lisp/calc/calc-units.el

   1 ;;; calc-units.el --- unit conversion functions for Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2013 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)
 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                                 calc-allow-units-as-numbers
 455                                 (eq (math-get-standard-units expr) 1))))
 456        (let ((uold (or old-units
 457                        (progn
 458                          (setq uoldname
 459                                (if unitscancel
 460                                    (read-string
 461                                     "(The expression is unitless when simplified) Old Units: ")
 462                                  (read-string "Old units: ")))
 463                          (if (equal uoldname "")
 464                              (progn
 465                                (setq nouold unitscancel)
 466                                (setq uoldname "1")
 467                                1)
 468                            (if (string-match "\\` */" uoldname)
 469                                (setq uoldname (concat "1" uoldname)))
 470                            (math-read-expr uoldname))))))
 471          (when (eq (car-safe uold) 'error)
 472            (error "Bad format in units expression: %s" (nth 1 uold)))
 473          (setq expr (math-mul expr uold))))
 474      (setq defunits (math-get-default-units expr))
 475      (unless new-units
 476        (setq new-units
 477              (read-string (concat
 478                            (if (and uoldname (not nouold))
 479                                (concat "Old units: "
 480                                        uoldname
 481                                        ", new units")
 482                              "New units")
 483                            (if defunits
 484                                (concat
 485                                 " (default "
 486                                 defunits
 487                                 "): ")
 488                              ": "))))
 489        (if (and
 490             (string= new-units "")
 491             defunits)
 492            (setq new-units defunits)))
 493      (when (string-match "\\` */" new-units)
 494        (setq new-units (concat "1" new-units)))
 495      (setq units (math-read-expr new-units))
 496      (when (eq (car-safe units) 'error)
 497        (error "Bad format in units expression: %s" (nth 2 units)))
 498      (if calc-ensure-consistent-units
 499          (math-check-unit-consistency expr units))
 500      (let ((unew (math-units-in-expr-p units t))
 501            (std (and (eq (car-safe units) 'var)
 502                      (assq (nth 1 units) math-standard-units-systems)))
 503            (comp (eq (car-safe units) '+)))
 504        (unless (or unew std)
 505          (error "No units specified"))
 506        (let ((res
 507               (if std
 508                   (math-simplify-units (math-to-standard-units expr (nth 1 std)))
 509                 (math-convert-units expr units (and uoldname (not (equal uoldname "1")))))))
 510          (math-put-default-units res (if comp units))
 511          (calc-enter-result 1 "cvun" res))))))
 512
 513 (defun calc-autorange-units (arg)
 514   (interactive "P")
 515   (calc-wrapper
 516    (calc-change-mode 'calc-autorange-units arg nil t)
 517    (message (if calc-autorange-units
 518                 "Adjusting target unit prefix automatically"
 519               "Using target units exactly"))))
 520
 521 (defun calc-convert-temperature (&optional old-units new-units)
 522   (interactive)
 523   (calc-slow-wrapper
 524    (let ((expr (calc-top-n 1))
 525          (uold nil)
 526          (uoldname nil)
 527          unew
 528          defunits)
 529      (setq uold (or old-units
 530                     (let ((units (math-single-units-in-expr-p expr)))
 531                       (if units
 532                           (if (consp units)
 533                               (list 'var (car units)
 534                                     (intern (concat "var-"
 535                                                     (symbol-name
 536                                                      (car units)))))
 537                             (error "Not a pure temperature expression"))
 538                         (math-read-expr
 539                          (setq uoldname (read-string
 540                                          "Old temperature units: ")))))))
 541      (when (eq (car-safe uold) 'error)
 542        (error "Bad format in units expression: %s" (nth 2 uold)))
 543      (or (math-units-in-expr-p expr nil)
 544          (setq expr (math-mul expr uold)))
 545      (setq defunits (math-get-default-units expr))
 546      (setq unew (or new-units
 547                     (read-string
 548                      (concat
 549                       (if uoldname
 550                           (concat "Old temperature units: "
 551                                   uoldname
 552                                   ", new units")
 553                         "New temperature units")
 554                       (if defunits
 555                           (concat " (default "
 556                                   defunits
 557                                   "): ")
 558                         ": ")))))
 559      (setq unew (math-read-expr (if (string= unew "") defunits unew)))
 560      (when (eq (car-safe unew) 'error)
 561        (error "Bad format in units expression: %s" (nth 2 unew)))
 562      (math-put-default-units unew)
 563      (let ((ntemp (calc-normalize
 564                    (math-simplify-units
 565                     (math-convert-temperature expr uold unew
 566                                               uoldname)))))
 567        (if (Math-zerop ntemp)
 568            (setq ntemp (list '* ntemp unew)))
 569        (let ((calc-simplify-mode 'none))
 570          (calc-enter-result 1 "cvtm" ntemp))))))
 571
 572 (defun calc-remove-units ()
 573   (interactive)
 574   (calc-slow-wrapper
 575    (calc-enter-result 1 "rmun" (math-simplify-units
 576                                 (math-remove-units (calc-top-n 1))))))
 577
 578 (defun calc-extract-units ()
 579   (interactive)
 580   (calc-slow-wrapper
 581    (calc-enter-result 1 "exun" (math-simplify-units
 582                                 (math-extract-units (calc-top-n 1))))))
 583
 584 ;; The variables calc-num-units and calc-den-units are local to
 585 ;; calc-explain-units, but are used by calc-explain-units-rec,
 586 ;; which is called by calc-explain-units.
 587 (defvar calc-num-units)
 588 (defvar calc-den-units)
 589
 590 (defun calc-explain-units ()
 591   (interactive)
 592   (calc-wrapper
 593    (let ((calc-num-units nil)
 594          (calc-den-units nil))
 595      (calc-explain-units-rec (calc-top-n 1) 1)
 596      (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
 597           (setq calc-den-units (concat "(" calc-den-units ")")))
 598      (if calc-num-units
 599          (if calc-den-units
 600              (message "%s per %s" calc-num-units calc-den-units)
 601            (message "%s" calc-num-units))
 602        (if calc-den-units
 603            (message "1 per %s" calc-den-units)
 604          (message "No units in expression"))))))
 605
 606 (defun calc-explain-units-rec (expr pow)
 607   (let ((u (math-check-unit-name expr))
 608         pos)
 609     (if (and u (not (math-zerop pow)))
 610         (let ((name (or (nth 2 u) (symbol-name (car u)))))
 611           (if (eq (aref name 0) ?\*)
 612               (setq name (substring name 1)))
 613           (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 614               (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name)
 615                   (while (setq pos (string-match "[ ()]" name))
 616                     (setq name (concat (substring name 0 pos)
 617                                        (if (eq (aref name pos) 32) "-" "")
 618                                        (substring name (1+ pos)))))
 619                 (setq name (concat "(" name ")"))))
 620           (or (eq (nth 1 expr) (car u))
 621               (setq name (concat (nth 2 (assq (aref (symbol-name
 622                                                      (nth 1 expr)) 0)
 623                                               math-unit-prefixes))
 624                                  (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 625                                           (not (memq (car u) '(mHg gf))))
 626                                      (concat "-" name)
 627                                    (downcase name)))))
 628           (cond ((or (math-equal-int pow 1)
 629                      (math-equal-int pow -1)))
 630                 ((or (math-equal-int pow 2)
 631                      (math-equal-int pow -2))
 632                  (if (equal (nth 4 u) '((m . 1)))
 633                      (setq name (concat "Square-" name))
 634                    (setq name (concat name "-squared"))))
 635                 ((or (math-equal-int pow 3)
 636                      (math-equal-int pow -3))
 637                  (if (equal (nth 4 u) '((m . 1)))
 638                      (setq name (concat "Cubic-" name))
 639                    (setq name (concat name "-cubed"))))
 640                 (t
 641                  (setq name (concat name "^"
 642                                     (math-format-number (math-abs pow))))))
 643           (if (math-posp pow)
 644               (setq calc-num-units (if calc-num-units
 645                                   (concat calc-num-units " " name)
 646                                 name))
 647             (setq calc-den-units (if calc-den-units
 648                                 (concat calc-den-units " " name)
 649                               name))))
 650       (cond ((eq (car-safe expr) '*)
 651              (calc-explain-units-rec (nth 1 expr) pow)
 652              (calc-explain-units-rec (nth 2 expr) pow))
 653             ((eq (car-safe expr) '/)
 654              (calc-explain-units-rec (nth 1 expr) pow)
 655              (calc-explain-units-rec (nth 2 expr) (- pow)))
 656             ((memq (car-safe expr) '(neg + -))
 657              (calc-explain-units-rec (nth 1 expr) pow))
 658             ((and (eq (car-safe expr) '^)
 659                   (math-realp (nth 2 expr)))
 660              (calc-explain-units-rec (nth 1 expr)
 661                                      (math-mul pow (nth 2 expr))))))))
 662
 663 (defun calc-simplify-units ()
 664   (interactive)
 665   (calc-slow-wrapper
 666    (calc-with-default-simplification
 667     (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
 668
 669 (defun calc-view-units-table (n)
 670   (interactive "P")
 671   (and n (setq math-units-table-buffer-valid nil))
 672   (let ((win (get-buffer-window "*Units Table*")))
 673     (if (and win
 674              math-units-table
 675              math-units-table-buffer-valid)
 676         (progn
 677           (bury-buffer (window-buffer win))
 678           (let ((curwin (selected-window)))
 679             (select-window win)
 680             (switch-to-buffer nil)
 681             (select-window curwin)))
 682       (math-build-units-table-buffer nil))))
 683
 684 (defun calc-enter-units-table (n)
 685   (interactive "P")
 686   (and n (setq math-units-table-buffer-valid nil))
 687   (math-build-units-table-buffer t)
 688   (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
 689
 690 (defun calc-define-unit (uname desc &optional disp)
 691   (interactive "SDefine unit name: \nsDescription: \nP")
 692   (if disp (setq disp (read-string "Display definition: ")))
 693   (calc-wrapper
 694    (let ((form (calc-top-n 1))
 695          (unit (assq uname math-additional-units)))
 696      (or unit
 697          (setq math-additional-units
 698                (cons (setq unit (list uname nil nil nil nil))
 699                      math-additional-units)
 700                math-units-table nil))
 701      (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
 702                                        (eq (nth 1 form) uname)))
 703                              (not (math-equal-int form 1))
 704                              (math-format-flat-expr form 0)))
 705      (setcar (cdr (cdr unit)) (and (not (equal desc ""))
 706                                    desc))
 707      (if disp
 708          (setcar (cdr (cdr (cdr (cdr unit)))) disp))))
 709   (calc-invalidate-units-table))
 710
 711 (defun calc-undefine-unit (uname)
 712   (interactive "SUndefine unit name: ")
 713   (calc-wrapper
 714    (let ((unit (assq uname math-additional-units)))
 715      (or unit
 716          (if (assq uname math-standard-units)
 717              (error "\"%s\" is a predefined unit name" uname)
 718            (error "Unit name \"%s\" not found" uname)))
 719      (setq math-additional-units (delq unit math-additional-units)
 720            math-units-table nil)))
 721   (calc-invalidate-units-table))
 722
 723 (defun calc-invalidate-units-table ()
 724   (setq math-units-table nil)
 725   (let ((buf (get-buffer "*Units Table*")))
 726     (and buf
 727          (with-current-buffer buf
 728            (save-excursion
 729              (goto-char (point-min))
 730              (if (looking-at "Calculator Units Table")
 731                  (let ((inhibit-read-only t))
 732                    (insert "(Obsolete) "))))))))
 733
 734 (defun calc-get-unit-definition (uname)
 735   (interactive "SGet definition for unit: ")
 736   (calc-wrapper
 737    (math-build-units-table)
 738    (let ((unit (assq uname math-units-table)))
 739      (or unit
 740          (error "Unit name \"%s\" not found" uname))
 741      (let ((msg (nth 2 unit)))
 742        (if (stringp msg)
 743            (if (string-match "^\\*" msg)
 744                (setq msg (substring msg 1)))
 745          (setq msg (symbol-name uname)))
 746        (if (nth 1 unit)
 747            (progn
 748              (calc-enter-result 0 "ugdf" (nth 1 unit))
 749              (message "Derived unit: %s" msg))
 750          (calc-enter-result 0 "ugdf" (list 'var uname
 751                                            (intern
 752                                             (concat "var-"
 753                                                     (symbol-name uname)))))
 754          (message "Base unit: %s" msg))))))
 755
 756 (defun calc-permanent-units ()
 757   (interactive)
 758   (calc-wrapper
 759    (let (pos)
 760      (set-buffer (find-file-noselect (substitute-in-file-name
 761                                       calc-settings-file)))
 762      (goto-char (point-min))
 763      (if (and (search-forward ";;; Custom units stored by Calc" nil t)
 764               (progn
 765                 (beginning-of-line)
 766                 (setq pos (point))
 767                 (search-forward "\n;;; End of custom units" nil t)))
 768          (progn
 769            (beginning-of-line)
 770            (forward-line 1)
 771            (delete-region pos (point)))
 772        (goto-char (point-max))
 773        (insert "\n\n")
 774        (forward-char -1))
 775      (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
 776      (if math-additional-units
 777          (progn
 778            (insert "(setq math-additional-units '(\n")
 779            (let ((list math-additional-units))
 780              (while list
 781                (insert "  (" (symbol-name (car (car list))) " "
 782                        (if (nth 1 (car list))
 783                            (if (stringp (nth 1 (car list)))
 784                                (prin1-to-string (nth 1 (car list)))
 785                              (prin1-to-string (math-format-flat-expr
 786                                                (nth 1 (car list)) 0)))
 787                          "nil")
 788                        " "
 789                        (prin1-to-string (nth 2 (car list)))
 790                        ")\n")
 791                (setq list (cdr list))))
 792            (insert "))\n"))
 793        (insert ";;; (no custom units defined)\n"))
 794      (insert ";;; End of custom units\n")
 795      (save-buffer))))
 796
 797
 798 ;; The variable math-cu-unit-list is local to math-build-units-table,
 799 ;; but is used by math-compare-unit-names, which is called (indirectly)
 800 ;; by math-build-units-table.
 801 ;; math-cu-unit-list is also local to math-convert-units, but is used
 802 ;; by math-convert-units-rec, which is called by math-convert-units.
 803 (defvar math-cu-unit-list)
 804
 805 (defun math-build-units-table ()
 806   (or math-units-table
 807       (let* ((combined-units (append math-additional-units
 808                                      math-standard-units))
 809              (math-cu-unit-list (mapcar 'car combined-units))
 810              tab)
 811         (message "Building units table...")
 812         (setq math-units-table-buffer-valid nil)
 813         (setq tab (mapcar (function
 814                            (lambda (x)
 815                              (list (car x)
 816                                    (and (nth 1 x)
 817                                         (if (stringp (nth 1 x))
 818                                             (let ((exp (math-read-plain-expr
 819                                                         (nth 1 x))))
 820                                               (if (eq (car-safe exp) 'error)
 821                                                   (error "Format error in definition of %s in units table: %s"
 822                                                          (car x) (nth 2 exp))
 823                                                 exp))
 824                                           (nth 1 x)))
 825                                    (nth 2 x)
 826                                    (nth 3 x)
 827                                    (and (not (nth 1 x))
 828                                         (list (cons (car x) 1)))
 829                                    (nth 4 x))))
 830                           combined-units))
 831         (let ((math-units-table tab))
 832           (mapc 'math-find-base-units tab))
 833         (message "Building units table...done")
 834         (setq math-units-table tab))))
 835
 836 ;; The variables math-fbu-base and math-fbu-entry are local to
 837 ;; math-find-base-units, but are used by math-find-base-units-rec,
 838 ;; which is called by math-find-base-units.
 839 (defvar math-fbu-base)
 840 (defvar math-fbu-entry)
 841
 842 (defun math-find-base-units (math-fbu-entry)
 843   (if (eq (nth 4 math-fbu-entry) 'boom)
 844       (error "Circular definition involving unit %s" (car math-fbu-entry)))
 845   (or (nth 4 math-fbu-entry)
 846       (let (math-fbu-base)
 847         (setcar (nthcdr 4 math-fbu-entry) 'boom)
 848         (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
 849         '(or math-fbu-base
 850             (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
 851         (while (eq (cdr (car math-fbu-base)) 0)
 852           (setq math-fbu-base (cdr math-fbu-base)))
 853         (let ((b math-fbu-base))
 854           (while (cdr b)
 855             (if (eq (cdr (car (cdr b))) 0)
 856                 (setcdr b (cdr (cdr b)))
 857               (setq b (cdr b)))))
 858         (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
 859         (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
 860         math-fbu-base)))
 861
 862 (defun math-compare-unit-names (a b)
 863   (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
 864
 865 (defun math-find-base-units-rec (expr pow)
 866   (let ((u (math-check-unit-name expr)))
 867     (cond (u
 868            (let ((ulist (math-find-base-units u)))
 869              (while ulist
 870                (let ((p (* (cdr (car ulist)) pow))
 871                      (old (assq (car (car ulist)) math-fbu-base)))
 872                  (if old
 873                      (setcdr old (+ (cdr old) p))
 874                    (setq math-fbu-base
 875                          (cons (cons (car (car ulist)) p) math-fbu-base))))
 876                (setq ulist (cdr ulist)))))
 877           ((math-scalarp expr))
 878           ((and (eq (car expr) '^)
 879                 (integerp (nth 2 expr)))
 880            (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
 881           ((eq (car expr) '*)
 882            (math-find-base-units-rec (nth 1 expr) pow)
 883            (math-find-base-units-rec (nth 2 expr) pow))
 884           ((eq (car expr) '/)
 885            (math-find-base-units-rec (nth 1 expr) pow)
 886            (math-find-base-units-rec (nth 2 expr) (- pow)))
 887           ((eq (car expr) 'neg)
 888            (math-find-base-units-rec (nth 1 expr) pow))
 889           ((eq (car expr) '+)
 890            (math-find-base-units-rec (nth 1 expr) pow))
 891           ((eq (car expr) 'var)
 892            (or (eq (nth 1 expr) 'pi)
 893                (error "Unknown name %s in defining expression for unit %s"
 894                       (nth 1 expr) (car math-fbu-entry))))
 895           ((equal expr '(calcFunc-ln 10)))
 896           (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
 897
 898
 899 (defun math-units-in-expr-p (expr sub-exprs)
 900   (and (consp expr)
 901        (if (eq (car expr) 'var)
 902            (math-check-unit-name expr)
 903          (and (or sub-exprs
 904                   (memq (car expr) '(* / ^)))
 905               (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
 906                   (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
 907
 908 (defun math-only-units-in-expr-p (expr)
 909   (and (consp expr)
 910        (if (eq (car expr) 'var)
 911            (math-check-unit-name expr)
 912          (if (memq (car expr) '(* /))
 913              (and (math-only-units-in-expr-p (nth 1 expr))
 914                   (math-only-units-in-expr-p (nth 2 expr)))
 915            (and (eq (car expr) '^)
 916                 (and (math-only-units-in-expr-p (nth 1 expr))
 917                      (math-realp (nth 2 expr))))))))
 918
 919 (defun math-single-units-in-expr-p (expr)
 920   (cond ((math-scalarp expr) nil)
 921         ((eq (car expr) 'var)
 922          (math-check-unit-name expr))
 923         ((eq (car expr) '*)
 924          (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
 925                (u2 (math-single-units-in-expr-p (nth 2 expr))))
 926            (or (and u1 u2 'wrong)
 927                u1
 928                u2)))
 929         ((eq (car expr) '/)
 930          (if (math-units-in-expr-p (nth 2 expr) nil)
 931              'wrong
 932            (math-single-units-in-expr-p (nth 1 expr))))
 933         (t 'wrong)))
 934
 935 (defun math-consistent-units-p (expr newunits)
 936   "Non-nil if EXPR and NEWUNITS have consistent units."
 937   (or
 938    (and (eq (car-safe newunits) 'var)
 939         (assq (nth 1 newunits) math-standard-units-systems))
 940    (math-numberp (math-get-units (list '/ expr newunits)))))
 941
 942 (defun math-check-unit-consistency (expr units)
 943   "Give an error if EXPR and UNITS do not have consistent units."
 944   (unless  (math-consistent-units-p expr units)
 945     (error "New units (%s) are inconsistent with current units (%s)"
 946            (math-format-value units)
 947            (math-format-value (math-get-units expr)))))
 948
 949 (defun math-check-unit-name (v)
 950   (and (eq (car-safe v) 'var)
 951        (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
 952            (let ((name (symbol-name (nth 1 v))))
 953              (and (> (length name) 1)
 954                   (assq (aref name 0) math-unit-prefixes)
 955                   (or (assq (intern (substring name 1)) math-units-table)
 956                       (and (eq (aref name 0) ?M)
 957                            (> (length name) 3)
 958                            (eq (aref name 1) ?e)
 959                            (eq (aref name 2) ?g)
 960                            (assq (intern (substring name 3))
 961                                  math-units-table))))))))
 962
 963 ;; The variable math-which-standard is local to math-to-standard-units,
 964 ;; but is used by math-to-standard-rec, which is called by
 965 ;; math-to-standard-units.
 966 (defvar math-which-standard)
 967
 968 (defun math-to-standard-units (expr math-which-standard)
 969   (math-to-standard-rec expr))
 970
 971 (defun math-to-standard-rec (expr)
 972   (if (eq (car-safe expr) 'var)
 973       (let ((u (math-check-unit-name expr))
 974             (base (nth 1 expr)))
 975         (if u
 976             (progn
 977               (if (nth 1 u)
 978                   (setq expr (math-to-standard-rec (nth 1 u)))
 979                 (let ((st (assq (car u) math-which-standard)))
 980                   (if st
 981                       (setq expr (nth 1 st))
 982                     (setq expr (list 'var (car u)
 983                                      (intern (concat "var-"
 984                                                      (symbol-name
 985                                                       (car u)))))))))
 986               (or (null u)
 987                   (eq base (car u))
 988                   (setq expr (list '*
 989                                    (nth 1 (assq (aref (symbol-name base) 0)
 990                                                 math-unit-prefixes))
 991                                    expr)))
 992               expr)
 993           (if (eq base 'pi)
 994               (math-pi)
 995             expr)))
 996     (if (or
 997          (Math-primp expr)
 998          (and (eq (car-safe expr) 'calcFunc-subscr)
 999               (eq (car-safe (nth 1 expr)) 'var)))
1000         expr
1001       (cons (car expr)
1002             (mapcar 'math-to-standard-rec (cdr expr))))))
1003
1004 (defun math-apply-units (expr units ulist &optional pure)
1005   (setq expr (math-simplify-units expr))
1006   (if ulist
1007       (let ((new 0)
1008             value)
1009         (or (math-numberp expr)
1010             (error "Incompatible units"))
1011         (while (cdr ulist)
1012           (setq value (math-div expr (nth 1 (car ulist)))
1013                 value (math-floor (let ((calc-internal-prec
1014                                          (1- calc-internal-prec)))
1015                                     (math-normalize value)))
1016                 new (math-add new (math-mul value (car (car ulist))))
1017                 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
1018                 ulist (cdr ulist)))
1019         (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
1020                                 (car (car ulist)))))
1021     (if pure
1022         expr
1023       (math-simplify-units (list '* expr units)))))
1024
1025 (defvar math-decompose-units-cache nil)
1026 (defun math-decompose-units (units)
1027   (let ((u (math-check-unit-name units)))
1028     (and u (eq (car-safe (nth 1 u)) '+)
1029          (setq units (nth 1 u))))
1030   (setq units (calcFunc-expand units))
1031   (and (eq (car-safe units) '+)
1032        (let ((entry (list units calc-internal-prec calc-prefer-frac)))
1033          (or (equal entry (car math-decompose-units-cache))
1034              (let ((ulist nil)
1035                    (utemp units)
1036                    qty unit)
1037                (while (eq (car-safe utemp) '+)
1038                  (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
1039                                    ulist)
1040                        utemp (nth 1 utemp)))
1041                (setq ulist (cons (math-decompose-unit-part utemp) ulist)
1042                      utemp ulist)
1043                (while (setq utemp (cdr utemp))
1044                  (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
1045                    (error "Inconsistent units in sum")))
1046                (setq math-decompose-units-cache
1047                      (cons entry
1048                            (sort ulist
1049                                  (function
1050                                   (lambda (x y)
1051                                     (not (Math-lessp (nth 1 x)
1052                                                      (nth 1 y))))))))))
1053          (cdr math-decompose-units-cache))))
1054
1055 (defun math-decompose-unit-part (unit)
1056   (cons unit
1057         (math-is-multiple (math-simplify-units (math-to-standard-units
1058                                                 unit nil))
1059                           t)))
1060
1061 ;; The variable math-fcu-u is local to math-find-compatible-unit,
1062 ;; but is used by math-find-compatible-rec which is called by
1063 ;; math-find-compatible-unit.
1064 (defvar math-fcu-u)
1065
1066 (defun math-find-compatible-unit (expr unit)
1067   (let ((math-fcu-u (math-check-unit-name unit)))
1068     (if math-fcu-u
1069         (math-find-compatible-unit-rec expr 1))))
1070
1071 (defun math-find-compatible-unit-rec (expr pow)
1072   (cond ((eq (car-safe expr) '*)
1073          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1074              (math-find-compatible-unit-rec (nth 2 expr) pow)))
1075         ((eq (car-safe expr) '/)
1076          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1077              (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
1078         ((and (eq (car-safe expr) '^)
1079               (integerp (nth 2 expr)))
1080          (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
1081         (t
1082          (let ((u2 (math-check-unit-name expr)))
1083            (if (equal (nth 4 math-fcu-u) (nth 4 u2))
1084                (cons expr pow))))))
1085
1086 ;; The variables math-cu-new-units and math-cu-pure are local to
1087 ;; math-convert-units, but are used by math-convert-units-rec,
1088 ;; which is called by math-convert-units.
1089 (defvar math-cu-new-units)
1090 (defvar math-cu-pure)
1091
1092 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
1093   (if (eq (car-safe math-cu-new-units) 'var)
1094       (let ((unew (assq (nth 1 math-cu-new-units)
1095                         (math-build-units-table))))
1096         (if (eq (car-safe (nth 1 unew)) '+)
1097             (setq math-cu-new-units (nth 1 unew)))))
1098   (math-with-extra-prec 2
1099     (let ((compat (and (not math-cu-pure)
1100                        (math-find-compatible-unit expr math-cu-new-units)))
1101           (math-cu-unit-list nil)
1102           (math-combining-units nil))
1103       (if compat
1104           (math-simplify-units
1105            (math-mul (math-mul (math-simplify-units
1106                                 (math-div expr (math-pow (car compat)
1107                                                          (cdr compat))))
1108                                (math-pow math-cu-new-units (cdr compat)))
1109                      (math-simplify-units
1110                       (math-to-standard-units
1111                        (math-pow (math-div (car compat) math-cu-new-units)
1112                                  (cdr compat))
1113                        nil))))
1114         (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
1115           (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
1116         (when (eq (car-safe expr) '+)
1117           (setq expr (math-simplify-units expr)))
1118         (if (math-units-in-expr-p expr t)
1119             (math-convert-units-rec expr)
1120           (math-apply-units (math-to-standard-units
1121                              (list '/ expr math-cu-new-units) nil)
1122                             math-cu-new-units math-cu-unit-list math-cu-pure))))))
1123
1124 (defun math-convert-units-rec (expr)
1125   (if (math-units-in-expr-p expr nil)
1126       (math-apply-units (math-to-standard-units
1127                          (list '/ expr math-cu-new-units) nil)
1128                         math-cu-new-units math-cu-unit-list math-cu-pure)
1129     (if (Math-primp expr)
1130         expr
1131       (cons (car expr)
1132             (mapcar 'math-convert-units-rec (cdr expr))))))
1133
1134 (defun math-convert-temperature (expr old new &optional pure)
1135   (let* ((units (math-single-units-in-expr-p expr))
1136          (uold (if old
1137                    (if (or (null units)
1138                            (equal (nth 1 old) (car units)))
1139                        (math-check-unit-name old)
1140                      (error "Inconsistent temperature units"))
1141                  units))
1142          (unew (math-check-unit-name new)))
1143     (unless (and (consp unew) (nth 3 unew))
1144       (error "Not a valid temperature unit"))
1145     (unless (and (consp uold) (nth 3 uold))
1146       (error "Not a pure temperature expression"))
1147     (let ((v (car uold)))
1148       (setq expr (list '/ expr (list 'var v
1149                                      (intern (concat "var-"
1150                                                      (symbol-name v)))))))
1151     (or (eq (nth 3 uold) (nth 3 unew))
1152         (cond ((eq (nth 3 uold) 'K)
1153                (setq expr (list '- expr '(/ 27315 100)))
1154                (if (eq (nth 3 unew) 'F)
1155                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
1156               ((eq (nth 3 uold) 'C)
1157                (if (eq (nth 3 unew) 'F)
1158                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))
1159                  (setq expr (list '+ expr '(/ 27315 100)))))
1160               (t
1161                (setq expr (list '* (list '- expr 32) '(/ 5 9)))
1162                (if (eq (nth 3 unew) 'K)
1163                    (setq expr (list '+ expr '(/ 27315 100)))))))
1164     (if pure
1165         expr
1166       (list '* expr new))))
1167
1168
1169
1170 (defun math-simplify-units (a)
1171   (let ((math-simplifying-units t)
1172         (calc-matrix-mode 'scalar))
1173     (math-simplify a)))
1174 (defalias 'calcFunc-usimplify 'math-simplify-units)
1175
1176 ;; The function created by math-defsimplify uses the variable
1177 ;; math-simplify-expr, and so is used by functions in math-defsimplify
1178 (defvar math-simplify-expr)
1179
1180 (math-defsimplify (+ -)
1181   (and math-simplifying-units
1182        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1183        (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1184               (ratio (math-simplify (math-to-standard-units
1185                                      (list '/ (nth 2 math-simplify-expr) units) nil))))
1186          (if (math-units-in-expr-p ratio nil)
1187              (progn
1188                (calc-record-why "*Inconsistent units" math-simplify-expr)
1189                math-simplify-expr)
1190            (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1191                               (if (eq (car math-simplify-expr) '-)
1192                                   (math-neg ratio) ratio))
1193                  units)))))
1194
1195 (math-defsimplify *
1196   (math-simplify-units-prod))
1197
1198 (defun math-simplify-units-prod ()
1199   (and math-simplifying-units
1200        calc-autorange-units
1201        (Math-realp (nth 1 math-simplify-expr))
1202        (let* ((num (math-float (nth 1 math-simplify-expr)))
1203               (xpon (calcFunc-xpon num))
1204               (unitp (cdr (cdr math-simplify-expr)))
1205               (unit (car unitp))
1206               (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1207               u)
1208          (and (eq (car-safe unit) '*)
1209               (setq unitp (cdr unit)
1210                     unit (car unitp)))
1211          (and (eq (car-safe unit) '^)
1212               (integerp (nth 2 unit))
1213               (setq pow (* pow (nth 2 unit))
1214                     unitp (cdr unit)
1215                     unit (car unitp)))
1216          (and (setq u (math-check-unit-name unit))
1217               (integerp xpon)
1218               (or (< xpon 0)
1219                   (>= xpon (if (eq (car u) 'm) 1 3)))
1220               (let* ((uxpon 0)
1221                      (pref (if (< pow 0)
1222                                (reverse math-unit-prefixes)
1223                              math-unit-prefixes))
1224                      (p pref)
1225                      pxpon pname)
1226                 (or (eq (car u) (nth 1 unit))
1227                     (setq uxpon (* pow
1228                                    (nth 2 (nth 1 (assq
1229                                                   (aref (symbol-name
1230                                                          (nth 1 unit)) 0)
1231                                                   math-unit-prefixes))))))
1232                 (setq xpon (+ xpon uxpon))
1233                 (while (and p
1234                             (or (memq (car (car p)) '(?d ?D ?h ?H))
1235                                 (and (eq (car (car p)) ?c)
1236                                      (not (eq (car u) 'm)))
1237                                 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1238                                                        pow)))
1239                                 (progn
1240                                   (setq pname (math-build-var-name
1241                                                (if (eq (car (car p)) 0)
1242                                                    (car u)
1243                                                  (concat (char-to-string
1244                                                           (car (car p)))
1245                                                          (symbol-name
1246                                                           (car u))))))
1247                                   (and (/= (car (car p)) 0)
1248                                        (assq (nth 1 pname)
1249                                              math-units-table)))))
1250                   (setq p (cdr p)))
1251                 (and p
1252                      (/= pxpon uxpon)
1253                      (or (not (eq p pref))
1254                          (< xpon (+ pxpon (* (math-abs pow) 3))))
1255                      (progn
1256                        (setcar (cdr math-simplify-expr)
1257                                (let ((calc-prefer-frac nil))
1258                                  (calcFunc-scf (nth 1 math-simplify-expr)
1259                                                (- uxpon pxpon))))
1260                        (setcar unitp pname)
1261                        math-simplify-expr)))))))
1262
1263 (defvar math-try-cancel-units)
1264
1265 (math-defsimplify /
1266   (and math-simplifying-units
1267        (let ((np (cdr math-simplify-expr))
1268              (math-try-cancel-units 0)
1269              n nn)
1270          (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1271                      (cdr (nth 2 math-simplify-expr))
1272                    (nthcdr 2 math-simplify-expr)))
1273          (if (math-realp (car n))
1274              (progn
1275                (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1276                                             (let ((calc-prefer-frac nil))
1277                                               (math-div 1 (car n)))))
1278                (setcar n 1)))
1279          (while (eq (car-safe (setq n (car np))) '*)
1280            (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1281            (setq np (cdr (cdr n))))
1282          (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1283          (if (eq math-try-cancel-units 0)
1284              (let* ((math-simplifying-units nil)
1285                     (base (math-simplify
1286                            (math-to-standard-units math-simplify-expr nil))))
1287                (if (Math-numberp base)
1288                    (setq math-simplify-expr base))))
1289          (if (eq (car-safe math-simplify-expr) '/)
1290              (math-simplify-units-prod))
1291          math-simplify-expr)))
1292
1293 (defun math-simplify-units-divisor (np dp)
1294   (let ((n (car np))
1295         d dd temp)
1296     (while (eq (car-safe (setq d (car dp))) '*)
1297       (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1298         (setcar np (setq n temp))
1299         (setcar (cdr d) 1))
1300       (setq dp (cdr (cdr d))))
1301     (when (setq temp (math-simplify-units-quotient n d))
1302       (setcar np (setq n temp))
1303       (setcar dp 1))))
1304
1305 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1306 (defun math-simplify-units-quotient (n d)
1307   (let ((pow1 1)
1308         (pow2 1))
1309     (when (and (eq (car-safe n) '^)
1310                (integerp (nth 2 n)))
1311       (setq pow1 (nth 2 n) n (nth 1 n)))
1312     (when (and (eq (car-safe d) '^)
1313                (integerp (nth 2 d)))
1314       (setq pow2 (nth 2 d) d (nth 1 d)))
1315     (let ((un (math-check-unit-name n))
1316           (ud (math-check-unit-name d)))
1317       (and un ud
1318            (if (and (equal (nth 4 un) (nth 4 ud))
1319                     (eq pow1 pow2))
1320                (if (eq pow1 1)
1321                    (math-to-standard-units (list '/ n d) nil)
1322                  (list '^ (math-to-standard-units (list '/ n d) nil) pow1))
1323              (let (ud1)
1324                (setq un (nth 4 un)
1325                      ud (nth 4 ud))
1326                (while un
1327                  (setq ud1 ud)
1328                  (while ud1
1329                    (and (eq (car (car un)) (car (car ud1)))
1330                         (setq math-try-cancel-units
1331                               (+ math-try-cancel-units
1332                                  (- (* (cdr (car un)) pow1)
1333                                     (* (cdr (car ud)) pow2)))))
1334                    (setq ud1 (cdr ud1)))
1335                  (setq un (cdr un)))
1336                nil))))))
1337
1338 (math-defsimplify ^
1339   (and math-simplifying-units
1340        (math-realp (nth 2 math-simplify-expr))
1341        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1342            (list (car (nth 1 math-simplify-expr))
1343                  (list '^ (nth 1 (nth 1 math-simplify-expr))
1344                        (nth 2 math-simplify-expr))
1345                  (list '^ (nth 2 (nth 1 math-simplify-expr))
1346                        (nth 2 math-simplify-expr)))
1347          (math-simplify-units-pow (nth 1 math-simplify-expr)
1348                                   (nth 2 math-simplify-expr)))))
1349
1350 (math-defsimplify calcFunc-sqrt
1351   (and math-simplifying-units
1352        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1353            (list (car (nth 1 math-simplify-expr))
1354                  (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1355                  (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1356          (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1357
1358 (math-defsimplify (calcFunc-floor
1359                    calcFunc-ceil
1360                    calcFunc-round
1361                    calcFunc-rounde
1362                    calcFunc-roundu
1363                    calcFunc-trunc
1364                    calcFunc-float
1365                    calcFunc-frac
1366                    calcFunc-abs
1367                    calcFunc-clean)
1368   (and math-simplifying-units
1369        (= (length math-simplify-expr) 2)
1370        (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1371            (nth 1 math-simplify-expr)
1372          (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1373                   (or (math-only-units-in-expr-p
1374                        (nth 1 (nth 1 math-simplify-expr)))
1375                       (math-only-units-in-expr-p
1376                        (nth 2 (nth 1 math-simplify-expr)))))
1377              (list (car (nth 1 math-simplify-expr))
1378                    (cons (car math-simplify-expr)
1379                          (cons (nth 1 (nth 1 math-simplify-expr))
1380                                (cdr (cdr math-simplify-expr))))
1381                    (cons (car math-simplify-expr)
1382                          (cons (nth 2 (nth 1 math-simplify-expr))
1383                                (cdr (cdr math-simplify-expr)))))))))
1384
1385 (defun math-simplify-units-pow (a pow)
1386   (if (and (eq (car-safe a) '^)
1387            (math-check-unit-name (nth 1 a))
1388            (math-realp (nth 2 a)))
1389       (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1390     (let* ((u (math-check-unit-name a))
1391            (pf (math-to-simple-fraction pow))
1392            (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1393       (and u d
1394            (math-units-are-multiple u d)
1395            (list '^ (math-to-standard-units a nil) pow)))))
1396
1397
1398 (defun math-units-are-multiple (u n)
1399   (setq u (nth 4 u))
1400   (while (and u (= (% (cdr (car u)) n) 0))
1401     (setq u (cdr u)))
1402   (null u))
1403
1404 (math-defsimplify calcFunc-sin
1405   (and math-simplifying-units
1406        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1407        (let ((rad (math-simplify-units
1408                    (math-evaluate-expr
1409                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1410              (calc-angle-mode 'rad))
1411          (and (eq (car-safe rad) '*)
1412               (math-realp (nth 1 rad))
1413               (eq (car-safe (nth 2 rad)) 'var)
1414               (eq (nth 1 (nth 2 rad)) 'rad)
1415               (list 'calcFunc-sin (nth 1 rad))))))
1416
1417 (math-defsimplify calcFunc-cos
1418   (and math-simplifying-units
1419        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1420        (let ((rad (math-simplify-units
1421                    (math-evaluate-expr
1422                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1423              (calc-angle-mode 'rad))
1424          (and (eq (car-safe rad) '*)
1425               (math-realp (nth 1 rad))
1426               (eq (car-safe (nth 2 rad)) 'var)
1427               (eq (nth 1 (nth 2 rad)) 'rad)
1428               (list 'calcFunc-cos (nth 1 rad))))))
1429
1430 (math-defsimplify calcFunc-tan
1431   (and math-simplifying-units
1432        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1433        (let ((rad (math-simplify-units
1434                    (math-evaluate-expr
1435                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1436              (calc-angle-mode 'rad))
1437          (and (eq (car-safe rad) '*)
1438               (math-realp (nth 1 rad))
1439               (eq (car-safe (nth 2 rad)) 'var)
1440               (eq (nth 1 (nth 2 rad)) 'rad)
1441               (list 'calcFunc-tan (nth 1 rad))))))
1442
1443 (math-defsimplify calcFunc-sec
1444   (and math-simplifying-units
1445        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1446        (let ((rad (math-simplify-units
1447                    (math-evaluate-expr
1448                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1449              (calc-angle-mode 'rad))
1450          (and (eq (car-safe rad) '*)
1451               (math-realp (nth 1 rad))
1452               (eq (car-safe (nth 2 rad)) 'var)
1453               (eq (nth 1 (nth 2 rad)) 'rad)
1454               (list 'calcFunc-sec (nth 1 rad))))))
1455
1456 (math-defsimplify calcFunc-csc
1457   (and math-simplifying-units
1458        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1459        (let ((rad (math-simplify-units
1460                    (math-evaluate-expr
1461                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1462              (calc-angle-mode 'rad))
1463          (and (eq (car-safe rad) '*)
1464               (math-realp (nth 1 rad))
1465               (eq (car-safe (nth 2 rad)) 'var)
1466               (eq (nth 1 (nth 2 rad)) 'rad)
1467               (list 'calcFunc-csc (nth 1 rad))))))
1468
1469 (math-defsimplify calcFunc-cot
1470   (and math-simplifying-units
1471        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1472        (let ((rad (math-simplify-units
1473                    (math-evaluate-expr
1474                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1475              (calc-angle-mode 'rad))
1476          (and (eq (car-safe rad) '*)
1477               (math-realp (nth 1 rad))
1478               (eq (car-safe (nth 2 rad)) 'var)
1479               (eq (nth 1 (nth 2 rad)) 'rad)
1480               (list 'calcFunc-cot (nth 1 rad))))))
1481
1482
1483 (defun math-remove-units (expr)
1484   (if (math-check-unit-name expr)
1485       1
1486     (if (Math-primp expr)
1487         expr
1488       (cons (car expr)
1489             (mapcar 'math-remove-units (cdr expr))))))
1490
1491 (defun math-extract-units (expr)
1492   (cond
1493    ((memq (car-safe expr) '(* /))
1494     (cons (car expr)
1495           (mapcar 'math-extract-units (cdr expr))))
1496    ((and
1497      (eq (car-safe expr) '^)
1498      (math-check-unit-name (nth 1 expr)))
1499     expr)
1500    ((math-check-unit-name expr) expr)
1501    (t 1)))
1502
1503 (defun math-build-units-table-buffer (enter-buffer)
1504   (if (not (and math-units-table math-units-table-buffer-valid
1505                 (get-buffer "*Units Table*")))
1506       (let ((buf (get-buffer-create "*Units Table*"))
1507             (uptr (math-build-units-table))
1508             (calc-language (if (eq calc-language 'big) nil calc-language))
1509             (calc-float-format '(float 0))
1510             (calc-group-digits nil)
1511             (calc-number-radix 10)
1512             (calc-twos-complement-mode nil)
1513             (calc-point-char ".")
1514             (std nil)
1515             u name shadowed)
1516         (save-excursion
1517           (message "Formatting units table...")
1518           (set-buffer buf)
1519           (let ((inhibit-read-only t))
1520             (erase-buffer)
1521             (insert "Calculator Units Table:\n\n")
1522             (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n")
1523             (insert "Unit    Type  Definition                  Description\n\n")
1524             (while uptr
1525               (setq u (car uptr)
1526                     name (nth 2 u))
1527               (when (eq (car u) 'm)
1528                 (setq std t))
1529               (setq shadowed (and std (assq (car u) math-additional-units)))
1530               (when (and name
1531                          (> (length name) 1)
1532                          (eq (aref name 0) ?\*))
1533                 (unless (eq uptr math-units-table)
1534                   (insert "\n"))
1535                 (setq name (substring name 1)))
1536               (insert " ")
1537               (and shadowed (insert "("))
1538               (insert (symbol-name (car u)))
1539               (and shadowed (insert ")"))
1540               (if (nth 3 u)
1541                   (progn
1542                     (indent-to 10)
1543                     (insert (symbol-name (nth 3 u))))
1544                 (or std
1545                     (progn
1546                       (indent-to 10)
1547                       (insert "U"))))
1548               (indent-to 14)
1549               (and shadowed (insert "("))
1550               (if (nth 5 u)
1551                   (insert (nth 5 u))
1552                 (if (nth 1 u)
1553                     (insert (math-format-value (nth 1 u) 80))
1554                   (insert (symbol-name (car u)))))
1555               (and shadowed (insert ")"))
1556               (indent-to 41)
1557               (insert " ")
1558               (when name
1559                 (insert name))
1560               (if shadowed
1561                   (insert " (redefined above)")
1562                 (unless (nth 1 u)
1563                   (insert " (base unit)")))
1564               (insert "\n")
1565               (setq uptr (cdr uptr)))
1566             (insert "\n\nUnit Prefix Table:\n\n")
1567             (setq uptr math-unit-prefixes)
1568             (while uptr
1569               (setq u (car uptr))
1570               (insert " " (char-to-string (car u)))
1571               (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1572                   (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1573                           "   ")
1574                 (insert "     "))
1575               (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1576               (indent-to 15)
1577               (insert "   " (nth 2 u) "\n")
1578               (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1579             (insert "\n\n")
1580             (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
1581                      "names will not use the `tex' prefix; the unit name for a\n"
1582                      "TeX point will be `pt' instead of `texpt', for example.\n"
1583                      "To avoid conflicts, the unit names for pint and parsec will\n"
1584                      "be `pint' and `parsec' instead of `pt' and `pc'."))
1585           (view-mode)
1586           (message "Formatting units table...done"))
1587         (setq math-units-table-buffer-valid t)
1588         (let ((oldbuf (current-buffer)))
1589           (set-buffer buf)
1590           (goto-char (point-min))
1591           (set-buffer oldbuf))
1592         (if enter-buffer
1593             (pop-to-buffer buf)
1594           (display-buffer buf)))
1595     (if enter-buffer
1596         (pop-to-buffer (get-buffer "*Units Table*"))
1597       (display-buffer (get-buffer "*Units Table*")))))
1598
1599 ;;; Logarithmic units functions
1600
1601 (defvar math-logunits '((var dB var-dB)
1602                         (var Np var-Np)))
1603
1604 (defun math-conditional-apply (fn &rest args)
1605   "Evaluate f(args) unless in symbolic mode.
1606 In symbolic mode, return the list (fn args)."
1607   (if calc-symbolic-mode
1608       (cons fn args)
1609     (apply fn args)))
1610
1611 (defun math-conditional-pow (a b)
1612   "Evaluate a^b unless in symbolic mode.
1613 In symbolic mode, return the list (^ a b)."
1614   (if calc-symbolic-mode
1615       (list '^ a b)
1616     (math-pow a b)))
1617
1618 (defun math-extract-logunits (expr)
1619   (if (memq (car-safe expr) '(* /))
1620       (cons (car expr)
1621             (mapcar 'math-extract-logunits (cdr expr)))
1622     (if (memq (car-safe expr) '(^))
1623         (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
1624       (if (member expr math-logunits) expr 1))))
1625
1626 (defun math-logunits-add (a b neg power)
1627   (let ((aunit (math-simplify (math-extract-logunits a))))
1628     (if (not (eq (car-safe aunit) 'var))
1629         (calc-record-why "*Improper logarithmic unit" aunit)
1630       (let* ((units (math-extract-units a))
1631             (acoeff (math-simplify (math-remove-units a)))
1632             (bcoeff (math-simplify (math-to-standard-units
1633                                     (list '/ b units) nil))))
1634         (if (math-units-in-expr-p bcoeff nil)
1635             (calc-record-why "*Inconsistent units" nil)
1636           (if (and neg
1637                    (or (math-lessp acoeff bcoeff)
1638                        (math-equal acoeff bcoeff)))
1639               (calc-record-why "*Improper coefficients" nil)
1640             (math-mul
1641              (if (equal aunit '(var dB var-dB))
1642                  (let ((coef (if power 10 20)))
1643                    (math-mul coef
1644                              (math-conditional-apply 'calcFunc-log10
1645                               (if neg
1646                                   (math-sub
1647                                    (math-conditional-pow 10 (math-div acoeff coef))
1648                                    (math-conditional-pow 10 (math-div bcoeff coef)))
1649                                 (math-add
1650                                  (math-conditional-pow 10 (math-div acoeff coef))
1651                                  (math-conditional-pow 10 (math-div bcoeff coef)))))))
1652                (let ((coef (if power 2 1)))
1653                  (math-div
1654                   (math-conditional-apply 'calcFunc-ln
1655                    (if neg
1656                        (math-sub
1657                         (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1658                         (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
1659                      (math-add
1660                       (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1661                       (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
1662                   coef)))
1663              units)))))))
1664
1665 (defun calcFunc-lufadd (a b)
1666   (math-logunits-add a b nil nil))
1667
1668 (defun calcFunc-lupadd (a b)
1669   (math-logunits-add a b nil t))
1670
1671 (defun calcFunc-lufsub (a b)
1672   (math-logunits-add a b t nil))
1673
1674 (defun calcFunc-lupsub (a b)
1675   (math-logunits-add a b t t))
1676
1677 (defun calc-lu-plus (arg)
1678   (interactive "P")
1679   (calc-slow-wrapper
1680    (if (calc-is-inverse)
1681        (if (calc-is-hyperbolic)
1682            (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1683          (calc-binary-op "lu-" 'calcFunc-lupsub arg))
1684      (if (calc-is-hyperbolic)
1685          (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1686        (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
1687
1688 (defun calc-lu-minus (arg)
1689   (interactive "P")
1690   (calc-slow-wrapper
1691    (if (calc-is-inverse)
1692        (if (calc-is-hyperbolic)
1693            (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1694          (calc-binary-op "lu+" 'calcFunc-lupadd arg))
1695      (if (calc-is-hyperbolic)
1696          (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1697        (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
1698
1699 (defun math-logunits-mul (a b power)
1700   (let (logunit coef units number)
1701     (cond
1702      ((and
1703        (setq logunit (math-simplify (math-extract-logunits a)))
1704        (eq (car-safe logunit) 'var)
1705        (eq (math-simplify (math-extract-units b)) 1))
1706       (setq coef (math-simplify (math-remove-units a))
1707             units (math-extract-units a)
1708             number b))
1709      ((and
1710        (setq logunit (math-simplify (math-extract-logunits b)))
1711        (eq (car-safe logunit) 'var)
1712        (eq (math-simplify (math-extract-units a)) 1))
1713       (setq coef (math-simplify (math-remove-units b))
1714             units (math-extract-units b)
1715             number a))
1716      (t (setq logunit nil)))
1717     (if logunit
1718         (cond
1719          ((equal logunit '(var dB var-dB))
1720           (math-simplify
1721            (math-mul
1722             (math-add
1723              coef
1724              (math-mul (if power 10 20)
1725                        (math-conditional-apply 'calcFunc-log10 number)))
1726             units)))
1727          (t
1728           (math-simplify
1729            (math-mul
1730             (math-add
1731              coef
1732              (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
1733             units))))
1734       (calc-record-why "*Improper units" nil))))
1735
1736 (defun math-logunits-divide (a b power)
1737   (let ((logunit (math-simplify (math-extract-logunits a))))
1738     (if (not (eq (car-safe logunit) 'var))
1739         (calc-record-why "*Improper logarithmic unit" logunit)
1740       (if (math-units-in-expr-p b nil)
1741           (calc-record-why "*Improper units quantity" b)
1742         (let* ((units (math-extract-units a))
1743                (coef (math-simplify (math-remove-units a))))
1744           (cond
1745            ((equal logunit '(var dB var-dB))
1746             (math-simplify
1747              (math-mul
1748               (math-sub
1749                coef
1750                (math-mul (if power 10 20)
1751                          (math-conditional-apply 'calcFunc-log10 b)))
1752               units)))
1753          (t
1754           (math-simplify
1755            (math-mul
1756             (math-sub
1757              coef
1758              (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
1759             units)))))))))
1760
1761 (defun calcFunc-lufmul (a b)
1762   (math-logunits-mul a b nil))
1763
1764 (defun calcFunc-lupmul (a b)
1765   (math-logunits-mul a b t))
1766
1767 (defun calc-lu-times (arg)
1768   (interactive "P")
1769   (calc-slow-wrapper
1770    (if (calc-is-inverse)
1771        (if (calc-is-hyperbolic)
1772            (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1773          (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
1774      (if (calc-is-hyperbolic)
1775          (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1776        (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
1777
1778 (defun calcFunc-lufdiv (a b)
1779   (math-logunits-divide a b nil))
1780
1781 (defun calcFunc-lupdiv (a b)
1782   (math-logunits-divide a b t))
1783
1784 (defun calc-lu-divide (arg)
1785   (interactive "P")
1786   (calc-slow-wrapper
1787    (if (calc-is-inverse)
1788        (if (calc-is-hyperbolic)
1789            (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1790          (calc-binary-op "lu*" 'calcFunc-lupmul arg))
1791      (if (calc-is-hyperbolic)
1792          (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1793        (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
1794
1795 (defun math-logunits-quant (val ref power)
1796   (let* ((units (math-simplify (math-extract-units val)))
1797          (lunit (math-simplify (math-extract-logunits units))))
1798     (if (not (eq (car-safe lunit) 'var))
1799         (calc-record-why "*Improper logarithmic unit" lunit)
1800       (let ((runits (math-simplify (math-div units lunit)))
1801             (coeff (math-simplify (math-div val units))))
1802         (math-mul
1803          (if (equal lunit '(var dB var-dB))
1804              (math-mul
1805               ref
1806               (math-conditional-pow
1807                10
1808                (math-div
1809                 coeff
1810                 (if power 10 20))))
1811            (math-mul
1812             ref
1813             (math-conditional-apply 'calcFunc-exp
1814              (if power
1815                  (math-mul 2 coeff)
1816                coeff))))
1817          runits)))))
1818
1819 (defvar calc-lu-field-reference)
1820 (defvar calc-lu-power-reference)
1821
1822 (defun calcFunc-lufquant (val &optional ref)
1823   (unless ref
1824     (setq ref (math-read-expr calc-lu-field-reference)))
1825   (math-logunits-quant val ref nil))
1826
1827 (defun calcFunc-lupquant (val &optional ref)
1828   (unless ref
1829     (setq ref (math-read-expr calc-lu-power-reference)))
1830   (math-logunits-quant val ref t))
1831
1832 (defun calc-lu-quant (arg)
1833   (interactive "P")
1834   (calc-slow-wrapper
1835    (if (calc-is-hyperbolic)
1836        (if (calc-is-option)
1837            (calc-binary-op "lupq" 'calcFunc-lufquant arg)
1838          (calc-unary-op "lupq" 'calcFunc-lufquant arg))
1839      (if (calc-is-option)
1840          (calc-binary-op "lufq" 'calcFunc-lupquant arg)
1841        (calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
1842
1843 (defun math-logunits-level (val ref db power)
1844   "Compute the value of VAL in decibels or nepers."
1845       (let* ((ratio (math-simplify-units (math-div val ref)))
1846              (ratiou (math-simplify-units (math-remove-units ratio)))
1847              (units (math-simplify (math-extract-units ratio))))
1848         (math-mul
1849          (if db
1850              (math-mul
1851               (math-mul (if power 10 20)
1852                         (math-conditional-apply 'calcFunc-log10 ratiou))
1853               '(var dB var-dB))
1854            (math-mul
1855             (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
1856             '(var Np var-Np)))
1857          units)))
1858
1859 (defun calcFunc-dbfield (val &optional ref)
1860   (unless ref
1861     (setq ref (math-read-expr calc-lu-field-reference)))
1862   (math-logunits-level val ref t nil))
1863
1864 (defun calcFunc-dbpower (val &optional ref)
1865   (unless ref
1866     (setq ref (math-read-expr calc-lu-power-reference)))
1867   (math-logunits-level val ref t t))
1868
1869 (defun calcFunc-npfield (val &optional ref)
1870   (unless ref
1871     (setq ref (math-read-expr calc-lu-field-reference)))
1872   (math-logunits-level val ref nil nil))
1873
1874 (defun calcFunc-nppower (val &optional ref)
1875   (unless ref
1876     (setq ref (math-read-expr calc-lu-power-reference)))
1877   (math-logunits-level val ref nil t))
1878
1879 (defun calc-db (arg)
1880   (interactive "P")
1881   (calc-slow-wrapper
1882    (if (calc-is-hyperbolic)
1883        (if (calc-is-option)
1884            (calc-binary-op "ludb" 'calcFunc-dbfield arg)
1885          (calc-unary-op "ludb" 'calcFunc-dbfield arg))
1886      (if (calc-is-option)
1887          (calc-binary-op "ludb" 'calcFunc-dbpower arg)
1888        (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
1889
1890 (defun calc-np (arg)
1891   (interactive "P")
1892   (calc-slow-wrapper
1893    (if (calc-is-hyperbolic)
1894        (if (calc-is-option)
1895            (calc-binary-op "lunp" 'calcFunc-npfield arg)
1896          (calc-unary-op "lunp" 'calcFunc-npfield arg))
1897      (if (calc-is-option)
1898          (calc-binary-op "lunp" 'calcFunc-nppower arg)
1899        (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
1900
1901 ;;; Musical notes
1902
1903
1904 (defvar calc-note-threshold)
1905
1906 (defun math-midi-round (num)
1907   "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
1908   (let* ((n (math-round num))
1909          (diff (math-abs
1910                 (math-sub num n))))
1911     (if (< (math-compare diff
1912                          (math-div (math-read-expr calc-note-threshold) 100)) 0)
1913         n
1914       num)))
1915
1916 (defconst math-notes
1917   '(((var C var-C) . 0)
1918     ((var Csharp var-Csharp) . 1)
1919 ;    ((var C♯ var-C♯) . 1)
1920     ((var Dflat var-Dflat) . 1)
1921 ;    ((var D♭ var-D♭) . 1)
1922     ((var D var-D) . 2)
1923     ((var Dsharp var-Dsharp) . 3)
1924 ;    ((var D♯ var-D♯) . 3)
1925     ((var E var-E) . 4)
1926     ((var F var-F) . 5)
1927     ((var Fsharp var-Fsharp) . 6)
1928 ;    ((var F♯ var-F♯) . 6)
1929     ((var Gflat var-Gflat) . 6)
1930 ;    ((var G♭ var-G♭) . 6)
1931     ((var G var-G) . 7)
1932     ((var Gsharp var-Gsharp) . 8)
1933 ;    ((var G♯ var-G♯) . 8)
1934     ((var A var-A) . 9)
1935     ((var Asharp var-Asharp) . 10)
1936 ;    ((var A♯ var-A♯) . 10)
1937     ((var Bflat var-Bflat) . 10)
1938 ;    ((var B♭ var-B♭) . 10)
1939     ((var B var-B) . 11))
1940   "An alist of notes with their number of semitones above C.")
1941
1942 (defun math-freqp (freq)
1943   "Non-nil if FREQ is a positive number times the unit Hz.
1944 If non-nil, return the coefficient of Hz."
1945   (let ((freqcoef (math-simplify-units
1946                    (math-div freq '(var Hz var-Hz)))))
1947     (if (Math-posp freqcoef) freqcoef)))
1948
1949 (defun math-midip (num)
1950   "Non-nil if NUM is a possible MIDI note number.
1951 If non-nil, return NUM."
1952   (if (Math-numberp num) num))
1953
1954 (defun math-spnp (spn)
1955   "Non-nil if NUM is a scientific pitch note (note + cents).
1956 If non-nil, return a list consisting of the note and the cents coefficient."
1957   (let (note cents rnote rcents)
1958     (if (eq (car-safe spn) '+)
1959         (setq note (nth 1 spn)
1960               cents (nth 2 spn))
1961       (setq note spn
1962             cents nil))
1963     (cond
1964      ((and  ;; NOTE is a note, CENTS is nil or cents.
1965        (eq (car-safe note) 'calcFunc-subscr)
1966        (assoc (nth 1 note) math-notes)
1967        (integerp (nth 2 note))
1968        (setq rnote note)
1969        (or
1970         (not cents)
1971         (Math-numberp (setq rcents
1972                             (math-simplify
1973                              (math-div cents '(var cents var-cents)))))))
1974       (list rnote rcents))
1975      ((and  ;; CENTS is a note, NOTE is cents.
1976        (eq (car-safe cents) 'calcFunc-subscr)
1977        (assoc (nth 1 cents) math-notes)
1978        (integerp (nth 2 cents))
1979        (setq rnote cents)
1980        (or
1981         (not note)
1982         (Math-numberp (setq rcents
1983                             (math-simplify
1984                              (math-div note '(var cents var-cents)))))))
1985       (list rnote rcents)))))
1986
1987 (defun math-freq-to-midi (freq)
1988   "Return the midi note number corresponding to FREQ Hz."
1989   (let ((midi (math-add
1990                69
1991                (math-mul
1992                 12
1993                 (calcFunc-log
1994                  (math-div freq 440)
1995                  2)))))
1996     (math-midi-round midi)))
1997
1998 (defun math-spn-to-midi (spn)
1999   "Return the MIDI number corresponding to SPN."
2000   (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
2001          (octave (math-add (nth 2 (car spn)) 1))
2002          (cents (nth 1 spn))
2003          (midi  (math-add
2004                  (math-mul 12 octave)
2005                  note)))
2006     (if cents
2007         (math-add midi (math-div cents 100))
2008       midi)))
2009
2010 (defun math-midi-to-spn (midi)
2011   "Return the scientific pitch notation corresponding to midi number MIDI."
2012   (let (midin cents)
2013     (if (math-integerp midi)
2014         (setq midin midi
2015               cents nil)
2016       (setq midin (math-floor midi)
2017             cents (math-mul 100 (math-sub midi midin))))
2018     (let* ((nr ;; This should be (math-idivmod midin 12), but with
2019                ;; better behavior for negative midin.
2020             (if (Math-negp midin)
2021                 (let ((dm (math-idivmod (math-neg midin) 12)))
2022                   (if (= (cdr dm) 0)
2023                       (cons (math-neg (car dm)) 0)
2024                     (cons
2025                      (math-sub (math-neg (car dm)) 1)
2026                      (math-sub 12 (cdr dm)))))
2027               (math-idivmod midin 12)))
2028            (n (math-sub (car nr) 1))
2029            (note (car (rassoc (cdr nr) math-notes))))
2030       (if cents
2031           (list '+ (list 'calcFunc-subscr note n)
2032                    (list '* cents '(var cents var-cents)))
2033         (list 'calcFunc-subscr note n)))))
2034
2035 (defun math-freq-to-spn (freq)
2036   "Return the scientific pitch notation corresponding to FREQ Hz."
2037   (math-with-extra-prec 3
2038     (math-midi-to-spn (math-freq-to-midi freq))))
2039
2040 (defun math-midi-to-freq (midi)
2041   "Return the frequency of the note with midi number MIDI."
2042   (list '*
2043         (math-mul
2044          440
2045          (math-pow
2046           2
2047           (math-div
2048            (math-sub
2049             midi
2050             69)
2051            12)))
2052         '(var Hz var-Hz)))
2053
2054 (defun math-spn-to-freq (spn)
2055   "Return the frequency of the note with scientific pitch notation SPN."
2056   (math-midi-to-freq (math-spn-to-midi spn)))
2057
2058 (defun calcFunc-spn (expr)
2059   "Return EXPR written as scientific pitch notation + cents."
2060   ;; Get the coefficient of Hz
2061   (let (note)
2062     (cond
2063      ((setq note (math-freqp expr))
2064       (math-freq-to-spn note))
2065      ((setq note (math-midip expr))
2066       (math-midi-to-spn note))
2067      ((math-spnp expr)
2068       expr)
2069      (t
2070       (math-reject-arg expr "*Improper expression")))))
2071
2072 (defun calcFunc-midi (expr)
2073   "Return EXPR written as a MIDI number."
2074   (let (note)
2075     (cond
2076      ((setq note (math-freqp expr))
2077       (math-freq-to-midi note))
2078      ((setq note (math-spnp expr))
2079       (math-spn-to-midi note))
2080      ((math-midip expr)
2081       expr)
2082      (t
2083       (math-reject-arg expr "*Improper expression")))))
2084
2085 (defun calcFunc-freq (expr)
2086   "Return the frequency corresponding to EXPR."
2087   (let (note)
2088     (cond
2089      ((setq note (math-midip expr))
2090       (math-midi-to-freq note))
2091      ((setq note (math-spnp expr))
2092       (math-spn-to-freq note))
2093      ((math-freqp expr)
2094       expr)
2095      (t
2096       (math-reject-arg expr "*Improper expression")))))
2097
2098 (defun calc-freq (arg)
2099   "Return the frequency corresponding to the expression on the stack."
2100   (interactive "P")
2101   (calc-slow-wrapper
2102    (calc-unary-op "freq" 'calcFunc-freq arg)))
2103
2104 (defun calc-midi (arg)
2105   "Return the MIDI number corresponding to the expression on the stack."
2106   (interactive "P")
2107   (calc-slow-wrapper
2108    (calc-unary-op "midi" 'calcFunc-midi arg)))
2109
2110 (defun calc-spn (arg)
2111   "Return the scientific pitch notation corresponding to the expression on the stack."
2112   (interactive "P")
2113   (calc-slow-wrapper
2114    (calc-unary-op "spn" 'calcFunc-spn arg)))
2115
2116
2117 (provide 'calc-units)
2118
2119 ;; Local variables:
2120 ;; coding: utf-8
2121 ;; End:
2122
2123 ;;; calc-units.el ends here