"      "Boltzmann's constant" nil
 282               "1.3806504 10^-23 J/K (*)")
 283     ( alpha   "7.2973525376*10^(-3)"        "Fine structure constant" nil
 284               "7.2973525376 10^-3 (*)")
 285     ( α       "alpha"                        "Fine structure constant" nil
 286               "7.2973525376 10^-3 (*)")
 287     ( muB     "927.400915*10^(-26) J/T"     "Bohr magneton" nil
 288               "927.400915 10^-26 J/T (*)")
 289     ( muN     "5.05078324*10^(-27) J/T"     "Nuclear magneton" nil
 290               "5.05078324 10^-27 J/T (*)")
 291     ( mue     "-928.476377*10^(-26) J/T"    "Electron magnetic moment" nil
 292               "-928.476377 10^-26 J/T (*)")
 293     ( mup     "1.410606662*10^(-26) J/T"    "Proton magnetic moment" nil
 294               "1.410606662 10^-26 J/T (*)")
 295     ( R0      "8.314472 J/(mol K)"          "Molar gas constant" nil
 296               "8.314472 J/(mol K) (*)")
 297     ( V0      "22.710981*10^(-3) m^3/mol"   "Standard volume of ideal gas" nil
 298               "22.710981 10^-3 m^3/mol (*)")
 299     ;; Logarithmic units
 300     ( Np      nil    "*Neper")
 301     ( dB      "(ln(10)/20) Np" "decibel")))
 302
 303
 304 (defvar math-additional-units nil
 305   "Additional units table for user-defined units.
 306 Must be formatted like `math-standard-units'.
 307 If you change this, be sure to set `math-units-table' to nil to ensure
 308 that the combined units table will be rebuilt.")
 309
 310 (defvar math-unit-prefixes
 311   '( ( ?Y  (^ 10 24)  "Yotta"  )
 312      ( ?Z  (^ 10 21)  "Zetta"  )
 313      ( ?E  (^ 10 18)  "Exa"    )
 314      ( ?P  (^ 10 15)  "Peta"   )
 315      ( ?T  (^ 10 12)  "Tera"   )
 316      ( ?G  (^ 10 9)   "Giga"   )
 317      ( ?M  (^ 10 6)   "Mega"   )
 318      ( ?k  (^ 10 3)   "Kilo"   )
 319      ( ?K  (^ 10 3)   "Kilo"   )
 320      ( ?h  (^ 10 2)   "Hecto"  )
 321      ( ?H  (^ 10 2)   "Hecto"  )
 322      ( ?D  (^ 10 1)   "Deka"   )
 323      ( 0   (^ 10 0)    nil     )
 324      ( ?d  (^ 10 -1)  "Deci"   )
 325      ( ?c  (^ 10 -2)  "Centi"  )
 326      ( ?m  (^ 10 -3)  "Milli"  )
 327      ( ?u  (^ 10 -6)  "Micro"  )
 328      ( ?μ  (^ 10 -6)  "Micro"  )
 329      ( ?n  (^ 10 -9)  "Nano"   )
 330      ( ?p  (^ 10 -12) "Pico"   )
 331      ( ?f  (^ 10 -15) "Femto"  )
 332      ( ?a  (^ 10 -18) "Atto"   )
 333      ( ?z  (^ 10 -21) "zepto"  )
 334      ( ?y  (^ 10 -24) "yocto"  )))
 335
 336 (defvar math-standard-units-systems
 337   '( ( base  nil )
 338      ( si    ( ( g   '(/ (var kg var-kg) 1000) ) ) )
 339      ( mks   ( ( g   '(/ (var kg var-kg) 1000) ) ) )
 340      ( cgs   ( ( m   '(* (var cm var-cm) 100 ) ) ) )))
 341
 342 (defvar math-units-table nil
 343   "Internal units table.
 344 Derived from `math-standard-units' and `math-additional-units'.
 345 Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).")
 346
 347 (defvar math-units-table-buffer-valid nil)
 348
 349 ;;; Units commands.
 350
 351 (defun calc-base-units ()
 352   (interactive)
 353   (calc-slow-wrapper
 354    (let ((calc-autorange-units nil))
 355      (calc-enter-result 1 "bsun" (math-simplify-units
 356                                   (math-to-standard-units (calc-top-n 1)
 357                                                           nil))))))
 358
 359 (defvar calc-ensure-consistent-units)
 360
 361 (defun calc-quick-units ()
 362   (interactive)
 363   (calc-slow-wrapper
 364    (let* ((num (- last-command-event ?0))
 365           (pos (if (= num 0) 10 num))
 366           (units (calc-var-value 'var-Units))
 367           (expr (calc-top-n 1)))
 368      (unless (and (>= num 0) (<= num 9))
 369        (error "Bad unit number"))
 370      (unless (math-vectorp units)
 371        (error "No \"quick units\" are defined"))
 372      (unless (< pos (length units))
 373        (error "Unit number %d not defined" pos))
 374      (if (math-units-in-expr-p expr nil)
 375          (progn
 376            (if calc-ensure-consistent-units
 377                (math-check-unit-consistency expr (nth pos units)))
 378            (calc-enter-result 1 (format "cun%d" num)
 379                               (math-convert-units expr (nth pos units))))
 380        (calc-enter-result 1 (format "*un%d" num)
 381                           (math-simplify-units
 382                            (math-mul expr (nth pos units))))))))
 383
 384 (defun math-get-standard-units (expr)
 385   "Return the standard units in EXPR."
 386   (math-simplify-units
 387    (math-extract-units
 388     (math-to-standard-units expr nil))))
 389
 390 (defun math-get-units (expr)
 391   "Return the units in EXPR."
 392   (math-simplify-units
 393    (math-extract-units expr)))
 394
 395 (defun math-make-unit-string (expr)
 396   "Return EXPR in string form.
 397 If EXPR is nil, return nil."
 398   (if expr
 399       (let ((cexpr (math-compose-expr expr 0)))
 400         (replace-regexp-in-string
 401          " / " "/"
 402          (if (stringp cexpr)
 403              cexpr
 404            (math-composition-to-string cexpr))))))
 405
 406 (defvar math-default-units-table
 407   (make-hash-table :test 'equal)
 408   "A table storing previously converted units.")
 409
 410 (defun math-get-default-units (expr)
 411   "Get default units to use when converting the units in EXPR."
 412   (let* ((units (math-get-units expr))
 413          (standard-units (math-get-standard-units expr))
 414          (default-units (gethash
 415                          standard-units
 416                          math-default-units-table)))
 417     (if (equal units (car default-units))
 418         (math-make-unit-string (cadr default-units))
 419       (math-make-unit-string (car default-units)))))
 420
 421 (defun math-put-default-units (expr &optional comp std)
 422   "Put the units in EXPR in the default units table.
 423 If COMP or STD is non-nil, put that in the units table instead."
 424   (let* ((new-units (or comp std (math-get-units expr)))
 425          (standard-units (math-get-standard-units
 426                           (cond
 427                            (comp (math-simplify-units expr))
 428                            (std expr)
 429                            (t new-units))))
 430          (default-units (gethash standard-units math-default-units-table)))
 431     (unless (eq standard-units 1)
 432       (cond
 433        ((not default-units)
 434         (puthash standard-units (list new-units) math-default-units-table))
 435        ((not (equal new-units (car default-units)))
 436         (puthash standard-units
 437                  (list new-units (car default-units))
 438                  math-default-units-table))))))
 439
 440 (defvar calc-allow-units-as-numbers t)
 441
 442 (defun calc-convert-units (&optional old-units new-units)
 443   (interactive)
 444   (calc-slow-wrapper
 445    (let ((expr (calc-top-n 1))
 446          (uoldname nil)
 447          (unitscancel nil)
 448          (nouold nil)
 449          unew
 450          units
 451          defunits)
 452      (if (or (not (math-units-in-expr-p expr t))
 453              (setq unitscancel (and
 454                                 (if (get 'calc-allow-units-as-numbers 'saved-value)
 455                                     (car (get 'calc-allow-units-as-numbers 'saved-value))
 456                                   calc-allow-units-as-numbers)
 457                                 (eq (math-get-standard-units expr) 1))))
 458        (let ((uold (or old-units
 459                        (progn
 460                          (setq uoldname
 461                                (if unitscancel
 462                                    (read-string
 463                                     "(The expression is unitless when simplified) Old Units: ")
 464                                  (read-string "Old units: ")))
 465                          (if (equal uoldname "")
 466                              (progn
 467                                (setq nouold unitscancel)
 468                                (setq uoldname "1")
 469                                1)
 470                            (if (string-match "\\` */" uoldname)
 471                                (setq uoldname (concat "1" uoldname)))
 472                            (math-read-expr uoldname))))))
 473          (unless (math-units-in-expr-p uold t)
 474            (error "No units specified"))
 475          (when (eq (car-safe uold) 'error)
 476            (error "Bad format in units expression: %s" (nth 1 uold)))
 477          (setq expr (math-mul expr uold))))
 478      (setq defunits (math-get-default-units expr))
 479      (unless new-units
 480        (setq new-units
 481              (read-string (concat
 482                            (if (and uoldname (not nouold))
 483                                (concat "Old units: "
 484                                        uoldname
 485                                        ", new units")
 486                              "New units")
 487                            (if defunits
 488                                (concat
 489                                 " (default "
 490                                 defunits
 491                                 "): ")
 492                              ": "))))
 493        (if (and
 494             (string= new-units "")
 495             defunits)
 496            (setq new-units defunits)))
 497      (when (string-match "\\` */" new-units)
 498        (setq new-units (concat "1" new-units)))
 499      (setq units (math-read-expr new-units))
 500      (when (eq (car-safe units) 'error)
 501        (error "Bad format in units expression: %s" (nth 2 units)))
 502      (if calc-ensure-consistent-units
 503          (math-check-unit-consistency expr units))
 504      (let ((unew (math-units-in-expr-p units t))
 505            (std (and (eq (car-safe units) 'var)
 506                      (assq (nth 1 units) math-standard-units-systems)))
 507            (comp (eq (car-safe units) '+)))
 508        (unless (or unew std)
 509          (error "No units specified"))
 510        (let* ((noold (and uoldname (not (equal uoldname "1"))))
 511               (res
 512                (if std
 513                    (math-simplify-units (math-to-standard-units expr (nth 1 std)))
 514                  (math-convert-units expr units noold))))
 515          (unless std
 516            (math-put-default-units (if noold units res) (if comp units)))
 517          (calc-enter-result 1 "cvun" res))))))
 518
 519 (defun calc-convert-exact-units ()
 520   (interactive)
 521   (calc-slow-wrapper
 522    (let* ((expr (calc-top-n 1)))
 523      (unless (math-units-in-expr-p expr t)
 524        (error "No units in expression."))
 525      (let* ((old-units (math-extract-units expr))
 526             (defunits (math-get-default-units expr))
 527             units
 528             (new-units
 529              (read-string (concat "New units"
 530                                   (if defunits
 531                                      (concat
 532                                       " (default "
 533                                       defunits
 534                                       "): ")
 535                                    ": ")))))
 536        (if (and
 537             (string= new-units "")
 538             defunits)
 539            (setq new-units defunits))
 540        (setq units (math-read-expr new-units))
 541        (when (eq (car-safe units) 'error)
 542          (error "Bad format in units expression: %s" (nth 2 units)))
 543        (math-check-unit-consistency old-units units)
 544        (let ((res
 545               (list '* (math-mul (math-remove-units expr)
 546                                  (math-simplify-units
 547                                   (math-to-standard-units (list '/ old-units units) nil)))
 548                     units)))
 549          (calc-enter-result 1 "cvxu" res))))))
 550
 551 (defun calc-autorange-units (arg)
 552   (interactive "P")
 553   (calc-wrapper
 554    (calc-change-mode 'calc-autorange-units arg nil t)
 555    (message (if calc-autorange-units
 556                 "Adjusting target unit prefix automatically"
 557               "Using target units exactly"))))
 558
 559 (defun calc-convert-temperature (&optional old-units new-units)
 560   (interactive)
 561   (calc-slow-wrapper
 562    (let ((expr (calc-top-n 1))
 563          (uold nil)
 564          (uoldname nil)
 565          unew
 566          defunits)
 567      (setq uold (or old-units
 568                     (let ((units (math-single-units-in-expr-p expr)))
 569                       (if units
 570                           (if (consp units)
 571                               (list 'var (car units)
 572                                     (intern (concat "var-"
 573                                                     (symbol-name
 574                                                      (car units)))))
 575                             (error "Not a pure temperature expression"))
 576                         (math-read-expr
 577                          (setq uoldname (read-string
 578                                          "Old temperature units: ")))))))
 579      (when (eq (car-safe uold) 'error)
 580        (error "Bad format in units expression: %s" (nth 2 uold)))
 581      (or (math-units-in-expr-p expr nil)
 582          (setq expr (math-mul expr uold)))
 583      (setq defunits (math-get-default-units expr))
 584      (setq unew (or new-units
 585                     (read-string
 586                      (concat
 587                       (if uoldname
 588                           (concat "Old temperature units: "
 589                                   uoldname
 590                                   ", new units")
 591                         "New temperature units")
 592                       (if defunits
 593                           (concat " (default "
 594                                   defunits
 595                                   "): ")
 596                         ": ")))))
 597      (setq unew (math-read-expr (if (string= unew "") defunits unew)))
 598      (when (eq (car-safe unew) 'error)
 599        (error "Bad format in units expression: %s" (nth 2 unew)))
 600      (math-put-default-units unew)
 601      (let ((ntemp (calc-normalize
 602                    (math-simplify-units
 603                     (math-convert-temperature expr uold unew
 604                                               uoldname)))))
 605        (if (Math-zerop ntemp)
 606            (setq ntemp (list '* ntemp unew)))
 607        (let ((calc-simplify-mode 'none))
 608          (calc-enter-result 1 "cvtm" ntemp))))))
 609
 610 (defun calc-remove-units ()
 611   (interactive)
 612   (calc-slow-wrapper
 613    (calc-enter-result 1 "rmun" (math-simplify-units
 614                                 (math-remove-units (calc-top-n 1))))))
 615
 616 (defun calc-extract-units ()
 617   (interactive)
 618   (calc-slow-wrapper
 619    (calc-enter-result 1 "exun" (math-simplify-units
 620                                 (math-extract-units (calc-top-n 1))))))
 621
 622 ;; The variables calc-num-units and calc-den-units are local to
 623 ;; calc-explain-units, but are used by calc-explain-units-rec,
 624 ;; which is called by calc-explain-units.
 625 (defvar calc-num-units)
 626 (defvar calc-den-units)
 627
 628 (defun calc-explain-units ()
 629   (interactive)
 630   (calc-wrapper
 631    (let ((calc-num-units nil)
 632          (calc-den-units nil))
 633      (calc-explain-units-rec (calc-top-n 1) 1)
 634      (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
 635           (setq calc-den-units (concat "(" calc-den-units ")")))
 636      (if calc-num-units
 637          (if calc-den-units
 638              (message "%s per %s" calc-num-units calc-den-units)
 639            (message "%s" calc-num-units))
 640        (if calc-den-units
 641            (message "1 per %s" calc-den-units)
 642          (message "No units in expression"))))))
 643
 644 (defun calc-explain-units-rec (expr pow)
 645   (let ((u (math-check-unit-name expr))
 646         pos)
 647     (if (and u (not (math-zerop pow)))
 648         (let ((name (or (nth 2 u) (symbol-name (car u)))))
 649           (if (eq (aref name 0) ?\*)
 650               (setq name (substring name 1)))
 651           (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 652               (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name)
 653                   (while (setq pos (string-match "[ ()]" name))
 654                     (setq name (concat (substring name 0 pos)
 655                                        (if (eq (aref name pos) 32) "-" "")
 656                                        (substring name (1+ pos)))))
 657                 (setq name (concat "(" name ")"))))
 658           (or (eq (nth 1 expr) (car u))
 659               (setq name (concat (nth 2 (assq (aref (symbol-name
 660                                                      (nth 1 expr)) 0)
 661                                               math-unit-prefixes))
 662                                  (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 663                                           (not (memq (car u) '(mHg gf))))
 664                                      (concat "-" name)
 665                                    (downcase name)))))
 666           (cond ((or (math-equal-int pow 1)
 667                      (math-equal-int pow -1)))
 668                 ((or (math-equal-int pow 2)
 669                      (math-equal-int pow -2))
 670                  (if (equal (nth 4 u) '((m . 1)))
 671                      (setq name (concat "Square-" name))
 672                    (setq name (concat name "-squared"))))
 673                 ((or (math-equal-int pow 3)
 674                      (math-equal-int pow -3))
 675                  (if (equal (nth 4 u) '((m . 1)))
 676                      (setq name (concat "Cubic-" name))
 677                    (setq name (concat name "-cubed"))))
 678                 (t
 679                  (setq name (concat name "^"
 680                                     (math-format-number (math-abs pow))))))
 681           (if (math-posp pow)
 682               (setq calc-num-units (if calc-num-units
 683                                   (concat calc-num-units " " name)
 684                                 name))
 685             (setq calc-den-units (if calc-den-units
 686                                 (concat calc-den-units " " name)
 687                               name))))
 688       (cond ((eq (car-safe expr) '*)
 689              (calc-explain-units-rec (nth 1 expr) pow)
 690              (calc-explain-units-rec (nth 2 expr) pow))
 691             ((eq (car-safe expr) '/)
 692              (calc-explain-units-rec (nth 1 expr) pow)
 693              (calc-explain-units-rec (nth 2 expr) (- pow)))
 694             ((memq (car-safe expr) '(neg + -))
 695              (calc-explain-units-rec (nth 1 expr) pow))
 696             ((and (eq (car-safe expr) '^)
 697                   (math-realp (nth 2 expr)))
 698              (calc-explain-units-rec (nth 1 expr)
 699                                      (math-mul pow (nth 2 expr))))))))
 700
 701 (defun calc-simplify-units ()
 702   (interactive)
 703   (calc-slow-wrapper
 704    (calc-with-default-simplification
 705     (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
 706
 707 (defun calc-view-units-table (n)
 708   (interactive "P")
 709   (and n (setq math-units-table-buffer-valid nil))
 710   (let ((win (get-buffer-window "*Units Table*")))
 711     (if (and win
 712              math-units-table
 713              math-units-table-buffer-valid)
 714         (progn
 715           (bury-buffer (window-buffer win))
 716           (let ((curwin (selected-window)))
 717             (select-window win)
 718             (switch-to-buffer nil)
 719             (select-window curwin)))
 720       (math-build-units-table-buffer nil))))
 721
 722 (defun calc-enter-units-table (n)
 723   (interactive "P")
 724   (and n (setq math-units-table-buffer-valid nil))
 725   (math-build-units-table-buffer t)
 726   (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
 727
 728 (defun calc-define-unit (uname desc &optional disp)
 729   (interactive "SDefine unit name: \nsDescription: \nP")
 730   (if disp (setq disp (read-string "Display definition: ")))
 731   (calc-wrapper
 732    (let ((form (calc-top-n 1))
 733          (unit (assq uname math-additional-units)))
 734      (or unit
 735          (setq math-additional-units
 736                (cons (setq unit (list uname nil nil nil nil))
 737                      math-additional-units)
 738                math-units-table nil))
 739      (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
 740                                        (eq (nth 1 form) uname)))
 741                              (not (math-equal-int form 1))
 742                              (math-format-flat-expr form 0)))
 743      (setcar (cdr (cdr unit)) (and (not (equal desc ""))
 744                                    desc))
 745      (if disp
 746          (setcar (cdr (cdr (cdr (cdr unit)))) disp))))
 747   (calc-invalidate-units-table))
 748
 749 (defun calc-undefine-unit (uname)
 750   (interactive "SUndefine unit name: ")
 751   (calc-wrapper
 752    (let ((unit (assq uname math-additional-units)))
 753      (or unit
 754          (if (assq uname math-standard-units)
 755              (error "\"%s\" is a predefined unit name" uname)
 756            (error "Unit name \"%s\" not found" uname)))
 757      (setq math-additional-units (delq unit math-additional-units)
 758            math-units-table nil)))
 759   (calc-invalidate-units-table))
 760
 761 (defun calc-invalidate-units-table ()
 762   (setq math-units-table nil)
 763   (let ((buf (get-buffer "*Units Table*")))
 764     (and buf
 765          (with-current-buffer buf
 766            (save-excursion
 767              (goto-char (point-min))
 768              (if (looking-at "Calculator Units Table")
 769                  (let ((inhibit-read-only t))
 770                    (insert "(Obsolete) "))))))))
 771
 772 (defun calc-get-unit-definition (uname)
 773   (interactive "SGet definition for unit: ")
 774   (calc-wrapper
 775    (math-build-units-table)
 776    (let ((unit (assq uname math-units-table)))
 777      (or unit
 778          (error "Unit name \"%s\" not found" uname))
 779      (let ((msg (nth 2 unit)))
 780        (if (stringp msg)
 781            (if (string-match "^\\*" msg)
 782                (setq msg (substring msg 1)))
 783          (setq msg (symbol-name uname)))
 784        (if (nth 1 unit)
 785            (progn
 786              (calc-enter-result 0 "ugdf" (nth 1 unit))
 787              (message "Derived unit: %s" msg))
 788          (calc-enter-result 0 "ugdf" (list 'var uname
 789                                            (intern
 790                                             (concat "var-"
 791                                                     (symbol-name uname)))))
 792          (message "Base unit: %s" msg))))))
 793
 794 (defun calc-permanent-units ()
 795   (interactive)
 796   (calc-wrapper
 797    (let (pos)
 798      (set-buffer (find-file-noselect (substitute-in-file-name
 799                                       calc-settings-file)))
 800      (goto-char (point-min))
 801      (if (and (search-forward ";;; Custom units stored by Calc" nil t)
 802               (progn
 803                 (beginning-of-line)
 804                 (setq pos (point))
 805                 (search-forward "\n;;; End of custom units" nil t)))
 806          (progn
 807            (beginning-of-line)
 808            (forward-line 1)
 809            (delete-region pos (point)))
 810        (goto-char (point-max))
 811        (insert "\n\n")
 812        (forward-char -1))
 813      (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
 814      (if math-additional-units
 815          (progn
 816            (insert "(setq math-additional-units '(\n")
 817            (let ((list math-additional-units))
 818              (while list
 819                (insert "  (" (symbol-name (car (car list))) " "
 820                        (if (nth 1 (car list))
 821                            (if (stringp (nth 1 (car list)))
 822                                (prin1-to-string (nth 1 (car list)))
 823                              (prin1-to-string (math-format-flat-expr
 824                                                (nth 1 (car list)) 0)))
 825                          "nil")
 826                        " "
 827                        (prin1-to-string (nth 2 (car list)))
 828                        ")\n")
 829                (setq list (cdr list))))
 830            (insert "))\n"))
 831        (insert ";;; (no custom units defined)\n"))
 832      (insert ";;; End of custom units\n")
 833      (save-buffer))))
 834
 835
 836 ;; The variable math-cu-unit-list is local to math-build-units-table,
 837 ;; but is used by math-compare-unit-names, which is called (indirectly)
 838 ;; by math-build-units-table.
 839 ;; math-cu-unit-list is also local to math-convert-units, but is used
 840 ;; by math-convert-units-rec, which is called by math-convert-units.
 841 (defvar math-cu-unit-list)
 842
 843 (defun math-build-units-table ()
 844   (or math-units-table
 845       (let* ((combined-units (append math-additional-units
 846                                      math-standard-units))
 847              (math-cu-unit-list (mapcar 'car combined-units))
 848              tab)
 849         (message "Building units table...")
 850         (setq math-units-table-buffer-valid nil)
 851         (setq tab (mapcar (function
 852                            (lambda (x)
 853                              (list (car x)
 854                                    (and (nth 1 x)
 855                                         (if (stringp (nth 1 x))
 856                                             (let ((exp (math-read-plain-expr
 857                                                         (nth 1 x))))
 858                                               (if (eq (car-safe exp) 'error)
 859                                                   (error "Format error in definition of %s in units table: %s"
 860                                                          (car x) (nth 2 exp))
 861                                                 exp))
 862                                           (nth 1 x)))
 863                                    (nth 2 x)
 864                                    (nth 3 x)
 865                                    (and (not (nth 1 x))
 866                                         (list (cons (car x) 1)))
 867                                    (nth 4 x))))
 868                           combined-units))
 869         (let ((math-units-table tab))
 870           (mapc 'math-find-base-units tab))
 871         (message "Building units table...done")
 872         (setq math-units-table tab))))
 873
 874 ;; The variables math-fbu-base and math-fbu-entry are local to
 875 ;; math-find-base-units, but are used by math-find-base-units-rec,
 876 ;; which is called by math-find-base-units.
 877 (defvar math-fbu-base)
 878 (defvar math-fbu-entry)
 879
 880 (defun math-find-base-units (math-fbu-entry)
 881   (if (eq (nth 4 math-fbu-entry) 'boom)
 882       (error "Circular definition involving unit %s" (car math-fbu-entry)))
 883   (or (nth 4 math-fbu-entry)
 884       (let (math-fbu-base)
 885         (setcar (nthcdr 4 math-fbu-entry) 'boom)
 886         (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
 887         '(or math-fbu-base
 888             (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
 889         (while (eq (cdr (car math-fbu-base)) 0)
 890           (setq math-fbu-base (cdr math-fbu-base)))
 891         (let ((b math-fbu-base))
 892           (while (cdr b)
 893             (if (eq (cdr (car (cdr b))) 0)
 894                 (setcdr b (cdr (cdr b)))
 895               (setq b (cdr b)))))
 896         (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
 897         (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
 898         math-fbu-base)))
 899
 900 (defun math-compare-unit-names (a b)
 901   (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
 902
 903 (defun math-find-base-units-rec (expr pow)
 904   (let ((u (math-check-unit-name expr)))
 905     (cond (u
 906            (let ((ulist (math-find-base-units u)))
 907              (while ulist
 908                (let ((p (* (cdr (car ulist)) pow))
 909                      (old (assq (car (car ulist)) math-fbu-base)))
 910                  (if old
 911                      (setcdr old (+ (cdr old) p))
 912                    (setq math-fbu-base
 913                          (cons (cons (car (car ulist)) p) math-fbu-base))))
 914                (setq ulist (cdr ulist)))))
 915           ((math-scalarp expr))
 916           ((and (eq (car expr) '^)
 917                 (integerp (nth 2 expr)))
 918            (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
 919           ((eq (car expr) '*)
 920            (math-find-base-units-rec (nth 1 expr) pow)
 921            (math-find-base-units-rec (nth 2 expr) pow))
 922           ((eq (car expr) '/)
 923            (math-find-base-units-rec (nth 1 expr) pow)
 924            (math-find-base-units-rec (nth 2 expr) (- pow)))
 925           ((eq (car expr) 'neg)
 926            (math-find-base-units-rec (nth 1 expr) pow))
 927           ((eq (car expr) '+)
 928            (math-find-base-units-rec (nth 1 expr) pow))
 929           ((eq (car expr) 'var)
 930            (or (eq (nth 1 expr) 'pi)
 931                (error "Unknown name %s in defining expression for unit %s"
 932                       (nth 1 expr) (car math-fbu-entry))))
 933           ((equal expr '(calcFunc-ln 10)))
 934           (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
 935
 936
 937 (defun math-units-in-expr-p (expr sub-exprs)
 938   (and (consp expr)
 939        (if (eq (car expr) 'var)
 940            (math-check-unit-name expr)
 941          (if (eq (car expr) 'neg)
 942              (math-units-in-expr-p (nth 1 expr) sub-exprs)
 943            (and (or sub-exprs
 944                     (memq (car expr) '(* / ^)))
 945                 (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
 946                     (math-units-in-expr-p (nth 2 expr) sub-exprs)))))))
 947
 948 (defun math-only-units-in-expr-p (expr)
 949   (and (consp expr)
 950        (if (eq (car expr) 'var)
 951            (math-check-unit-name expr)
 952          (if (memq (car expr) '(* /))
 953              (and (math-only-units-in-expr-p (nth 1 expr))
 954                   (math-only-units-in-expr-p (nth 2 expr)))
 955            (and (eq (car expr) '^)
 956                 (and (math-only-units-in-expr-p (nth 1 expr))
 957                      (math-realp (nth 2 expr))))))))
 958
 959 (defun math-single-units-in-expr-p (expr)
 960   (cond ((math-scalarp expr) nil)
 961         ((eq (car expr) 'var)
 962          (math-check-unit-name expr))
 963         ((eq (car expr) 'neg)
 964          (math-single-units-in-expr-p (nth 1 expr)))
 965         ((eq (car expr) '*)
 966          (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
 967                (u2 (math-single-units-in-expr-p (nth 2 expr))))
 968            (or (and u1 u2 'wrong)
 969                u1
 970                u2)))
 971         ((eq (car expr) '/)
 972          (if (math-units-in-expr-p (nth 2 expr) nil)
 973              'wrong
 974            (math-single-units-in-expr-p (nth 1 expr))))
 975         (t 'wrong)))
 976
 977 (defun math-consistent-units-p (expr newunits)
 978   "Non-nil if EXPR and NEWUNITS have consistent units."
 979   (or
 980    (and (eq (car-safe newunits) 'var)
 981         (assq (nth 1 newunits) math-standard-units-systems))
 982    (math-numberp (math-get-units (math-to-standard-units (list '/ expr newunits) nil)))))
 983
 984 (defun math-check-unit-consistency (expr units)
 985   "Give an error if EXPR and UNITS do not have consistent units."
 986   (unless  (math-consistent-units-p expr units)
 987     (error "New units (%s) are inconsistent with current units (%s)"
 988            (math-format-value units)
 989            (math-format-value (math-get-units expr)))))
 990
 991 (defun math-check-unit-name (v)
 992   (and (eq (car-safe v) 'var)
 993        (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
 994            (let ((name (symbol-name (nth 1 v))))
 995              (and (> (length name) 1)
 996                   (assq (aref name 0) math-unit-prefixes)
 997                   (or (assq (intern (substring name 1)) math-units-table)
 998                       (and (eq (aref name 0) ?M)
 999                            (> (length name) 3)
1000                            (eq (aref name 1) ?e)
1001                            (eq (aref name 2) ?g)
1002                            (assq (intern (substring name 3))
1003                                  math-units-table))))))))
1004
1005 ;; The variable math-which-standard is local to math-to-standard-units,
1006 ;; but is used by math-to-standard-rec, which is called by
1007 ;; math-to-standard-units.
1008 (defvar math-which-standard)
1009
1010 (defun math-to-standard-units (expr math-which-standard)
1011   (math-to-standard-rec expr))
1012
1013 (defun math-to-standard-rec (expr)
1014   (if (eq (car-safe expr) 'var)
1015       (let ((u (math-check-unit-name expr))
1016             (base (nth 1 expr)))
1017         (if u
1018             (progn
1019               (if (nth 1 u)
1020                   (setq expr (math-to-standard-rec (nth 1 u)))
1021                 (let ((st (assq (car u) math-which-standard)))
1022                   (if st
1023                       (setq expr (nth 1 st))
1024                     (setq expr (list 'var (car u)
1025                                      (intern (concat "var-"
1026                                                      (symbol-name
1027                                                       (car u)))))))))
1028               (or (null u)
1029                   (eq base (car u))
1030                   (setq expr (list '*
1031                                    (nth 1 (assq (aref (symbol-name base) 0)
1032                                                 math-unit-prefixes))
1033                                    expr)))
1034               expr)
1035           (if (eq base 'pi)
1036               (math-pi)
1037             expr)))
1038     (if (or
1039          (Math-primp expr)
1040          (and (eq (car-safe expr) 'calcFunc-subscr)
1041               (eq (car-safe (nth 1 expr)) 'var)))
1042         expr
1043       (cons (car expr)
1044             (mapcar 'math-to-standard-rec (cdr expr))))))
1045
1046 (defun math-apply-units (expr units ulist &optional pure)
1047   (setq expr (math-simplify-units expr))
1048   (if ulist
1049       (let ((new 0)
1050             value)
1051         (or (math-numberp expr)
1052             (error "Incompatible units"))
1053         (while (cdr ulist)
1054           (setq value (math-div expr (nth 1 (car ulist)))
1055                 value (math-floor (let ((calc-internal-prec
1056                                          (1- calc-internal-prec)))
1057                                     (math-normalize value)))
1058                 new (math-add new (math-mul value (car (car ulist))))
1059                 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
1060                 ulist (cdr ulist)))
1061         (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
1062                                 (car (car ulist)))))
1063     (if pure
1064         expr
1065       (math-simplify-units (list '* expr units)))))
1066
1067 (defvar math-decompose-units-cache nil)
1068 (defun math-decompose-units (units)
1069   (let ((u (math-check-unit-name units)))
1070     (and u (eq (car-safe (nth 1 u)) '+)
1071          (setq units (nth 1 u))))
1072   (setq units (calcFunc-expand units))
1073   (and (eq (car-safe units) '+)
1074        (let ((entry (list units calc-internal-prec calc-prefer-frac)))
1075          (or (equal entry (car math-decompose-units-cache))
1076              (let ((ulist nil)
1077                    (utemp units)
1078                    qty unit)
1079                (while (eq (car-safe utemp) '+)
1080                  (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
1081                                    ulist)
1082                        utemp (nth 1 utemp)))
1083                (setq ulist (cons (math-decompose-unit-part utemp) ulist)
1084                      utemp ulist)
1085                (while (setq utemp (cdr utemp))
1086                  (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
1087                    (error "Inconsistent units in sum")))
1088                (setq math-decompose-units-cache
1089                      (cons entry
1090                            (sort ulist
1091                                  (function
1092                                   (lambda (x y)
1093                                     (not (Math-lessp (nth 1 x)
1094                                                      (nth 1 y))))))))))
1095          (cdr math-decompose-units-cache))))
1096
1097 (defun math-decompose-unit-part (unit)
1098   (cons unit
1099         (math-is-multiple (math-simplify-units (math-to-standard-units
1100                                                 unit nil))
1101                           t)))
1102
1103 ;; The variable math-fcu-u is local to math-find-compatible-unit,
1104 ;; but is used by math-find-compatible-rec which is called by
1105 ;; math-find-compatible-unit.
1106 (defvar math-fcu-u)
1107
1108 (defun math-find-compatible-unit (expr unit)
1109   (let ((math-fcu-u (math-check-unit-name unit)))
1110     (if math-fcu-u
1111         (math-find-compatible-unit-rec expr 1))))
1112
1113 (defun math-find-compatible-unit-rec (expr pow)
1114   (cond ((eq (car-safe expr) '*)
1115          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1116              (math-find-compatible-unit-rec (nth 2 expr) pow)))
1117         ((eq (car-safe expr) '/)
1118          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1119              (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
1120         ((eq (car-safe expr) 'neg)
1121          (math-find-compatible-unit-rec (nth 1 expr) pow))
1122         ((and (eq (car-safe expr) '^)
1123               (integerp (nth 2 expr)))
1124          (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
1125         (t
1126          (let ((u2 (math-check-unit-name expr)))
1127            (if (equal (nth 4 math-fcu-u) (nth 4 u2))
1128                (cons expr pow))))))
1129
1130 ;; The variables math-cu-new-units and math-cu-pure are local to
1131 ;; math-convert-units, but are used by math-convert-units-rec,
1132 ;; which is called by math-convert-units.
1133 (defvar math-cu-new-units)
1134 (defvar math-cu-pure)
1135
1136 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
1137   (if (eq (car-safe math-cu-new-units) 'var)
1138       (let ((unew (assq (nth 1 math-cu-new-units)
1139                         (math-build-units-table))))
1140         (if (eq (car-safe (nth 1 unew)) '+)
1141             (setq math-cu-new-units (nth 1 unew)))))
1142   (math-with-extra-prec 2
1143     (let ((compat (and (not math-cu-pure)
1144                        (math-find-compatible-unit expr math-cu-new-units)))
1145           (math-cu-unit-list nil)
1146           (math-combining-units nil))
1147       (if compat
1148           (math-simplify-units
1149            (math-mul (math-mul (math-simplify-units
1150                                 (math-div expr (math-pow (car compat)
1151                                                          (cdr compat))))
1152                                (math-pow math-cu-new-units (cdr compat)))
1153                      (math-simplify-units
1154                       (math-to-standard-units
1155                        (math-pow (math-div (car compat) math-cu-new-units)
1156                                  (cdr compat))
1157                        nil))))
1158         (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
1159           (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
1160         (when (eq (car-safe expr) '+)
1161           (setq expr (math-simplify-units expr)))
1162         (if (math-units-in-expr-p expr t)
1163             (math-convert-units-rec expr)
1164           (math-apply-units (math-to-standard-units
1165                              (list '/ expr math-cu-new-units) nil)
1166                             math-cu-new-units math-cu-unit-list math-cu-pure))))))
1167
1168 (defun math-convert-units-rec (expr)
1169   (if (math-units-in-expr-p expr nil)
1170       (math-apply-units (math-to-standard-units
1171                          (list '/ expr math-cu-new-units) nil)
1172                         math-cu-new-units math-cu-unit-list math-cu-pure)
1173     (if (Math-primp expr)
1174         expr
1175       (cons (car expr)
1176             (mapcar 'math-convert-units-rec (cdr expr))))))
1177
1178 (defun math-convert-temperature (expr old new &optional pure)
1179   (let* ((units (math-single-units-in-expr-p expr))
1180          (uold (if old
1181                    (if (or (null units)
1182                            (equal (nth 1 old) (car units)))
1183                        (math-check-unit-name old)
1184                      (error "Inconsistent temperature units"))
1185                  units))
1186          (unew (math-check-unit-name new)))
1187     (unless (and (consp unew) (nth 3 unew))
1188       (error "Not a valid temperature unit"))
1189     (unless (and (consp uold) (nth 3 uold))
1190       (error "Not a pure temperature expression"))
1191     (let ((v (car uold)))
1192       (setq expr (list '/ expr (list 'var v
1193                                      (intern (concat "var-"
1194                                                      (symbol-name v)))))))
1195     (or (eq (nth 3 uold) (nth 3 unew))
1196         (cond ((eq (nth 3 uold) 'K)
1197                (setq expr (list '- expr '(/ 27315 100)))
1198                (if (eq (nth 3 unew) 'F)
1199                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
1200               ((eq (nth 3 uold) 'C)
1201                (if (eq (nth 3 unew) 'F)
1202                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))
1203                  (setq expr (list '+ expr '(/ 27315 100)))))
1204               (t
1205                (setq expr (list '* (list '- expr 32) '(/ 5 9)))
1206                (if (eq (nth 3 unew) 'K)
1207                    (setq expr (list '+ expr '(/ 27315 100)))))))
1208     (if pure
1209         expr
1210       (list '* expr new))))
1211
1212
1213
1214 (defun math-simplify-units (a)
1215   (let ((math-simplifying-units t)
1216         (calc-matrix-mode 'scalar))
1217     (math-simplify a)))
1218 (defalias 'calcFunc-usimplify 'math-simplify-units)
1219
1220 ;; The function created by math-defsimplify uses the variable
1221 ;; math-simplify-expr, and so is used by functions in math-defsimplify
1222 (defvar math-simplify-expr)
1223
1224 (math-defsimplify (+ -)
1225   (and math-simplifying-units
1226        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1227        (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1228               (ratio (math-simplify (math-to-standard-units
1229                                      (list '/ (nth 2 math-simplify-expr) units) nil))))
1230          (if (math-units-in-expr-p ratio nil)
1231              (progn
1232                (calc-record-why "*Inconsistent units" math-simplify-expr)
1233                math-simplify-expr)
1234            (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1235                               (if (eq (car math-simplify-expr) '-)
1236                                   (math-neg ratio) ratio))
1237                  units)))))
1238
1239 (math-defsimplify *
1240   (math-simplify-units-prod))
1241
1242 (defun math-simplify-units-prod ()
1243   (and math-simplifying-units
1244        calc-autorange-units
1245        (Math-realp (nth 1 math-simplify-expr))
1246        (let* ((num (math-float (nth 1 math-simplify-expr)))
1247               (xpon (calcFunc-xpon num))
1248               (unitp (cdr (cdr math-simplify-expr)))
1249               (unit (car unitp))
1250               (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1251               u)
1252          (and (eq (car-safe unit) '*)
1253               (setq unitp (cdr unit)
1254                     unit (car unitp)))
1255          (and (eq (car-safe unit) '^)
1256               (integerp (nth 2 unit))
1257               (setq pow (* pow (nth 2 unit))
1258                     unitp (cdr unit)
1259                     unit (car unitp)))
1260          (and (setq u (math-check-unit-name unit))
1261               (integerp xpon)
1262               (or (< xpon 0)
1263                   (>= xpon (if (eq (car u) 'm) 1 3)))
1264               (let* ((uxpon 0)
1265                      (pref (if (< pow 0)
1266                                (reverse math-unit-prefixes)
1267                              math-unit-prefixes))
1268                      (p pref)
1269                      pxpon pname)
1270                 (or (eq (car u) (nth 1 unit))
1271                     (setq uxpon (* pow
1272                                    (nth 2 (nth 1 (assq
1273                                                   (aref (symbol-name
1274                                                          (nth 1 unit)) 0)
1275                                                   math-unit-prefixes))))))
1276                 (setq xpon (+ xpon uxpon))
1277                 (while (and p
1278                             (or (memq (car (car p)) '(?d ?D ?h ?H))
1279                                 (and (eq (car (car p)) ?c)
1280                                      (not (eq (car u) 'm)))
1281                                 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1282                                                        pow)))
1283                                 (progn
1284                                   (setq pname (math-build-var-name
1285                                                (if (eq (car (car p)) 0)
1286                                                    (car u)
1287                                                  (concat (char-to-string
1288                                                           (car (car p)))
1289                                                          (symbol-name
1290                                                           (car u))))))
1291                                   (and (/= (car (car p)) 0)
1292                                        (assq (nth 1 pname)
1293                                              math-units-table)))))
1294                   (setq p (cdr p)))
1295                 (and p
1296                      (/= pxpon uxpon)
1297                      (or (not (eq p pref))
1298                          (< xpon (+ pxpon (* (math-abs pow) 3))))
1299                      (progn
1300                        (setcar (cdr math-simplify-expr)
1301                                (let ((calc-prefer-frac nil))
1302                                  (calcFunc-scf (nth 1 math-simplify-expr)
1303                                                (- uxpon pxpon))))
1304                        (setcar unitp pname)
1305                        math-simplify-expr)))))))
1306
1307 (defvar math-try-cancel-units)
1308
1309 (math-defsimplify /
1310   (and math-simplifying-units
1311        (let ((np (cdr math-simplify-expr))
1312              (math-try-cancel-units 0)
1313              n nn)
1314          (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1315                      (cdr (nth 2 math-simplify-expr))
1316                    (nthcdr 2 math-simplify-expr)))
1317          (if (math-realp (car n))
1318              (progn
1319                (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1320                                             (let ((calc-prefer-frac nil))
1321                                               (math-div 1 (car n)))))
1322                (setcar n 1)))
1323          (while (eq (car-safe (setq n (car np))) '*)
1324            (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1325            (setq np (cdr (cdr n))))
1326          (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1327          (if (eq math-try-cancel-units 0)
1328              (let* ((math-simplifying-units nil)
1329                     (base (math-simplify
1330                            (math-to-standard-units math-simplify-expr nil))))
1331                (if (Math-numberp base)
1332                    (setq math-simplify-expr base))))
1333          (if (eq (car-safe math-simplify-expr) '/)
1334              (math-simplify-units-prod))
1335          math-simplify-expr)))
1336
1337 (defun math-simplify-units-divisor (np dp)
1338   (let ((n (car np))
1339         d dd temp)
1340     (while (eq (car-safe (setq d (car dp))) '*)
1341       (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1342         (setcar np (setq n temp))
1343         (setcar (cdr d) 1))
1344       (setq dp (cdr (cdr d))))
1345     (when (setq temp (math-simplify-units-quotient n d))
1346       (setcar np (setq n temp))
1347       (setcar dp 1))))
1348
1349 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1350 (defun math-simplify-units-quotient (n d)
1351   (let ((pow1 1)
1352         (pow2 1))
1353     (when (and (eq (car-safe n) '^)
1354                (integerp (nth 2 n)))
1355       (setq pow1 (nth 2 n) n (nth 1 n)))
1356     (when (and (eq (car-safe d) '^)
1357                (integerp (nth 2 d)))
1358       (setq pow2 (nth 2 d) d (nth 1 d)))
1359     (let ((un (math-check-unit-name n))
1360           (ud (math-check-unit-name d)))
1361       (and un ud
1362            (if (and (equal (nth 4 un) (nth 4 ud))
1363                     (eq pow1 pow2))
1364                (if (eq pow1 1)
1365                    (math-to-standard-units (list '/ n d) nil)
1366                  (list '^ (math-to-standard-units (list '/ n d) nil) pow1))
1367              (let (ud1)
1368                (setq un (nth 4 un)
1369                      ud (nth 4 ud))
1370                (while un
1371                  (setq ud1 ud)
1372                  (while ud1
1373                    (and (eq (car (car un)) (car (car ud1)))
1374                         (setq math-try-cancel-units
1375                               (+ math-try-cancel-units
1376                                  (- (* (cdr (car un)) pow1)
1377                                     (* (cdr (car ud)) pow2)))))
1378                    (setq ud1 (cdr ud1)))
1379                  (setq un (cdr un)))
1380                nil))))))
1381
1382 (math-defsimplify ^
1383   (and math-simplifying-units
1384        (math-realp (nth 2 math-simplify-expr))
1385        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1386            (list (car (nth 1 math-simplify-expr))
1387                  (list '^ (nth 1 (nth 1 math-simplify-expr))
1388                        (nth 2 math-simplify-expr))
1389                  (list '^ (nth 2 (nth 1 math-simplify-expr))
1390                        (nth 2 math-simplify-expr)))
1391          (math-simplify-units-pow (nth 1 math-simplify-expr)
1392                                   (nth 2 math-simplify-expr)))))
1393
1394 (math-defsimplify calcFunc-sqrt
1395   (and math-simplifying-units
1396        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1397            (list (car (nth 1 math-simplify-expr))
1398                  (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1399                  (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1400          (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1401
1402 (math-defsimplify (calcFunc-floor
1403                    calcFunc-ceil
1404                    calcFunc-round
1405                    calcFunc-rounde
1406                    calcFunc-roundu
1407                    calcFunc-trunc
1408                    calcFunc-float
1409                    calcFunc-frac
1410                    calcFunc-abs
1411                    calcFunc-clean)
1412   (and math-simplifying-units
1413        (= (length math-simplify-expr) 2)
1414        (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1415            (nth 1 math-simplify-expr)
1416          (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1417                   (or (math-only-units-in-expr-p
1418                        (nth 1 (nth 1 math-simplify-expr)))
1419                       (math-only-units-in-expr-p
1420                        (nth 2 (nth 1 math-simplify-expr)))))
1421              (list (car (nth 1 math-simplify-expr))
1422                    (cons (car math-simplify-expr)
1423                          (cons (nth 1 (nth 1 math-simplify-expr))
1424                                (cdr (cdr math-simplify-expr))))
1425                    (cons (car math-simplify-expr)
1426                          (cons (nth 2 (nth 1 math-simplify-expr))
1427                                (cdr (cdr math-simplify-expr)))))))))
1428
1429 (defun math-simplify-units-pow (a pow)
1430   (if (and (eq (car-safe a) '^)
1431            (math-check-unit-name (nth 1 a))
1432            (math-realp (nth 2 a)))
1433       (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1434     (let* ((u (math-check-unit-name a))
1435            (pf (math-to-simple-fraction pow))
1436            (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1437       (and u d
1438            (math-units-are-multiple u d)
1439            (list '^ (math-to-standard-units a nil) pow)))))
1440
1441
1442 (defun math-units-are-multiple (u n)
1443   (setq u (nth 4 u))
1444   (while (and u (= (% (cdr (car u)) n) 0))
1445     (setq u (cdr u)))
1446   (null u))
1447
1448 (math-defsimplify calcFunc-sin
1449   (and math-simplifying-units
1450        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1451        (let ((rad (math-simplify-units
1452                    (math-evaluate-expr
1453                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1454              (calc-angle-mode 'rad))
1455          (and (eq (car-safe rad) '*)
1456               (math-realp (nth 1 rad))
1457               (eq (car-safe (nth 2 rad)) 'var)
1458               (eq (nth 1 (nth 2 rad)) 'rad)
1459               (list 'calcFunc-sin (nth 1 rad))))))
1460
1461 (math-defsimplify calcFunc-cos
1462   (and math-simplifying-units
1463        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1464        (let ((rad (math-simplify-units
1465                    (math-evaluate-expr
1466                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1467              (calc-angle-mode 'rad))
1468          (and (eq (car-safe rad) '*)
1469               (math-realp (nth 1 rad))
1470               (eq (car-safe (nth 2 rad)) 'var)
1471               (eq (nth 1 (nth 2 rad)) 'rad)
1472               (list 'calcFunc-cos (nth 1 rad))))))
1473
1474 (math-defsimplify calcFunc-tan
1475   (and math-simplifying-units
1476        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1477        (let ((rad (math-simplify-units
1478                    (math-evaluate-expr
1479                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1480              (calc-angle-mode 'rad))
1481          (and (eq (car-safe rad) '*)
1482               (math-realp (nth 1 rad))
1483               (eq (car-safe (nth 2 rad)) 'var)
1484               (eq (nth 1 (nth 2 rad)) 'rad)
1485               (list 'calcFunc-tan (nth 1 rad))))))
1486
1487 (math-defsimplify calcFunc-sec
1488   (and math-simplifying-units
1489        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1490        (let ((rad (math-simplify-units
1491                    (math-evaluate-expr
1492                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1493              (calc-angle-mode 'rad))
1494          (and (eq (car-safe rad) '*)
1495               (math-realp (nth 1 rad))
1496               (eq (car-safe (nth 2 rad)) 'var)
1497               (eq (nth 1 (nth 2 rad)) 'rad)
1498               (list 'calcFunc-sec (nth 1 rad))))))
1499
1500 (math-defsimplify calcFunc-csc
1501   (and math-simplifying-units
1502        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1503        (let ((rad (math-simplify-units
1504                    (math-evaluate-expr
1505                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1506              (calc-angle-mode 'rad))
1507          (and (eq (car-safe rad) '*)
1508               (math-realp (nth 1 rad))
1509               (eq (car-safe (nth 2 rad)) 'var)
1510               (eq (nth 1 (nth 2 rad)) 'rad)
1511               (list 'calcFunc-csc (nth 1 rad))))))
1512
1513 (math-defsimplify calcFunc-cot
1514   (and math-simplifying-units
1515        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1516        (let ((rad (math-simplify-units
1517                    (math-evaluate-expr
1518                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1519              (calc-angle-mode 'rad))
1520          (and (eq (car-safe rad) '*)
1521               (math-realp (nth 1 rad))
1522               (eq (car-safe (nth 2 rad)) 'var)
1523               (eq (nth 1 (nth 2 rad)) 'rad)
1524               (list 'calcFunc-cot (nth 1 rad))))))
1525
1526
1527 (defun math-remove-units (expr)
1528   (if (math-check-unit-name expr)
1529       1
1530     (if (Math-primp expr)
1531         expr
1532       (cons (car expr)
1533             (mapcar 'math-remove-units (cdr expr))))))
1534
1535 (defun math-extract-units (expr)
1536   (cond
1537    ((memq (car-safe expr) '(* /))
1538     (cons (car expr)
1539           (mapcar 'math-extract-units (cdr expr))))
1540    ((eq (car-safe expr) 'neg)
1541     (math-extract-units (nth 1 expr)))
1542    ((eq (car-safe expr) '^)
1543     (list '^ (math-extract-units (nth 1 expr)) (nth 2 expr)))
1544    ((math-check-unit-name expr) expr)
1545    (t 1)))
1546
1547 (defun math-build-units-table-buffer (enter-buffer)
1548   (if (not (and math-units-table math-units-table-buffer-valid
1549                 (get-buffer "*Units Table*")))
1550       (let ((buf (get-buffer-create "*Units Table*"))
1551             (uptr (math-build-units-table))
1552             (calc-language (if (eq calc-language 'big) nil calc-language))
1553             (calc-float-format '(float 0))
1554             (calc-group-digits nil)
1555             (calc-number-radix 10)
1556             (calc-twos-complement-mode nil)
1557             (calc-point-char ".")
1558             (std nil)
1559             u name shadowed)
1560         (save-excursion
1561           (message "Formatting units table...")
1562           (set-buffer buf)
1563           (let ((inhibit-read-only t))
1564             (erase-buffer)
1565             (insert "Calculator Units Table:\n\n")
1566             (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n")
1567             (insert "Unit    Type  Definition                  Description\n\n")
1568             (while uptr
1569               (setq u (car uptr)
1570                     name (nth 2 u))
1571               (when (eq (car u) 'm)
1572                 (setq std t))
1573               (setq shadowed (and std (assq (car u) math-additional-units)))
1574               (when (and name
1575                          (> (length name) 1)
1576                          (eq (aref name 0) ?\*))
1577                 (unless (eq uptr math-units-table)
1578                   (insert "\n"))
1579                 (setq name (substring name 1)))
1580               (insert " ")
1581               (and shadowed (insert "("))
1582               (insert (symbol-name (car u)))
1583               (and shadowed (insert ")"))
1584               (if (nth 3 u)
1585                   (progn
1586                     (indent-to 10)
1587                     (insert (symbol-name (nth 3 u))))
1588                 (or std
1589                     (progn
1590                       (indent-to 10)
1591                       (insert "U"))))
1592               (indent-to 14)
1593               (and shadowed (insert "("))
1594               (if (nth 5 u)
1595                   (insert (nth 5 u))
1596                 (if (nth 1 u)
1597                     (insert (math-format-value (nth 1 u) 80))
1598                   (insert (symbol-name (car u)))))
1599               (and shadowed (insert ")"))
1600               (indent-to 41)
1601               (insert " ")
1602               (when name
1603                 (insert name))
1604               (if shadowed
1605                   (insert " (redefined above)")
1606                 (unless (nth 1 u)
1607                   (insert " (base unit)")))
1608               (insert "\n")
1609               (setq uptr (cdr uptr)))
1610             (insert "\n\nUnit Prefix Table:\n\n")
1611             (setq uptr math-unit-prefixes)
1612             (while uptr
1613               (setq u (car uptr))
1614               (insert " " (char-to-string (car u)))
1615               (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1616                   (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1617                           "   ")
1618                 (insert "     "))
1619               (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1620               (indent-to 15)
1621               (insert "   " (nth 2 u) "\n")
1622               (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1623             (insert "\n\n")
1624             (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
1625                      "names will not use the `tex' prefix; the unit name for a\n"
1626                      "TeX point will be `pt' instead of `texpt', for example.\n"
1627                      "To avoid conflicts, the unit names for pint and parsec will\n"
1628                      "be `pint' and `parsec' instead of `pt' and `pc'."))
1629           (view-mode)
1630           (message "Formatting units table...done"))
1631         (setq math-units-table-buffer-valid t)
1632         (let ((oldbuf (current-buffer)))
1633           (set-buffer buf)
1634           (goto-char (point-min))
1635           (set-buffer oldbuf))
1636         (if enter-buffer
1637             (pop-to-buffer buf)
1638           (display-buffer buf)))
1639     (if enter-buffer
1640         (pop-to-buffer (get-buffer "*Units Table*"))
1641       (display-buffer (get-buffer "*Units Table*")))))
1642
1643 ;;; Logarithmic units functions
1644
1645 (defvar math-logunits '((var dB var-dB)
1646                         (var Np var-Np)))
1647
1648 (defun math-conditional-apply (fn &rest args)
1649   "Evaluate f(args) unless in symbolic mode.
1650 In symbolic mode, return the list (fn args)."
1651   (if calc-symbolic-mode
1652       (cons fn args)
1653     (apply fn args)))
1654
1655 (defun math-conditional-pow (a b)
1656   "Evaluate a^b unless in symbolic mode.
1657 In symbolic mode, return the list (^ a b)."
1658   (if calc-symbolic-mode
1659       (list '^ a b)
1660     (math-pow a b)))
1661
1662 (defun math-extract-logunits (expr)
1663   (if (memq (car-safe expr) '(* /))
1664       (cons (car expr)
1665             (mapcar 'math-extract-logunits (cdr expr)))
1666     (if (memq (car-safe expr) '(^))
1667         (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
1668       (if (member expr math-logunits) expr 1))))
1669
1670 (defun math-logunits-add (a b neg power)
1671   (let ((aunit (math-simplify (math-extract-logunits a))))
1672     (if (not (eq (car-safe aunit) 'var))
1673         (calc-record-why "*Improper logarithmic unit" aunit)
1674       (let* ((units (math-extract-units a))
1675             (acoeff (math-simplify (math-remove-units a)))
1676             (bcoeff (math-simplify (math-to-standard-units
1677                                     (list '/ b units) nil))))
1678         (if (math-units-in-expr-p bcoeff nil)
1679             (calc-record-why "*Inconsistent units" nil)
1680           (if (and neg
1681                    (or (math-lessp acoeff bcoeff)
1682                        (math-equal acoeff bcoeff)))
1683               (calc-record-why "*Improper coefficients" nil)
1684             (math-mul
1685              (if (equal aunit '(var dB var-dB))
1686                  (let ((coef (if power 10 20)))
1687                    (math-mul coef
1688                              (math-conditional-apply 'calcFunc-log10
1689                               (if neg
1690                                   (math-sub
1691                                    (math-conditional-pow 10 (math-div acoeff coef))
1692                                    (math-conditional-pow 10 (math-div bcoeff coef)))
1693                                 (math-add
1694                                  (math-conditional-pow 10 (math-div acoeff coef))
1695                                  (math-conditional-pow 10 (math-div bcoeff coef)))))))
1696                (let ((coef (if power 2 1)))
1697                  (math-div
1698                   (math-conditional-apply 'calcFunc-ln
1699                    (if neg
1700                        (math-sub
1701                         (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1702                         (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
1703                      (math-add
1704                       (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1705                       (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
1706                   coef)))
1707              units)))))))
1708
1709 (defun calcFunc-lufadd (a b)
1710   (math-logunits-add a b nil nil))
1711
1712 (defun calcFunc-lupadd (a b)
1713   (math-logunits-add a b nil t))
1714
1715 (defun calcFunc-lufsub (a b)
1716   (math-logunits-add a b t nil))
1717
1718 (defun calcFunc-lupsub (a b)
1719   (math-logunits-add a b t t))
1720
1721 (defun calc-lu-plus (arg)
1722   (interactive "P")
1723   (calc-slow-wrapper
1724    (if (calc-is-inverse)
1725        (if (calc-is-hyperbolic)
1726            (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1727          (calc-binary-op "lu-" 'calcFunc-lupsub arg))
1728      (if (calc-is-hyperbolic)
1729          (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1730        (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
1731
1732 (defun calc-lu-minus (arg)
1733   (interactive "P")
1734   (calc-slow-wrapper
1735    (if (calc-is-inverse)
1736        (if (calc-is-hyperbolic)
1737            (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1738          (calc-binary-op "lu+" 'calcFunc-lupadd arg))
1739      (if (calc-is-hyperbolic)
1740          (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1741        (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
1742
1743 (defun math-logunits-mul (a b power)
1744   (let (logunit coef units number)
1745     (cond
1746      ((and
1747        (setq logunit (math-simplify (math-extract-logunits a)))
1748        (eq (car-safe logunit) 'var)
1749        (eq (math-simplify (math-extract-units b)) 1))
1750       (setq coef (math-simplify (math-remove-units a))
1751             units (math-extract-units a)
1752             number b))
1753      ((and
1754        (setq logunit (math-simplify (math-extract-logunits b)))
1755        (eq (car-safe logunit) 'var)
1756        (eq (math-simplify (math-extract-units a)) 1))
1757       (setq coef (math-simplify (math-remove-units b))
1758             units (math-extract-units b)
1759             number a))
1760      (t (setq logunit nil)))
1761     (if logunit
1762         (cond
1763          ((equal logunit '(var dB var-dB))
1764           (math-simplify
1765            (math-mul
1766             (math-add
1767              coef
1768              (math-mul (if power 10 20)
1769                        (math-conditional-apply 'calcFunc-log10 number)))
1770             units)))
1771          (t
1772           (math-simplify
1773            (math-mul
1774             (math-add
1775              coef
1776              (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
1777             units))))
1778       (calc-record-why "*Improper units" nil))))
1779
1780 (defun math-logunits-divide (a b power)
1781   (let ((logunit (math-simplify (math-extract-logunits a))))
1782     (if (not (eq (car-safe logunit) 'var))
1783         (calc-record-why "*Improper logarithmic unit" logunit)
1784       (if (math-units-in-expr-p b nil)
1785           (calc-record-why "*Improper units quantity" b)
1786         (let* ((units (math-extract-units a))
1787                (coef (math-simplify (math-remove-units a))))
1788           (cond
1789            ((equal logunit '(var dB var-dB))
1790             (math-simplify
1791              (math-mul
1792               (math-sub
1793                coef
1794                (math-mul (if power 10 20)
1795                          (math-conditional-apply 'calcFunc-log10 b)))
1796               units)))
1797          (t
1798           (math-simplify
1799            (math-mul
1800             (math-sub
1801              coef
1802              (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
1803             units)))))))))
1804
1805 (defun calcFunc-lufmul (a b)
1806   (math-logunits-mul a b nil))
1807
1808 (defun calcFunc-lupmul (a b)
1809   (math-logunits-mul a b t))
1810
1811 (defun calc-lu-times (arg)
1812   (interactive "P")
1813   (calc-slow-wrapper
1814    (if (calc-is-inverse)
1815        (if (calc-is-hyperbolic)
1816            (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1817          (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
1818      (if (calc-is-hyperbolic)
1819          (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1820        (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
1821
1822 (defun calcFunc-lufdiv (a b)
1823   (math-logunits-divide a b nil))
1824
1825 (defun calcFunc-lupdiv (a b)
1826   (math-logunits-divide a b t))
1827
1828 (defun calc-lu-divide (arg)
1829   (interactive "P")
1830   (calc-slow-wrapper
1831    (if (calc-is-inverse)
1832        (if (calc-is-hyperbolic)
1833            (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1834          (calc-binary-op "lu*" 'calcFunc-lupmul arg))
1835      (if (calc-is-hyperbolic)
1836          (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1837        (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
1838
1839 (defun math-logunits-quant (val ref power)
1840   (let* ((units (math-simplify (math-extract-units val)))
1841          (lunit (math-simplify (math-extract-logunits units))))
1842     (if (not (eq (car-safe lunit) 'var))
1843         (calc-record-why "*Improper logarithmic unit" lunit)
1844       (let ((runits (math-simplify (math-div units lunit)))
1845             (coeff (math-simplify (math-div val units))))
1846         (math-mul
1847          (if (equal lunit '(var dB var-dB))
1848              (math-mul
1849               ref
1850               (math-conditional-pow
1851                10
1852                (math-div
1853                 coeff
1854                 (if power 10 20))))
1855            (math-mul
1856             ref
1857             (math-conditional-apply 'calcFunc-exp
1858              (if power
1859                  (math-mul 2 coeff)
1860                coeff))))
1861          runits)))))
1862
1863 (defvar calc-lu-field-reference)
1864 (defvar calc-lu-power-reference)
1865
1866 (defun calcFunc-lufquant (val &optional ref)
1867   (unless ref
1868     (setq ref (math-read-expr calc-lu-field-reference)))
1869   (math-logunits-quant val ref nil))
1870
1871 (defun calcFunc-lupquant (val &optional ref)
1872   (unless ref
1873     (setq ref (math-read-expr calc-lu-power-reference)))
1874   (math-logunits-quant val ref t))
1875
1876 (defun calc-lu-quant (arg)
1877   (interactive "P")
1878   (calc-slow-wrapper
1879    (if (calc-is-hyperbolic)
1880        (if (calc-is-option)
1881            (calc-binary-op "lupq" 'calcFunc-lufquant arg)
1882          (calc-unary-op "lupq" 'calcFunc-lufquant arg))
1883      (if (calc-is-option)
1884          (calc-binary-op "lufq" 'calcFunc-lupquant arg)
1885        (calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
1886
1887 (defun math-logunits-level (val ref db power)
1888   "Compute the value of VAL in decibels or nepers."
1889       (let* ((ratio (math-simplify-units (math-div val ref)))
1890              (ratiou (math-simplify-units (math-remove-units ratio)))
1891              (units (math-simplify (math-extract-units ratio))))
1892         (math-mul
1893          (if db
1894              (math-mul
1895               (math-mul (if power 10 20)
1896                         (math-conditional-apply 'calcFunc-log10 ratiou))
1897               '(var dB var-dB))
1898            (math-mul
1899             (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
1900             '(var Np var-Np)))
1901          units)))
1902
1903 (defun calcFunc-dbfield (val &optional ref)
1904   (unless ref
1905     (setq ref (math-read-expr calc-lu-field-reference)))
1906   (math-logunits-level val ref t nil))
1907
1908 (defun calcFunc-dbpower (val &optional ref)
1909   (unless ref
1910     (setq ref (math-read-expr calc-lu-power-reference)))
1911   (math-logunits-level val ref t t))
1912
1913 (defun calcFunc-npfield (val &optional ref)
1914   (unless ref
1915     (setq ref (math-read-expr calc-lu-field-reference)))
1916   (math-logunits-level val ref nil nil))
1917
1918 (defun calcFunc-nppower (val &optional ref)
1919   (unless ref
1920     (setq ref (math-read-expr calc-lu-power-reference)))
1921   (math-logunits-level val ref nil t))
1922
1923 (defun calc-db (arg)
1924   (interactive "P")
1925   (calc-slow-wrapper
1926    (if (calc-is-hyperbolic)
1927        (if (calc-is-option)
1928            (calc-binary-op "ludb" 'calcFunc-dbfield arg)
1929          (calc-unary-op "ludb" 'calcFunc-dbfield arg))
1930      (if (calc-is-option)
1931          (calc-binary-op "ludb" 'calcFunc-dbpower arg)
1932        (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
1933
1934 (defun calc-np (arg)
1935   (interactive "P")
1936   (calc-slow-wrapper
1937    (if (calc-is-hyperbolic)
1938        (if (calc-is-option)
1939            (calc-binary-op "lunp" 'calcFunc-npfield arg)
1940          (calc-unary-op "lunp" 'calcFunc-npfield arg))
1941      (if (calc-is-option)
1942          (calc-binary-op "lunp" 'calcFunc-nppower arg)
1943        (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
1944
1945 ;;; Musical notes
1946
1947
1948 (defvar calc-note-threshold)
1949
1950 (defun math-midi-round (num)
1951   "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
1952   (let* ((n (math-round num))
1953          (diff (math-abs
1954                 (math-sub num n))))
1955     (if (< (math-compare diff
1956                          (math-div (math-read-expr calc-note-threshold) 100)) 0)
1957         n
1958       num)))
1959
1960 (defconst math-notes
1961   '(((var C var-C) . 0)
1962     ((var Csharp var-Csharp) . 1)
1963 ;    ((var C♯ var-C♯) . 1)
1964     ((var Dflat var-Dflat) . 1)
1965 ;    ((var D♭ var-D♭) . 1)
1966     ((var D var-D) . 2)
1967     ((var Dsharp var-Dsharp) . 3)
1968 ;    ((var D♯ var-D♯) . 3)
1969     ((var E var-E) . 4)
1970     ((var F var-F) . 5)
1971     ((var Fsharp var-Fsharp) . 6)
1972 ;    ((var F♯ var-F♯) . 6)
1973     ((var Gflat var-Gflat) . 6)
1974 ;    ((var G♭ var-G♭) . 6)
1975     ((var G var-G) . 7)
1976     ((var Gsharp var-Gsharp) . 8)
1977 ;    ((var G♯ var-G♯) . 8)
1978     ((var A var-A) . 9)
1979     ((var Asharp var-Asharp) . 10)
1980 ;    ((var A♯ var-A♯) . 10)
1981     ((var Bflat var-Bflat) . 10)
1982 ;    ((var B♭ var-B♭) . 10)
1983     ((var B var-B) . 11))
1984   "An alist of notes with their number of semitones above C.")
1985
1986 (defun math-freqp (freq)
1987   "Non-nil if FREQ is a positive number times the unit Hz.
1988 If non-nil, return the coefficient of Hz."
1989   (let ((freqcoef (math-simplify-units
1990                    (math-div freq '(var Hz var-Hz)))))
1991     (if (Math-posp freqcoef) freqcoef)))
1992
1993 (defun math-midip (num)
1994   "Non-nil if NUM is a possible MIDI note number.
1995 If non-nil, return NUM."
1996   (if (Math-numberp num) num))
1997
1998 (defun math-spnp (spn)
1999   "Non-nil if NUM is a scientific pitch note (note + cents).
2000 If non-nil, return a list consisting of the note and the cents coefficient."
2001   (let (note cents rnote rcents)
2002     (if (eq (car-safe spn) '+)
2003         (setq note (nth 1 spn)
2004               cents (nth 2 spn))
2005       (setq note spn
2006             cents nil))
2007     (cond
2008      ((and  ;; NOTE is a note, CENTS is nil or cents.
2009        (eq (car-safe note) 'calcFunc-subscr)
2010        (assoc (nth 1 note) math-notes)
2011        (integerp (nth 2 note))
2012        (setq rnote note)
2013        (or
2014         (not cents)
2015         (Math-numberp (setq rcents
2016                             (math-simplify
2017                              (math-div cents '(var cents var-cents)))))))
2018       (list rnote rcents))
2019      ((and  ;; CENTS is a note, NOTE is cents.
2020        (eq (car-safe cents) 'calcFunc-subscr)
2021        (assoc (nth 1 cents) math-notes)
2022        (integerp (nth 2 cents))
2023        (setq rnote cents)
2024        (or
2025         (not note)
2026         (Math-numberp (setq rcents
2027                             (math-simplify
2028                              (math-div note '(var cents var-cents)))))))
2029       (list rnote rcents)))))
2030
2031 (defun math-freq-to-midi (freq)
2032   "Return the midi note number corresponding to FREQ Hz."
2033   (let ((midi (math-add
2034                69
2035                (math-mul
2036                 12
2037                 (calcFunc-log
2038                  (math-div freq 440)
2039                  2)))))
2040     (math-midi-round midi)))
2041
2042 (defun math-spn-to-midi (spn)
2043   "Return the MIDI number corresponding to SPN."
2044   (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
2045          (octave (math-add (nth 2 (car spn)) 1))
2046          (cents (nth 1 spn))
2047          (midi  (math-add
2048                  (math-mul 12 octave)
2049                  note)))
2050     (if cents
2051         (math-add midi (math-div cents 100))
2052       midi)))
2053
2054 (defun math-midi-to-spn (midi)
2055   "Return the scientific pitch notation corresponding to midi number MIDI."
2056   (let (midin cents)
2057     (if (math-integerp midi)
2058         (setq midin midi
2059               cents nil)
2060       (setq midin (math-floor midi)
2061             cents (math-mul 100 (math-sub midi midin))))
2062     (let* ((nr ;; This should be (math-idivmod midin 12), but with
2063                ;; better behavior for negative midin.
2064             (if (Math-negp midin)
2065                 (let ((dm (math-idivmod (math-neg midin) 12)))
2066                   (if (= (cdr dm) 0)
2067                       (cons (math-neg (car dm)) 0)
2068                     (cons
2069                      (math-sub (math-neg (car dm)) 1)
2070                      (math-sub 12 (cdr dm)))))
2071               (math-idivmod midin 12)))
2072            (n (math-sub (car nr) 1))
2073            (note (car (rassoc (cdr nr) math-notes))))
2074       (if cents
2075           (list '+ (list 'calcFunc-subscr note n)
2076                    (list '* cents '(var cents var-cents)))
2077         (list 'calcFunc-subscr note n)))))
2078
2079 (defun math-freq-to-spn (freq)
2080   "Return the scientific pitch notation corresponding to FREQ Hz."
2081   (math-with-extra-prec 3
2082     (math-midi-to-spn (math-freq-to-midi freq))))
2083
2084 (defun math-midi-to-freq (midi)
2085   "Return the frequency of the note with midi number MIDI."
2086   (list '*
2087         (math-mul
2088          440
2089          (math-pow
2090           2
2091           (math-div
2092            (math-sub
2093             midi
2094             69)
2095            12)))
2096         '(var Hz var-Hz)))
2097
2098 (defun math-spn-to-freq (spn)
2099   "Return the frequency of the note with scientific pitch notation SPN."
2100   (math-midi-to-freq (math-spn-to-midi spn)))
2101
2102 (defun calcFunc-spn (expr)
2103   "Return EXPR written as scientific pitch notation + cents."
2104   ;; Get the coefficient of Hz
2105   (let (note)
2106     (cond
2107      ((setq note (math-freqp expr))
2108       (math-freq-to-spn note))
2109      ((setq note (math-midip expr))
2110       (math-midi-to-spn note))
2111      ((math-spnp expr)
2112       expr)
2113      (t
2114       (math-reject-arg expr "*Improper expression")))))
2115
2116 (defun calcFunc-midi (expr)
2117   "Return EXPR written as a MIDI number."
2118   (let (note)
2119     (cond
2120      ((setq note (math-freqp expr))
2121       (math-freq-to-midi note))
2122      ((setq note (math-spnp expr))
2123       (math-spn-to-midi note))
2124      ((math-midip expr)
2125       expr)
2126      (t
2127       (math-reject-arg expr "*Improper expression")))))
2128
2129 (defun calcFunc-freq (expr)
2130   "Return the frequency corresponding to EXPR."
2131   (let (note)
2132     (cond
2133      ((setq note (math-midip expr))
2134       (math-midi-to-freq note))
2135      ((setq note (math-spnp expr))
2136       (math-spn-to-freq note))
2137      ((math-freqp expr)
2138       expr)
2139      (t
2140       (math-reject-arg expr "*Improper expression")))))
2141
2142 (defun calc-freq (arg)
2143   "Return the frequency corresponding to the expression on the stack."
2144   (interactive "P")
2145   (calc-slow-wrapper
2146    (calc-unary-op "freq" 'calcFunc-freq arg)))
2147
2148 (defun calc-midi (arg)
2149   "Return the MIDI number corresponding to the expression on the stack."
2150   (interactive "P")
2151   (calc-slow-wrapper
2152    (calc-unary-op "midi" 'calcFunc-midi arg)))
2153
2154 (defun calc-spn (arg)
2155   "Return the scientific pitch notation corresponding to the expression on the stack."
2156   (interactive "P")
2157   (calc-slow-wrapper
2158    (calc-unary-op "spn" 'calcFunc-spn arg)))
2159
2160
2161 (provide 'calc-units)
2162
2163 ;; Local variables:
2164 ;; coding: utf-8
2165 ;; End:
2166
2167 ;;; calc-units.el ends here