lisp/calc/calc-units.el

   1 ;;; calc-units.el --- unit conversion functions for Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2012  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)
 422   "Put the units in EXPR in the default units table."
 423   (let ((units (math-get-units expr)))
 424     (unless (eq units 1)
 425       (let* ((standard-units (math-get-standard-units expr))
 426          (default-units (gethash
 427                          standard-units
 428                          math-default-units-table)))
 429         (cond
 430          ((not default-units)
 431           (puthash standard-units (list units) math-default-units-table))
 432          ((not (equal units (car default-units)))
 433           (puthash standard-units
 434                    (list units (car default-units))
 435                    math-default-units-table)))))))
 436
 437
 438 (defun calc-convert-units (&optional old-units new-units)
 439   (interactive)
 440   (calc-slow-wrapper
 441    (let ((expr (calc-top-n 1))
 442          (uoldname nil)
 443          unew
 444          units
 445          defunits)
 446      (unless (math-units-in-expr-p expr t)
 447        (let ((uold (or old-units
 448                        (progn
 449                          (setq uoldname (read-string "Old units: "))
 450                          (if (equal uoldname "")
 451                              (progn
 452                                (setq uoldname "1")
 453                                1)
 454                            (if (string-match "\\` */" uoldname)
 455                                (setq uoldname (concat "1" uoldname)))
 456                            (math-read-expr uoldname))))))
 457          (when (eq (car-safe uold) 'error)
 458            (error "Bad format in units expression: %s" (nth 1 uold)))
 459          (setq expr (math-mul expr uold))))
 460      (unless new-units
 461        (setq defunits (math-get-default-units expr))
 462        (setq new-units
 463              (read-string (concat
 464                            (if uoldname
 465                                (concat "Old units: "
 466                                        uoldname
 467                                        ", new units")
 468                             "New units")
 469                            (if defunits
 470                                (concat
 471                                 " (default "
 472                                 defunits
 473                                 "): ")
 474                              ": "))))
 475
 476        (if (and
 477             (string= new-units "")
 478             defunits)
 479            (setq new-units defunits)))
 480      (when (string-match "\\` */" new-units)
 481        (setq new-units (concat "1" new-units)))
 482      (setq units (math-read-expr new-units))
 483      (when (eq (car-safe units) 'error)
 484        (error "Bad format in units expression: %s" (nth 2 units)))
 485      (if calc-ensure-consistent-units
 486          (math-check-unit-consistency expr units))
 487      (math-put-default-units units)
 488      (let ((unew (math-units-in-expr-p units t))
 489            (std (and (eq (car-safe units) 'var)
 490                      (assq (nth 1 units) math-standard-units-systems))))
 491        (if std
 492            (calc-enter-result 1 "cvun" (math-simplify-units
 493                                         (math-to-standard-units expr
 494                                                                 (nth 1 std))))
 495          (unless unew
 496            (error "No units specified"))
 497          (calc-enter-result 1 "cvun"
 498                             (math-convert-units
 499                              expr units
 500                              (and uoldname (not (equal uoldname "1"))))))))))
 501
 502 (defun calc-autorange-units (arg)
 503   (interactive "P")
 504   (calc-wrapper
 505    (calc-change-mode 'calc-autorange-units arg nil t)
 506    (message (if calc-autorange-units
 507                 "Adjusting target unit prefix automatically"
 508               "Using target units exactly"))))
 509
 510 (defun calc-convert-temperature (&optional old-units new-units)
 511   (interactive)
 512   (calc-slow-wrapper
 513    (let ((expr (calc-top-n 1))
 514          (uold nil)
 515          (uoldname nil)
 516          unew
 517          defunits)
 518      (setq uold (or old-units
 519                     (let ((units (math-single-units-in-expr-p expr)))
 520                       (if units
 521                           (if (consp units)
 522                               (list 'var (car units)
 523                                     (intern (concat "var-"
 524                                                     (symbol-name
 525                                                      (car units)))))
 526                             (error "Not a pure temperature expression"))
 527                         (math-read-expr
 528                          (setq uoldname (read-string
 529                                          "Old temperature units: ")))))))
 530      (when (eq (car-safe uold) 'error)
 531        (error "Bad format in units expression: %s" (nth 2 uold)))
 532      (or (math-units-in-expr-p expr nil)
 533          (setq expr (math-mul expr uold)))
 534      (setq defunits (math-get-default-units expr))
 535      (setq unew (or new-units
 536                     (read-string
 537                      (concat
 538                       (if uoldname
 539                           (concat "Old temperature units: "
 540                                   uoldname
 541                                   ", new units")
 542                         "New temperature units")
 543                       (if defunits
 544                           (concat " (default "
 545                                   defunits
 546                                   "): ")
 547                         ": ")))))
 548      (setq unew (math-read-expr (if (string= unew "") defunits unew)))
 549      (when (eq (car-safe unew) 'error)
 550        (error "Bad format in units expression: %s" (nth 2 unew)))
 551      (math-put-default-units unew)
 552      (let ((ntemp (calc-normalize
 553                    (math-simplify-units
 554                     (math-convert-temperature expr uold unew
 555                                               uoldname)))))
 556        (if (Math-zerop ntemp)
 557            (setq ntemp (list '* ntemp unew)))
 558        (let ((calc-simplify-mode 'none))
 559          (calc-enter-result 1 "cvtm" ntemp))))))
 560
 561 (defun calc-remove-units ()
 562   (interactive)
 563   (calc-slow-wrapper
 564    (calc-enter-result 1 "rmun" (math-simplify-units
 565                                 (math-remove-units (calc-top-n 1))))))
 566
 567 (defun calc-extract-units ()
 568   (interactive)
 569   (calc-slow-wrapper
 570    (calc-enter-result 1 "exun" (math-simplify-units
 571                                 (math-extract-units (calc-top-n 1))))))
 572
 573 ;; The variables calc-num-units and calc-den-units are local to
 574 ;; calc-explain-units, but are used by calc-explain-units-rec,
 575 ;; which is called by calc-explain-units.
 576 (defvar calc-num-units)
 577 (defvar calc-den-units)
 578
 579 (defun calc-explain-units ()
 580   (interactive)
 581   (calc-wrapper
 582    (let ((calc-num-units nil)
 583          (calc-den-units nil))
 584      (calc-explain-units-rec (calc-top-n 1) 1)
 585      (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
 586           (setq calc-den-units (concat "(" calc-den-units ")")))
 587      (if calc-num-units
 588          (if calc-den-units
 589              (message "%s per %s" calc-num-units calc-den-units)
 590            (message "%s" calc-num-units))
 591        (if calc-den-units
 592            (message "1 per %s" calc-den-units)
 593          (message "No units in expression"))))))
 594
 595 (defun calc-explain-units-rec (expr pow)
 596   (let ((u (math-check-unit-name expr))
 597         pos)
 598     (if (and u (not (math-zerop pow)))
 599         (let ((name (or (nth 2 u) (symbol-name (car u)))))
 600           (if (eq (aref name 0) ?\*)
 601               (setq name (substring name 1)))
 602           (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 603               (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name)
 604                   (while (setq pos (string-match "[ ()]" name))
 605                     (setq name (concat (substring name 0 pos)
 606                                        (if (eq (aref name pos) 32) "-" "")
 607                                        (substring name (1+ pos)))))
 608                 (setq name (concat "(" name ")"))))
 609           (or (eq (nth 1 expr) (car u))
 610               (setq name (concat (nth 2 (assq (aref (symbol-name
 611                                                      (nth 1 expr)) 0)
 612                                               math-unit-prefixes))
 613                                  (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 614                                           (not (memq (car u) '(mHg gf))))
 615                                      (concat "-" name)
 616                                    (downcase name)))))
 617           (cond ((or (math-equal-int pow 1)
 618                      (math-equal-int pow -1)))
 619                 ((or (math-equal-int pow 2)
 620                      (math-equal-int pow -2))
 621                  (if (equal (nth 4 u) '((m . 1)))
 622                      (setq name (concat "Square-" name))
 623                    (setq name (concat name "-squared"))))
 624                 ((or (math-equal-int pow 3)
 625                      (math-equal-int pow -3))
 626                  (if (equal (nth 4 u) '((m . 1)))
 627                      (setq name (concat "Cubic-" name))
 628                    (setq name (concat name "-cubed"))))
 629                 (t
 630                  (setq name (concat name "^"
 631                                     (math-format-number (math-abs pow))))))
 632           (if (math-posp pow)
 633               (setq calc-num-units (if calc-num-units
 634                                   (concat calc-num-units " " name)
 635                                 name))
 636             (setq calc-den-units (if calc-den-units
 637                                 (concat calc-den-units " " name)
 638                               name))))
 639       (cond ((eq (car-safe expr) '*)
 640              (calc-explain-units-rec (nth 1 expr) pow)
 641              (calc-explain-units-rec (nth 2 expr) pow))
 642             ((eq (car-safe expr) '/)
 643              (calc-explain-units-rec (nth 1 expr) pow)
 644              (calc-explain-units-rec (nth 2 expr) (- pow)))
 645             ((memq (car-safe expr) '(neg + -))
 646              (calc-explain-units-rec (nth 1 expr) pow))
 647             ((and (eq (car-safe expr) '^)
 648                   (math-realp (nth 2 expr)))
 649              (calc-explain-units-rec (nth 1 expr)
 650                                      (math-mul pow (nth 2 expr))))))))
 651
 652 (defun calc-simplify-units ()
 653   (interactive)
 654   (calc-slow-wrapper
 655    (calc-with-default-simplification
 656     (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
 657
 658 (defun calc-view-units-table (n)
 659   (interactive "P")
 660   (and n (setq math-units-table-buffer-valid nil))
 661   (let ((win (get-buffer-window "*Units Table*")))
 662     (if (and win
 663              math-units-table
 664              math-units-table-buffer-valid)
 665         (progn
 666           (bury-buffer (window-buffer win))
 667           (let ((curwin (selected-window)))
 668             (select-window win)
 669             (switch-to-buffer nil)
 670             (select-window curwin)))
 671       (math-build-units-table-buffer nil))))
 672
 673 (defun calc-enter-units-table (n)
 674   (interactive "P")
 675   (and n (setq math-units-table-buffer-valid nil))
 676   (math-build-units-table-buffer t)
 677   (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
 678
 679 (defun calc-define-unit (uname desc &optional disp)
 680   (interactive "SDefine unit name: \nsDescription: \nP")
 681   (if disp (setq disp (read-string "Display definition: ")))
 682   (calc-wrapper
 683    (let ((form (calc-top-n 1))
 684          (unit (assq uname math-additional-units)))
 685      (or unit
 686          (setq math-additional-units
 687                (cons (setq unit (list uname nil nil nil nil))
 688                      math-additional-units)
 689                math-units-table nil))
 690      (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
 691                                        (eq (nth 1 form) uname)))
 692                              (not (math-equal-int form 1))
 693                              (math-format-flat-expr form 0)))
 694      (setcar (cdr (cdr unit)) (and (not (equal desc ""))
 695                                    desc))
 696      (if disp
 697          (setcar (cdr (cdr (cdr (cdr unit)))) disp))))
 698   (calc-invalidate-units-table))
 699
 700 (defun calc-undefine-unit (uname)
 701   (interactive "SUndefine unit name: ")
 702   (calc-wrapper
 703    (let ((unit (assq uname math-additional-units)))
 704      (or unit
 705          (if (assq uname math-standard-units)
 706              (error "\"%s\" is a predefined unit name" uname)
 707            (error "Unit name \"%s\" not found" uname)))
 708      (setq math-additional-units (delq unit math-additional-units)
 709            math-units-table nil)))
 710   (calc-invalidate-units-table))
 711
 712 (defun calc-invalidate-units-table ()
 713   (setq math-units-table nil)
 714   (let ((buf (get-buffer "*Units Table*")))
 715     (and buf
 716          (with-current-buffer buf
 717            (save-excursion
 718              (goto-char (point-min))
 719              (if (looking-at "Calculator Units Table")
 720                  (let ((inhibit-read-only t))
 721                    (insert "(Obsolete) "))))))))
 722
 723 (defun calc-get-unit-definition (uname)
 724   (interactive "SGet definition for unit: ")
 725   (calc-wrapper
 726    (math-build-units-table)
 727    (let ((unit (assq uname math-units-table)))
 728      (or unit
 729          (error "Unit name \"%s\" not found" uname))
 730      (let ((msg (nth 2 unit)))
 731        (if (stringp msg)
 732            (if (string-match "^\\*" msg)
 733                (setq msg (substring msg 1)))
 734          (setq msg (symbol-name uname)))
 735        (if (nth 1 unit)
 736            (progn
 737              (calc-enter-result 0 "ugdf" (nth 1 unit))
 738              (message "Derived unit: %s" msg))
 739          (calc-enter-result 0 "ugdf" (list 'var uname
 740                                            (intern
 741                                             (concat "var-"
 742                                                     (symbol-name uname)))))
 743          (message "Base unit: %s" msg))))))
 744
 745 (defun calc-permanent-units ()
 746   (interactive)
 747   (calc-wrapper
 748    (let (pos)
 749      (set-buffer (find-file-noselect (substitute-in-file-name
 750                                       calc-settings-file)))
 751      (goto-char (point-min))
 752      (if (and (search-forward ";;; Custom units stored by Calc" nil t)
 753               (progn
 754                 (beginning-of-line)
 755                 (setq pos (point))
 756                 (search-forward "\n;;; End of custom units" nil t)))
 757          (progn
 758            (beginning-of-line)
 759            (forward-line 1)
 760            (delete-region pos (point)))
 761        (goto-char (point-max))
 762        (insert "\n\n")
 763        (forward-char -1))
 764      (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
 765      (if math-additional-units
 766          (progn
 767            (insert "(setq math-additional-units '(\n")
 768            (let ((list math-additional-units))
 769              (while list
 770                (insert "  (" (symbol-name (car (car list))) " "
 771                        (if (nth 1 (car list))
 772                            (if (stringp (nth 1 (car list)))
 773                                (prin1-to-string (nth 1 (car list)))
 774                              (prin1-to-string (math-format-flat-expr
 775                                                (nth 1 (car list)) 0)))
 776                          "nil")
 777                        " "
 778                        (prin1-to-string (nth 2 (car list)))
 779                        ")\n")
 780                (setq list (cdr list))))
 781            (insert "))\n"))
 782        (insert ";;; (no custom units defined)\n"))
 783      (insert ";;; End of custom units\n")
 784      (save-buffer))))
 785
 786
 787 ;; The variable math-cu-unit-list is local to math-build-units-table,
 788 ;; but is used by math-compare-unit-names, which is called (indirectly)
 789 ;; by math-build-units-table.
 790 ;; math-cu-unit-list is also local to math-convert-units, but is used
 791 ;; by math-convert-units-rec, which is called by math-convert-units.
 792 (defvar math-cu-unit-list)
 793
 794 (defun math-build-units-table ()
 795   (or math-units-table
 796       (let* ((combined-units (append math-additional-units
 797                                      math-standard-units))
 798              (math-cu-unit-list (mapcar 'car combined-units))
 799              tab)
 800         (message "Building units table...")
 801         (setq math-units-table-buffer-valid nil)
 802         (setq tab (mapcar (function
 803                            (lambda (x)
 804                              (list (car x)
 805                                    (and (nth 1 x)
 806                                         (if (stringp (nth 1 x))
 807                                             (let ((exp (math-read-plain-expr
 808                                                         (nth 1 x))))
 809                                               (if (eq (car-safe exp) 'error)
 810                                                   (error "Format error in definition of %s in units table: %s"
 811                                                          (car x) (nth 2 exp))
 812                                                 exp))
 813                                           (nth 1 x)))
 814                                    (nth 2 x)
 815                                    (nth 3 x)
 816                                    (and (not (nth 1 x))
 817                                         (list (cons (car x) 1)))
 818                                    (nth 4 x))))
 819                           combined-units))
 820         (let ((math-units-table tab))
 821           (mapc 'math-find-base-units tab))
 822         (message "Building units table...done")
 823         (setq math-units-table tab))))
 824
 825 ;; The variables math-fbu-base and math-fbu-entry are local to
 826 ;; math-find-base-units, but are used by math-find-base-units-rec,
 827 ;; which is called by math-find-base-units.
 828 (defvar math-fbu-base)
 829 (defvar math-fbu-entry)
 830
 831 (defun math-find-base-units (math-fbu-entry)
 832   (if (eq (nth 4 math-fbu-entry) 'boom)
 833       (error "Circular definition involving unit %s" (car math-fbu-entry)))
 834   (or (nth 4 math-fbu-entry)
 835       (let (math-fbu-base)
 836         (setcar (nthcdr 4 math-fbu-entry) 'boom)
 837         (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
 838         '(or math-fbu-base
 839             (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
 840         (while (eq (cdr (car math-fbu-base)) 0)
 841           (setq math-fbu-base (cdr math-fbu-base)))
 842         (let ((b math-fbu-base))
 843           (while (cdr b)
 844             (if (eq (cdr (car (cdr b))) 0)
 845                 (setcdr b (cdr (cdr b)))
 846               (setq b (cdr b)))))
 847         (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
 848         (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
 849         math-fbu-base)))
 850
 851 (defun math-compare-unit-names (a b)
 852   (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
 853
 854 (defun math-find-base-units-rec (expr pow)
 855   (let ((u (math-check-unit-name expr)))
 856     (cond (u
 857            (let ((ulist (math-find-base-units u)))
 858              (while ulist
 859                (let ((p (* (cdr (car ulist)) pow))
 860                      (old (assq (car (car ulist)) math-fbu-base)))
 861                  (if old
 862                      (setcdr old (+ (cdr old) p))
 863                    (setq math-fbu-base
 864                          (cons (cons (car (car ulist)) p) math-fbu-base))))
 865                (setq ulist (cdr ulist)))))
 866           ((math-scalarp expr))
 867           ((and (eq (car expr) '^)
 868                 (integerp (nth 2 expr)))
 869            (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
 870           ((eq (car expr) '*)
 871            (math-find-base-units-rec (nth 1 expr) pow)
 872            (math-find-base-units-rec (nth 2 expr) pow))
 873           ((eq (car expr) '/)
 874            (math-find-base-units-rec (nth 1 expr) pow)
 875            (math-find-base-units-rec (nth 2 expr) (- pow)))
 876           ((eq (car expr) 'neg)
 877            (math-find-base-units-rec (nth 1 expr) pow))
 878           ((eq (car expr) '+)
 879            (math-find-base-units-rec (nth 1 expr) pow))
 880           ((eq (car expr) 'var)
 881            (or (eq (nth 1 expr) 'pi)
 882                (error "Unknown name %s in defining expression for unit %s"
 883                       (nth 1 expr) (car math-fbu-entry))))
 884           ((equal expr '(calcFunc-ln 10)))
 885           (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
 886
 887
 888 (defun math-units-in-expr-p (expr sub-exprs)
 889   (and (consp expr)
 890        (if (eq (car expr) 'var)
 891            (math-check-unit-name expr)
 892          (and (or sub-exprs
 893                   (memq (car expr) '(* / ^)))
 894               (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
 895                   (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
 896
 897 (defun math-only-units-in-expr-p (expr)
 898   (and (consp expr)
 899        (if (eq (car expr) 'var)
 900            (math-check-unit-name expr)
 901          (if (memq (car expr) '(* /))
 902              (and (math-only-units-in-expr-p (nth 1 expr))
 903                   (math-only-units-in-expr-p (nth 2 expr)))
 904            (and (eq (car expr) '^)
 905                 (and (math-only-units-in-expr-p (nth 1 expr))
 906                      (math-realp (nth 2 expr))))))))
 907
 908 (defun math-single-units-in-expr-p (expr)
 909   (cond ((math-scalarp expr) nil)
 910         ((eq (car expr) 'var)
 911          (math-check-unit-name expr))
 912         ((eq (car expr) '*)
 913          (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
 914                (u2 (math-single-units-in-expr-p (nth 2 expr))))
 915            (or (and u1 u2 'wrong)
 916                u1
 917                u2)))
 918         ((eq (car expr) '/)
 919          (if (math-units-in-expr-p (nth 2 expr) nil)
 920              'wrong
 921            (math-single-units-in-expr-p (nth 1 expr))))
 922         (t 'wrong)))
 923
 924 (defun math-consistent-units-p (expr newunits)
 925   "Non-nil if EXPR and NEWUNITS have consistent units."
 926   (or
 927    (and (eq (car-safe newunits) 'var)
 928         (assq (nth 1 newunits) math-standard-units-systems))
 929    (math-numberp (math-get-units (list '/ expr newunits)))))
 930
 931 (defun math-check-unit-consistency (expr units)
 932   "Give an error if EXPR and UNITS do not have consistent units."
 933   (unless  (math-consistent-units-p expr units)
 934     (error "New units (%s) are inconsistent with current units (%s)"
 935            (math-format-value units)
 936            (math-format-value (math-get-units expr)))))
 937
 938 (defun math-check-unit-name (v)
 939   (and (eq (car-safe v) 'var)
 940        (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
 941            (let ((name (symbol-name (nth 1 v))))
 942              (and (> (length name) 1)
 943                   (assq (aref name 0) math-unit-prefixes)
 944                   (or (assq (intern (substring name 1)) math-units-table)
 945                       (and (eq (aref name 0) ?M)
 946                            (> (length name) 3)
 947                            (eq (aref name 1) ?e)
 948                            (eq (aref name 2) ?g)
 949                            (assq (intern (substring name 3))
 950                                  math-units-table))))))))
 951
 952 ;; The variable math-which-standard is local to math-to-standard-units,
 953 ;; but is used by math-to-standard-rec, which is called by
 954 ;; math-to-standard-units.
 955 (defvar math-which-standard)
 956
 957 (defun math-to-standard-units (expr math-which-standard)
 958   (math-to-standard-rec expr))
 959
 960 (defun math-to-standard-rec (expr)
 961   (if (eq (car-safe expr) 'var)
 962       (let ((u (math-check-unit-name expr))
 963             (base (nth 1 expr)))
 964         (if u
 965             (progn
 966               (if (nth 1 u)
 967                   (setq expr (math-to-standard-rec (nth 1 u)))
 968                 (let ((st (assq (car u) math-which-standard)))
 969                   (if st
 970                       (setq expr (nth 1 st))
 971                     (setq expr (list 'var (car u)
 972                                      (intern (concat "var-"
 973                                                      (symbol-name
 974                                                       (car u)))))))))
 975               (or (null u)
 976                   (eq base (car u))
 977                   (setq expr (list '*
 978                                    (nth 1 (assq (aref (symbol-name base) 0)
 979                                                 math-unit-prefixes))
 980                                    expr)))
 981               expr)
 982           (if (eq base 'pi)
 983               (math-pi)
 984             expr)))
 985     (if (or
 986          (Math-primp expr)
 987          (and (eq (car-safe expr) 'calcFunc-subscr)
 988               (eq (car-safe (nth 1 expr)) 'var)))
 989         expr
 990       (cons (car expr)
 991             (mapcar 'math-to-standard-rec (cdr expr))))))
 992
 993 (defun math-apply-units (expr units ulist &optional pure)
 994   (setq expr (math-simplify-units expr))
 995   (if ulist
 996       (let ((new 0)
 997             value)
 998         (or (math-numberp expr)
 999             (error "Incompatible units"))
1000         (while (cdr ulist)
1001           (setq value (math-div expr (nth 1 (car ulist)))
1002                 value (math-floor (let ((calc-internal-prec
1003                                          (1- calc-internal-prec)))
1004                                     (math-normalize value)))
1005                 new (math-add new (math-mul value (car (car ulist))))
1006                 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
1007                 ulist (cdr ulist)))
1008         (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
1009                                 (car (car ulist)))))
1010     (if pure
1011         expr
1012       (math-simplify-units (list '* expr units)))))
1013
1014 (defvar math-decompose-units-cache nil)
1015 (defun math-decompose-units (units)
1016   (let ((u (math-check-unit-name units)))
1017     (and u (eq (car-safe (nth 1 u)) '+)
1018          (setq units (nth 1 u))))
1019   (setq units (calcFunc-expand units))
1020   (and (eq (car-safe units) '+)
1021        (let ((entry (list units calc-internal-prec calc-prefer-frac)))
1022          (or (equal entry (car math-decompose-units-cache))
1023              (let ((ulist nil)
1024                    (utemp units)
1025                    qty unit)
1026                (while (eq (car-safe utemp) '+)
1027                  (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
1028                                    ulist)
1029                        utemp (nth 1 utemp)))
1030                (setq ulist (cons (math-decompose-unit-part utemp) ulist)
1031                      utemp ulist)
1032                (while (setq utemp (cdr utemp))
1033                  (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
1034                    (error "Inconsistent units in sum")))
1035                (setq math-decompose-units-cache
1036                      (cons entry
1037                            (sort ulist
1038                                  (function
1039                                   (lambda (x y)
1040                                     (not (Math-lessp (nth 1 x)
1041                                                      (nth 1 y))))))))))
1042          (cdr math-decompose-units-cache))))
1043
1044 (defun math-decompose-unit-part (unit)
1045   (cons unit
1046         (math-is-multiple (math-simplify-units (math-to-standard-units
1047                                                 unit nil))
1048                           t)))
1049
1050 ;; The variable math-fcu-u is local to math-find-compatible-unit,
1051 ;; but is used by math-find-compatible-rec which is called by
1052 ;; math-find-compatible-unit.
1053 (defvar math-fcu-u)
1054
1055 (defun math-find-compatible-unit (expr unit)
1056   (let ((math-fcu-u (math-check-unit-name unit)))
1057     (if math-fcu-u
1058         (math-find-compatible-unit-rec expr 1))))
1059
1060 (defun math-find-compatible-unit-rec (expr pow)
1061   (cond ((eq (car-safe expr) '*)
1062          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1063              (math-find-compatible-unit-rec (nth 2 expr) pow)))
1064         ((eq (car-safe expr) '/)
1065          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1066              (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
1067         ((and (eq (car-safe expr) '^)
1068               (integerp (nth 2 expr)))
1069          (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
1070         (t
1071          (let ((u2 (math-check-unit-name expr)))
1072            (if (equal (nth 4 math-fcu-u) (nth 4 u2))
1073                (cons expr pow))))))
1074
1075 ;; The variables math-cu-new-units and math-cu-pure are local to
1076 ;; math-convert-units, but are used by math-convert-units-rec,
1077 ;; which is called by math-convert-units.
1078 (defvar math-cu-new-units)
1079 (defvar math-cu-pure)
1080
1081 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
1082   (if (eq (car-safe math-cu-new-units) 'var)
1083       (let ((unew (assq (nth 1 math-cu-new-units)
1084                         (math-build-units-table))))
1085         (if (eq (car-safe (nth 1 unew)) '+)
1086             (setq math-cu-new-units (nth 1 unew)))))
1087   (math-with-extra-prec 2
1088     (let ((compat (and (not math-cu-pure)
1089                        (math-find-compatible-unit expr math-cu-new-units)))
1090           (math-cu-unit-list nil)
1091           (math-combining-units nil))
1092       (if compat
1093           (math-simplify-units
1094            (math-mul (math-mul (math-simplify-units
1095                                 (math-div expr (math-pow (car compat)
1096                                                          (cdr compat))))
1097                                (math-pow math-cu-new-units (cdr compat)))
1098                      (math-simplify-units
1099                       (math-to-standard-units
1100                        (math-pow (math-div (car compat) math-cu-new-units)
1101                                  (cdr compat))
1102                        nil))))
1103         (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
1104           (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
1105         (when (eq (car-safe expr) '+)
1106           (setq expr (math-simplify-units expr)))
1107         (if (math-units-in-expr-p expr t)
1108             (math-convert-units-rec expr)
1109           (math-apply-units (math-to-standard-units
1110                              (list '/ expr math-cu-new-units) nil)
1111                             math-cu-new-units math-cu-unit-list math-cu-pure))))))
1112
1113 (defun math-convert-units-rec (expr)
1114   (if (math-units-in-expr-p expr nil)
1115       (math-apply-units (math-to-standard-units
1116                          (list '/ expr math-cu-new-units) nil)
1117                         math-cu-new-units math-cu-unit-list math-cu-pure)
1118     (if (Math-primp expr)
1119         expr
1120       (cons (car expr)
1121             (mapcar 'math-convert-units-rec (cdr expr))))))
1122
1123 (defun math-convert-temperature (expr old new &optional pure)
1124   (let* ((units (math-single-units-in-expr-p expr))
1125          (uold (if old
1126                    (if (or (null units)
1127                            (equal (nth 1 old) (car units)))
1128                        (math-check-unit-name old)
1129                      (error "Inconsistent temperature units"))
1130                  units))
1131          (unew (math-check-unit-name new)))
1132     (unless (and (consp unew) (nth 3 unew))
1133       (error "Not a valid temperature unit"))
1134     (unless (and (consp uold) (nth 3 uold))
1135       (error "Not a pure temperature expression"))
1136     (let ((v (car uold)))
1137       (setq expr (list '/ expr (list 'var v
1138                                      (intern (concat "var-"
1139                                                      (symbol-name v)))))))
1140     (or (eq (nth 3 uold) (nth 3 unew))
1141         (cond ((eq (nth 3 uold) 'K)
1142                (setq expr (list '- expr '(/ 27315 100)))
1143                (if (eq (nth 3 unew) 'F)
1144                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
1145               ((eq (nth 3 uold) 'C)
1146                (if (eq (nth 3 unew) 'F)
1147                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))
1148                  (setq expr (list '+ expr '(/ 27315 100)))))
1149               (t
1150                (setq expr (list '* (list '- expr 32) '(/ 5 9)))
1151                (if (eq (nth 3 unew) 'K)
1152                    (setq expr (list '+ expr '(/ 27315 100)))))))
1153     (if pure
1154         expr
1155       (list '* expr new))))
1156
1157
1158
1159 (defun math-simplify-units (a)
1160   (let ((math-simplifying-units t)
1161         (calc-matrix-mode 'scalar))
1162     (math-simplify a)))
1163 (defalias 'calcFunc-usimplify 'math-simplify-units)
1164
1165 ;; The function created by math-defsimplify uses the variable
1166 ;; math-simplify-expr, and so is used by functions in math-defsimplify
1167 (defvar math-simplify-expr)
1168
1169 (math-defsimplify (+ -)
1170   (and math-simplifying-units
1171        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1172        (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1173               (ratio (math-simplify (math-to-standard-units
1174                                      (list '/ (nth 2 math-simplify-expr) units) nil))))
1175          (if (math-units-in-expr-p ratio nil)
1176              (progn
1177                (calc-record-why "*Inconsistent units" math-simplify-expr)
1178                math-simplify-expr)
1179            (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1180                               (if (eq (car math-simplify-expr) '-)
1181                                   (math-neg ratio) ratio))
1182                  units)))))
1183
1184 (math-defsimplify *
1185   (math-simplify-units-prod))
1186
1187 (defun math-simplify-units-prod ()
1188   (and math-simplifying-units
1189        calc-autorange-units
1190        (Math-realp (nth 1 math-simplify-expr))
1191        (let* ((num (math-float (nth 1 math-simplify-expr)))
1192               (xpon (calcFunc-xpon num))
1193               (unitp (cdr (cdr math-simplify-expr)))
1194               (unit (car unitp))
1195               (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1196               u)
1197          (and (eq (car-safe unit) '*)
1198               (setq unitp (cdr unit)
1199                     unit (car unitp)))
1200          (and (eq (car-safe unit) '^)
1201               (integerp (nth 2 unit))
1202               (setq pow (* pow (nth 2 unit))
1203                     unitp (cdr unit)
1204                     unit (car unitp)))
1205          (and (setq u (math-check-unit-name unit))
1206               (integerp xpon)
1207               (or (< xpon 0)
1208                   (>= xpon (if (eq (car u) 'm) 1 3)))
1209               (let* ((uxpon 0)
1210                      (pref (if (< pow 0)
1211                                (reverse math-unit-prefixes)
1212                              math-unit-prefixes))
1213                      (p pref)
1214                      pxpon pname)
1215                 (or (eq (car u) (nth 1 unit))
1216                     (setq uxpon (* pow
1217                                    (nth 2 (nth 1 (assq
1218                                                   (aref (symbol-name
1219                                                          (nth 1 unit)) 0)
1220                                                   math-unit-prefixes))))))
1221                 (setq xpon (+ xpon uxpon))
1222                 (while (and p
1223                             (or (memq (car (car p)) '(?d ?D ?h ?H))
1224                                 (and (eq (car (car p)) ?c)
1225                                      (not (eq (car u) 'm)))
1226                                 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1227                                                        pow)))
1228                                 (progn
1229                                   (setq pname (math-build-var-name
1230                                                (if (eq (car (car p)) 0)
1231                                                    (car u)
1232                                                  (concat (char-to-string
1233                                                           (car (car p)))
1234                                                          (symbol-name
1235                                                           (car u))))))
1236                                   (and (/= (car (car p)) 0)
1237                                        (assq (nth 1 pname)
1238                                              math-units-table)))))
1239                   (setq p (cdr p)))
1240                 (and p
1241                      (/= pxpon uxpon)
1242                      (or (not (eq p pref))
1243                          (< xpon (+ pxpon (* (math-abs pow) 3))))
1244                      (progn
1245                        (setcar (cdr math-simplify-expr)
1246                                (let ((calc-prefer-frac nil))
1247                                  (calcFunc-scf (nth 1 math-simplify-expr)
1248                                                (- uxpon pxpon))))
1249                        (setcar unitp pname)
1250                        math-simplify-expr)))))))
1251
1252 (defvar math-try-cancel-units)
1253
1254 (math-defsimplify /
1255   (and math-simplifying-units
1256        (let ((np (cdr math-simplify-expr))
1257              (math-try-cancel-units 0)
1258              n nn)
1259          (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1260                      (cdr (nth 2 math-simplify-expr))
1261                    (nthcdr 2 math-simplify-expr)))
1262          (if (math-realp (car n))
1263              (progn
1264                (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1265                                             (let ((calc-prefer-frac nil))
1266                                               (math-div 1 (car n)))))
1267                (setcar n 1)))
1268          (while (eq (car-safe (setq n (car np))) '*)
1269            (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1270            (setq np (cdr (cdr n))))
1271          (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1272          (if (eq math-try-cancel-units 0)
1273              (let* ((math-simplifying-units nil)
1274                     (base (math-simplify
1275                            (math-to-standard-units math-simplify-expr nil))))
1276                (if (Math-numberp base)
1277                    (setq math-simplify-expr base))))
1278          (if (eq (car-safe math-simplify-expr) '/)
1279              (math-simplify-units-prod))
1280          math-simplify-expr)))
1281
1282 (defun math-simplify-units-divisor (np dp)
1283   (let ((n (car np))
1284         d dd temp)
1285     (while (eq (car-safe (setq d (car dp))) '*)
1286       (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1287         (setcar np (setq n temp))
1288         (setcar (cdr d) 1))
1289       (setq dp (cdr (cdr d))))
1290     (when (setq temp (math-simplify-units-quotient n d))
1291       (setcar np (setq n temp))
1292       (setcar dp 1))))
1293
1294 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1295 (defun math-simplify-units-quotient (n d)
1296   (let ((pow1 1)
1297         (pow2 1))
1298     (when (and (eq (car-safe n) '^)
1299                (integerp (nth 2 n)))
1300       (setq pow1 (nth 2 n) n (nth 1 n)))
1301     (when (and (eq (car-safe d) '^)
1302                (integerp (nth 2 d)))
1303       (setq pow2 (nth 2 d) d (nth 1 d)))
1304     (let ((un (math-check-unit-name n))
1305           (ud (math-check-unit-name d)))
1306       (and un ud
1307            (if (and (equal (nth 4 un) (nth 4 ud))
1308                     (eq pow1 pow2))
1309                (if (eq pow1 1)
1310                    (math-to-standard-units (list '/ n d) nil)
1311                  (list '^ (math-to-standard-units (list '/ n d) nil) pow1))
1312              (let (ud1)
1313                (setq un (nth 4 un)
1314                      ud (nth 4 ud))
1315                (while un
1316                  (setq ud1 ud)
1317                  (while ud1
1318                    (and (eq (car (car un)) (car (car ud1)))
1319                         (setq math-try-cancel-units
1320                               (+ math-try-cancel-units
1321                                  (- (* (cdr (car un)) pow1)
1322                                     (* (cdr (car ud)) pow2)))))
1323                    (setq ud1 (cdr ud1)))
1324                  (setq un (cdr un)))
1325                nil))))))
1326
1327 (math-defsimplify ^
1328   (and math-simplifying-units
1329        (math-realp (nth 2 math-simplify-expr))
1330        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1331            (list (car (nth 1 math-simplify-expr))
1332                  (list '^ (nth 1 (nth 1 math-simplify-expr))
1333                        (nth 2 math-simplify-expr))
1334                  (list '^ (nth 2 (nth 1 math-simplify-expr))
1335                        (nth 2 math-simplify-expr)))
1336          (math-simplify-units-pow (nth 1 math-simplify-expr)
1337                                   (nth 2 math-simplify-expr)))))
1338
1339 (math-defsimplify calcFunc-sqrt
1340   (and math-simplifying-units
1341        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1342            (list (car (nth 1 math-simplify-expr))
1343                  (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1344                  (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1345          (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1346
1347 (math-defsimplify (calcFunc-floor
1348                    calcFunc-ceil
1349                    calcFunc-round
1350                    calcFunc-rounde
1351                    calcFunc-roundu
1352                    calcFunc-trunc
1353                    calcFunc-float
1354                    calcFunc-frac
1355                    calcFunc-abs
1356                    calcFunc-clean)
1357   (and math-simplifying-units
1358        (= (length math-simplify-expr) 2)
1359        (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1360            (nth 1 math-simplify-expr)
1361          (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1362                   (or (math-only-units-in-expr-p
1363                        (nth 1 (nth 1 math-simplify-expr)))
1364                       (math-only-units-in-expr-p
1365                        (nth 2 (nth 1 math-simplify-expr)))))
1366              (list (car (nth 1 math-simplify-expr))
1367                    (cons (car math-simplify-expr)
1368                          (cons (nth 1 (nth 1 math-simplify-expr))
1369                                (cdr (cdr math-simplify-expr))))
1370                    (cons (car math-simplify-expr)
1371                          (cons (nth 2 (nth 1 math-simplify-expr))
1372                                (cdr (cdr math-simplify-expr)))))))))
1373
1374 (defun math-simplify-units-pow (a pow)
1375   (if (and (eq (car-safe a) '^)
1376            (math-check-unit-name (nth 1 a))
1377            (math-realp (nth 2 a)))
1378       (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1379     (let* ((u (math-check-unit-name a))
1380            (pf (math-to-simple-fraction pow))
1381            (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1382       (and u d
1383            (math-units-are-multiple u d)
1384            (list '^ (math-to-standard-units a nil) pow)))))
1385
1386
1387 (defun math-units-are-multiple (u n)
1388   (setq u (nth 4 u))
1389   (while (and u (= (% (cdr (car u)) n) 0))
1390     (setq u (cdr u)))
1391   (null u))
1392
1393 (math-defsimplify calcFunc-sin
1394   (and math-simplifying-units
1395        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1396        (let ((rad (math-simplify-units
1397                    (math-evaluate-expr
1398                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1399              (calc-angle-mode 'rad))
1400          (and (eq (car-safe rad) '*)
1401               (math-realp (nth 1 rad))
1402               (eq (car-safe (nth 2 rad)) 'var)
1403               (eq (nth 1 (nth 2 rad)) 'rad)
1404               (list 'calcFunc-sin (nth 1 rad))))))
1405
1406 (math-defsimplify calcFunc-cos
1407   (and math-simplifying-units
1408        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1409        (let ((rad (math-simplify-units
1410                    (math-evaluate-expr
1411                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1412              (calc-angle-mode 'rad))
1413          (and (eq (car-safe rad) '*)
1414               (math-realp (nth 1 rad))
1415               (eq (car-safe (nth 2 rad)) 'var)
1416               (eq (nth 1 (nth 2 rad)) 'rad)
1417               (list 'calcFunc-cos (nth 1 rad))))))
1418
1419 (math-defsimplify calcFunc-tan
1420   (and math-simplifying-units
1421        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1422        (let ((rad (math-simplify-units
1423                    (math-evaluate-expr
1424                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1425              (calc-angle-mode 'rad))
1426          (and (eq (car-safe rad) '*)
1427               (math-realp (nth 1 rad))
1428               (eq (car-safe (nth 2 rad)) 'var)
1429               (eq (nth 1 (nth 2 rad)) 'rad)
1430               (list 'calcFunc-tan (nth 1 rad))))))
1431
1432 (math-defsimplify calcFunc-sec
1433   (and math-simplifying-units
1434        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1435        (let ((rad (math-simplify-units
1436                    (math-evaluate-expr
1437                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1438              (calc-angle-mode 'rad))
1439          (and (eq (car-safe rad) '*)
1440               (math-realp (nth 1 rad))
1441               (eq (car-safe (nth 2 rad)) 'var)
1442               (eq (nth 1 (nth 2 rad)) 'rad)
1443               (list 'calcFunc-sec (nth 1 rad))))))
1444
1445 (math-defsimplify calcFunc-csc
1446   (and math-simplifying-units
1447        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1448        (let ((rad (math-simplify-units
1449                    (math-evaluate-expr
1450                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1451              (calc-angle-mode 'rad))
1452          (and (eq (car-safe rad) '*)
1453               (math-realp (nth 1 rad))
1454               (eq (car-safe (nth 2 rad)) 'var)
1455               (eq (nth 1 (nth 2 rad)) 'rad)
1456               (list 'calcFunc-csc (nth 1 rad))))))
1457
1458 (math-defsimplify calcFunc-cot
1459   (and math-simplifying-units
1460        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1461        (let ((rad (math-simplify-units
1462                    (math-evaluate-expr
1463                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1464              (calc-angle-mode 'rad))
1465          (and (eq (car-safe rad) '*)
1466               (math-realp (nth 1 rad))
1467               (eq (car-safe (nth 2 rad)) 'var)
1468               (eq (nth 1 (nth 2 rad)) 'rad)
1469               (list 'calcFunc-cot (nth 1 rad))))))
1470
1471
1472 (defun math-remove-units (expr)
1473   (if (math-check-unit-name expr)
1474       1
1475     (if (Math-primp expr)
1476         expr
1477       (cons (car expr)
1478             (mapcar 'math-remove-units (cdr expr))))))
1479
1480 (defun math-extract-units (expr)
1481   (if (memq (car-safe expr) '(* /))
1482       (cons (car expr)
1483             (mapcar 'math-extract-units (cdr expr)))
1484     (if (math-check-unit-name expr) expr 1)))
1485
1486 (defun math-build-units-table-buffer (enter-buffer)
1487   (if (not (and math-units-table math-units-table-buffer-valid
1488                 (get-buffer "*Units Table*")))
1489       (let ((buf (get-buffer-create "*Units Table*"))
1490             (uptr (math-build-units-table))
1491             (calc-language (if (eq calc-language 'big) nil calc-language))
1492             (calc-float-format '(float 0))
1493             (calc-group-digits nil)
1494             (calc-number-radix 10)
1495             (calc-twos-complement-mode nil)
1496             (calc-point-char ".")
1497             (std nil)
1498             u name shadowed)
1499         (save-excursion
1500           (message "Formatting units table...")
1501           (set-buffer buf)
1502           (let ((inhibit-read-only t))
1503             (erase-buffer)
1504             (insert "Calculator Units Table:\n\n")
1505             (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n")
1506             (insert "Unit    Type  Definition                  Description\n\n")
1507             (while uptr
1508               (setq u (car uptr)
1509                     name (nth 2 u))
1510               (when (eq (car u) 'm)
1511                 (setq std t))
1512               (setq shadowed (and std (assq (car u) math-additional-units)))
1513               (when (and name
1514                          (> (length name) 1)
1515                          (eq (aref name 0) ?\*))
1516                 (unless (eq uptr math-units-table)
1517                   (insert "\n"))
1518                 (setq name (substring name 1)))
1519               (insert " ")
1520               (and shadowed (insert "("))
1521               (insert (symbol-name (car u)))
1522               (and shadowed (insert ")"))
1523               (if (nth 3 u)
1524                   (progn
1525                     (indent-to 10)
1526                     (insert (symbol-name (nth 3 u))))
1527                 (or std
1528                     (progn
1529                       (indent-to 10)
1530                       (insert "U"))))
1531               (indent-to 14)
1532               (and shadowed (insert "("))
1533               (if (nth 5 u)
1534                   (insert (nth 5 u))
1535                 (if (nth 1 u)
1536                     (insert (math-format-value (nth 1 u) 80))
1537                   (insert (symbol-name (car u)))))
1538               (and shadowed (insert ")"))
1539               (indent-to 41)
1540               (insert " ")
1541               (when name
1542                 (insert name))
1543               (if shadowed
1544                   (insert " (redefined above)")
1545                 (unless (nth 1 u)
1546                   (insert " (base unit)")))
1547               (insert "\n")
1548               (setq uptr (cdr uptr)))
1549             (insert "\n\nUnit Prefix Table:\n\n")
1550             (setq uptr math-unit-prefixes)
1551             (while uptr
1552               (setq u (car uptr))
1553               (insert " " (char-to-string (car u)))
1554               (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1555                   (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1556                           "   ")
1557                 (insert "     "))
1558               (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1559               (indent-to 15)
1560               (insert "   " (nth 2 u) "\n")
1561               (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1562             (insert "\n\n")
1563             (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
1564                      "names will not use the `tex' prefix; the unit name for a\n"
1565                      "TeX point will be `pt' instead of `texpt', for example.\n"
1566                      "To avoid conflicts, the unit names for pint and parsec will\n"
1567                      "be `pint' and `parsec' instead of `pt' and `pc'."))
1568           (view-mode)
1569           (message "Formatting units table...done"))
1570         (setq math-units-table-buffer-valid t)
1571         (let ((oldbuf (current-buffer)))
1572           (set-buffer buf)
1573           (goto-char (point-min))
1574           (set-buffer oldbuf))
1575         (if enter-buffer
1576             (pop-to-buffer buf)
1577           (display-buffer buf)))
1578     (if enter-buffer
1579         (pop-to-buffer (get-buffer "*Units Table*"))
1580       (display-buffer (get-buffer "*Units Table*")))))
1581
1582 ;;; Logarithmic units functions
1583
1584 (defvar math-logunits '((var dB var-dB)
1585                         (var Np var-Np)))
1586
1587 (defun math-conditional-apply (fn &rest args)
1588   "Evaluate f(args) unless in symbolic mode.
1589 In symbolic mode, return the list (fn args)."
1590   (if calc-symbolic-mode
1591       (cons fn args)
1592     (apply fn args)))
1593
1594 (defun math-conditional-pow (a b)
1595   "Evaluate a^b unless in symbolic mode.
1596 In symbolic mode, return the list (^ a b)."
1597   (if calc-symbolic-mode
1598       (list '^ a b)
1599     (math-pow a b)))
1600
1601 (defun math-extract-logunits (expr)
1602   (if (memq (car-safe expr) '(* /))
1603       (cons (car expr)
1604             (mapcar 'math-extract-logunits (cdr expr)))
1605     (if (memq (car-safe expr) '(^))
1606         (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
1607       (if (member expr math-logunits) expr 1))))
1608
1609 (defun math-logunits-add (a b neg power)
1610   (let ((aunit (math-simplify (math-extract-logunits a))))
1611     (if (not (eq (car-safe aunit) 'var))
1612         (calc-record-why "*Improper logarithmic unit" aunit)
1613       (let* ((units (math-extract-units a))
1614             (acoeff (math-simplify (math-remove-units a)))
1615             (bcoeff (math-simplify (math-to-standard-units
1616                                     (list '/ b units) nil))))
1617         (if (math-units-in-expr-p bcoeff nil)
1618             (calc-record-why "*Inconsistent units" nil)
1619           (if (and neg
1620                    (or (math-lessp acoeff bcoeff)
1621                        (math-equal acoeff bcoeff)))
1622               (calc-record-why "*Improper coefficients" nil)
1623             (math-mul
1624              (if (equal aunit '(var dB var-dB))
1625                  (let ((coef (if power 10 20)))
1626                    (math-mul coef
1627                              (math-conditional-apply 'calcFunc-log10
1628                               (if neg
1629                                   (math-sub
1630                                    (math-conditional-pow 10 (math-div acoeff coef))
1631                                    (math-conditional-pow 10 (math-div bcoeff coef)))
1632                                 (math-add
1633                                  (math-conditional-pow 10 (math-div acoeff coef))
1634                                  (math-conditional-pow 10 (math-div bcoeff coef)))))))
1635                (let ((coef (if power 2 1)))
1636                  (math-div
1637                   (math-conditional-apply 'calcFunc-ln
1638                    (if neg
1639                        (math-sub
1640                         (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1641                         (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
1642                      (math-add
1643                       (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1644                       (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
1645                   coef)))
1646              units)))))))
1647
1648 (defun calcFunc-lufadd (a b)
1649   (math-logunits-add a b nil nil))
1650
1651 (defun calcFunc-lupadd (a b)
1652   (math-logunits-add a b nil t))
1653
1654 (defun calcFunc-lufsub (a b)
1655   (math-logunits-add a b t nil))
1656
1657 (defun calcFunc-lupsub (a b)
1658   (math-logunits-add a b t t))
1659
1660 (defun calc-lu-plus (arg)
1661   (interactive "P")
1662   (calc-slow-wrapper
1663    (if (calc-is-inverse)
1664        (if (calc-is-hyperbolic)
1665            (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1666          (calc-binary-op "lu-" 'calcFunc-lupsub arg))
1667      (if (calc-is-hyperbolic)
1668          (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1669        (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
1670
1671 (defun calc-lu-minus (arg)
1672   (interactive "P")
1673   (calc-slow-wrapper
1674    (if (calc-is-inverse)
1675        (if (calc-is-hyperbolic)
1676            (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1677          (calc-binary-op "lu+" 'calcFunc-lupadd arg))
1678      (if (calc-is-hyperbolic)
1679          (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1680        (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
1681
1682 (defun math-logunits-mul (a b power)
1683   (let (logunit coef units number)
1684     (cond
1685      ((and
1686        (setq logunit (math-simplify (math-extract-logunits a)))
1687        (eq (car-safe logunit) 'var)
1688        (eq (math-simplify (math-extract-units b)) 1))
1689       (setq coef (math-simplify (math-remove-units a))
1690             units (math-extract-units a)
1691             number b))
1692      ((and
1693        (setq logunit (math-simplify (math-extract-logunits b)))
1694        (eq (car-safe logunit) 'var)
1695        (eq (math-simplify (math-extract-units a)) 1))
1696       (setq coef (math-simplify (math-remove-units b))
1697             units (math-extract-units b)
1698             number a))
1699      (t (setq logunit nil)))
1700     (if logunit
1701         (cond
1702          ((equal logunit '(var dB var-dB))
1703           (math-simplify
1704            (math-mul
1705             (math-add
1706              coef
1707              (math-mul (if power 10 20)
1708                        (math-conditional-apply 'calcFunc-log10 number)))
1709             units)))
1710          (t
1711           (math-simplify
1712            (math-mul
1713             (math-add
1714              coef
1715              (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
1716             units))))
1717       (calc-record-why "*Improper units" nil))))
1718
1719 (defun math-logunits-divide (a b power)
1720   (let ((logunit (math-simplify (math-extract-logunits a))))
1721     (if (not (eq (car-safe logunit) 'var))
1722         (calc-record-why "*Improper logarithmic unit" logunit)
1723       (if (math-units-in-expr-p b nil)
1724           (calc-record-why "*Improper units quantity" b)
1725         (let* ((units (math-extract-units a))
1726                (coef (math-simplify (math-remove-units a))))
1727           (cond
1728            ((equal logunit '(var dB var-dB))
1729             (math-simplify
1730              (math-mul
1731               (math-sub
1732                coef
1733                (math-mul (if power 10 20)
1734                          (math-conditional-apply 'calcFunc-log10 b)))
1735               units)))
1736          (t
1737           (math-simplify
1738            (math-mul
1739             (math-sub
1740              coef
1741              (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
1742             units)))))))))
1743
1744 (defun calcFunc-lufmul (a b)
1745   (math-logunits-mul a b nil))
1746
1747 (defun calcFunc-lupmul (a b)
1748   (math-logunits-mul a b t))
1749
1750 (defun calc-lu-times (arg)
1751   (interactive "P")
1752   (calc-slow-wrapper
1753    (if (calc-is-inverse)
1754        (if (calc-is-hyperbolic)
1755            (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1756          (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
1757      (if (calc-is-hyperbolic)
1758          (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1759        (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
1760
1761 (defun calcFunc-lufdiv (a b)
1762   (math-logunits-divide a b nil))
1763
1764 (defun calcFunc-lupdiv (a b)
1765   (math-logunits-divide a b t))
1766
1767 (defun calc-lu-divide (arg)
1768   (interactive "P")
1769   (calc-slow-wrapper
1770    (if (calc-is-inverse)
1771        (if (calc-is-hyperbolic)
1772            (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1773          (calc-binary-op "lu*" 'calcFunc-lupmul arg))
1774      (if (calc-is-hyperbolic)
1775          (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1776        (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
1777
1778 (defun math-logunits-quant (val ref power)
1779   (let* ((units (math-simplify (math-extract-units val)))
1780          (lunit (math-simplify (math-extract-logunits units))))
1781     (if (not (eq (car-safe lunit) 'var))
1782         (calc-record-why "*Improper logarithmic unit" lunit)
1783       (let ((runits (math-simplify (math-div units lunit)))
1784             (coeff (math-simplify (math-div val units))))
1785         (math-mul
1786          (if (equal lunit '(var dB var-dB))
1787              (math-mul
1788               ref
1789               (math-conditional-pow
1790                10
1791                (math-div
1792                 coeff
1793                 (if power 10 20))))
1794            (math-mul
1795             ref
1796             (math-conditional-apply 'calcFunc-exp
1797              (if power
1798                  (math-mul 2 coeff)
1799                coeff))))
1800          runits)))))
1801
1802 (defvar calc-lu-field-reference)
1803 (defvar calc-lu-power-reference)
1804
1805 (defun calcFunc-lufquant (val &optional ref)
1806   (unless ref
1807     (setq ref (math-read-expr calc-lu-field-reference)))
1808   (math-logunits-quant val ref nil))
1809
1810 (defun calcFunc-lupquant (val &optional ref)
1811   (unless ref
1812     (setq ref (math-read-expr calc-lu-power-reference)))
1813   (math-logunits-quant val ref t))
1814
1815 (defun calc-lu-quant (arg)
1816   (interactive "P")
1817   (calc-slow-wrapper
1818    (if (calc-is-hyperbolic)
1819        (if (calc-is-option)
1820            (calc-binary-op "lupq" 'calcFunc-lufquant arg)
1821          (calc-unary-op "lupq" 'calcFunc-lufquant arg))
1822      (if (calc-is-option)
1823          (calc-binary-op "lufq" 'calcFunc-lupquant arg)
1824        (calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
1825
1826 (defun math-logunits-level (val ref db power)
1827   "Compute the value of VAL in decibels or nepers."
1828       (let* ((ratio (math-simplify-units (math-div val ref)))
1829              (ratiou (math-simplify-units (math-remove-units ratio)))
1830              (units (math-simplify (math-extract-units ratio))))
1831         (math-mul
1832          (if db
1833              (math-mul
1834               (math-mul (if power 10 20)
1835                         (math-conditional-apply 'calcFunc-log10 ratiou))
1836               '(var dB var-dB))
1837            (math-mul
1838             (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
1839             '(var Np var-Np)))
1840          units)))
1841
1842 (defun calcFunc-dbfield (val &optional ref)
1843   (unless ref
1844     (setq ref (math-read-expr calc-lu-field-reference)))
1845   (math-logunits-level val ref t nil))
1846
1847 (defun calcFunc-dbpower (val &optional ref)
1848   (unless ref
1849     (setq ref (math-read-expr calc-lu-power-reference)))
1850   (math-logunits-level val ref t t))
1851
1852 (defun calcFunc-npfield (val &optional ref)
1853   (unless ref
1854     (setq ref (math-read-expr calc-lu-field-reference)))
1855   (math-logunits-level val ref nil nil))
1856
1857 (defun calcFunc-nppower (val &optional ref)
1858   (unless ref
1859     (setq ref (math-read-expr calc-lu-power-reference)))
1860   (math-logunits-level val ref nil t))
1861
1862 (defun calc-db (arg)
1863   (interactive "P")
1864   (calc-slow-wrapper
1865    (if (calc-is-hyperbolic)
1866        (if (calc-is-option)
1867            (calc-binary-op "ludb" 'calcFunc-dbfield arg)
1868          (calc-unary-op "ludb" 'calcFunc-dbfield arg))
1869      (if (calc-is-option)
1870          (calc-binary-op "ludb" 'calcFunc-dbpower arg)
1871        (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
1872
1873 (defun calc-np (arg)
1874   (interactive "P")
1875   (calc-slow-wrapper
1876    (if (calc-is-hyperbolic)
1877        (if (calc-is-option)
1878            (calc-binary-op "lunp" 'calcFunc-npfield arg)
1879          (calc-unary-op "lunp" 'calcFunc-npfield arg))
1880      (if (calc-is-option)
1881          (calc-binary-op "lunp" 'calcFunc-nppower arg)
1882        (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
1883
1884 ;;; Musical notes
1885
1886
1887 (defvar calc-note-threshold)
1888
1889 (defun math-midi-round (num)
1890   "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
1891   (let* ((n (math-round num))
1892          (diff (math-abs
1893                 (math-sub num n))))
1894     (if (< (math-compare diff
1895                          (math-div (math-read-expr calc-note-threshold) 100)) 0)
1896         n
1897       num)))
1898
1899 (defconst math-notes
1900   '(((var C var-C) . 0)
1901     ((var Csharp var-Csharp) . 1)
1902 ;    ((var C♯ var-C♯) . 1)
1903     ((var Dflat var-Dflat) . 1)
1904 ;    ((var D♭ var-D♭) . 1)
1905     ((var D var-D) . 2)
1906     ((var Dsharp var-Dsharp) . 3)
1907 ;    ((var D♯ var-D♯) . 3)
1908     ((var E var-E) . 4)
1909     ((var F var-F) . 5)
1910     ((var Fsharp var-Fsharp) . 6)
1911 ;    ((var F♯ var-F♯) . 6)
1912     ((var Gflat var-Gflat) . 6)
1913 ;    ((var G♭ var-G♭) . 6)
1914     ((var G var-G) . 7)
1915     ((var Gsharp var-Gsharp) . 8)
1916 ;    ((var G♯ var-G♯) . 8)
1917     ((var A var-A) . 9)
1918     ((var Asharp var-Asharp) . 10)
1919 ;    ((var A♯ var-A♯) . 10)
1920     ((var Bflat var-Bflat) . 10)
1921 ;    ((var B♭ var-B♭) . 10)
1922     ((var B var-B) . 11))
1923   "An alist of notes with their number of semitones above C.")
1924
1925 (defun math-freqp (freq)
1926   "Non-nil if FREQ is a positive number times the unit Hz.
1927 If non-nil, return the coefficient of Hz."
1928   (let ((freqcoef (math-simplify-units
1929                    (math-div freq '(var Hz var-Hz)))))
1930     (if (Math-posp freqcoef) freqcoef)))
1931
1932 (defun math-midip (num)
1933   "Non-nil if NUM is a possible MIDI note number.
1934 If non-nil, return NUM."
1935   (if (Math-numberp num) num))
1936
1937 (defun math-spnp (spn)
1938   "Non-nil if NUM is a scientific pitch note (note + cents).
1939 If non-nil, return a list consisting of the note and the cents coefficient."
1940   (let (note cents rnote rcents)
1941     (if (eq (car-safe spn) '+)
1942         (setq note (nth 1 spn)
1943               cents (nth 2 spn))
1944       (setq note spn
1945             cents nil))
1946     (cond
1947      ((and  ;; NOTE is a note, CENTS is nil or cents.
1948        (eq (car-safe note) 'calcFunc-subscr)
1949        (assoc (nth 1 note) math-notes)
1950        (integerp (nth 2 note))
1951        (setq rnote note)
1952        (or
1953         (not cents)
1954         (Math-numberp (setq rcents
1955                             (math-simplify
1956                              (math-div cents '(var cents var-cents)))))))
1957       (list rnote rcents))
1958      ((and  ;; CENTS is a note, NOTE is cents.
1959        (eq (car-safe cents) 'calcFunc-subscr)
1960        (assoc (nth 1 cents) math-notes)
1961        (integerp (nth 2 cents))
1962        (setq rnote cents)
1963        (or
1964         (not note)
1965         (Math-numberp (setq rcents
1966                             (math-simplify
1967                              (math-div note '(var cents var-cents)))))))
1968       (list rnote rcents)))))
1969
1970 (defun math-freq-to-midi (freq)
1971   "Return the midi note number corresponding to FREQ Hz."
1972   (let ((midi (math-add
1973                69
1974                (math-mul
1975                 12
1976                 (calcFunc-log
1977                  (math-div freq 440)
1978                  2)))))
1979     (math-midi-round midi)))
1980
1981 (defun math-spn-to-midi (spn)
1982   "Return the MIDI number corresponding to SPN."
1983   (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
1984          (octave (math-add (nth 2 (car spn)) 1))
1985          (cents (nth 1 spn))
1986          (midi  (math-add
1987                  (math-mul 12 octave)
1988                  note)))
1989     (if cents
1990         (math-add midi (math-div cents 100))
1991       midi)))
1992
1993 (defun math-midi-to-spn (midi)
1994   "Return the scientific pitch notation corresponding to midi number MIDI."
1995   (let (midin cents)
1996     (if (math-integerp midi)
1997         (setq midin midi
1998               cents nil)
1999       (setq midin (math-floor midi)
2000             cents (math-mul 100 (math-sub midi midin))))
2001     (let* ((nr ;; This should be (math-idivmod midin 12), but with
2002                ;; better behavior for negative midin.
2003             (if (Math-negp midin)
2004                 (let ((dm (math-idivmod (math-neg midin) 12)))
2005                   (if (= (cdr dm) 0)
2006                       (cons (math-neg (car dm)) 0)
2007                     (cons
2008                      (math-sub (math-neg (car dm)) 1)
2009                      (math-sub 12 (cdr dm)))))
2010               (math-idivmod midin 12)))
2011            (n (math-sub (car nr) 1))
2012            (note (car (rassoc (cdr nr) math-notes))))
2013       (if cents
2014           (list '+ (list 'calcFunc-subscr note n)
2015                    (list '* cents '(var cents var-cents)))
2016         (list 'calcFunc-subscr note n)))))
2017
2018 (defun math-freq-to-spn (freq)
2019   "Return the scientific pitch notation corresponding to FREQ Hz."
2020   (math-with-extra-prec 3
2021     (math-midi-to-spn (math-freq-to-midi freq))))
2022
2023 (defun math-midi-to-freq (midi)
2024   "Return the frequency of the note with midi number MIDI."
2025   (list '*
2026         (math-mul
2027          440
2028          (math-pow
2029           2
2030           (math-div
2031            (math-sub
2032             midi
2033             69)
2034            12)))
2035         '(var Hz var-Hz)))
2036
2037 (defun math-spn-to-freq (spn)
2038   "Return the frequency of the note with scientific pitch notation SPN."
2039   (math-midi-to-freq (math-spn-to-midi spn)))
2040
2041 (defun calcFunc-spn (expr)
2042   "Return EXPR written as scientific pitch notation + cents."
2043   ;; Get the coefficient of Hz
2044   (let (note)
2045     (cond
2046      ((setq note (math-freqp expr))
2047       (math-freq-to-spn note))
2048      ((setq note (math-midip expr))
2049       (math-midi-to-spn note))
2050      ((math-spnp expr)
2051       expr)
2052      (t
2053       (math-reject-arg expr "*Improper expression")))))
2054
2055 (defun calcFunc-midi (expr)
2056   "Return EXPR written as a MIDI number."
2057   (let (note)
2058     (cond
2059      ((setq note (math-freqp expr))
2060       (math-freq-to-midi note))
2061      ((setq note (math-spnp expr))
2062       (math-spn-to-midi note))
2063      ((math-midip expr)
2064       expr)
2065      (t
2066       (math-reject-arg expr "*Improper expression")))))
2067
2068 (defun calcFunc-freq (expr)
2069   "Return the frequency corresponding to EXPR."
2070   (let (note)
2071     (cond
2072      ((setq note (math-midip expr))
2073       (math-midi-to-freq note))
2074      ((setq note (math-spnp expr))
2075       (math-spn-to-freq note))
2076      ((math-freqp expr)
2077       expr)
2078      (t
2079       (math-reject-arg expr "*Improper expression")))))
2080
2081 (defun calc-freq (arg)
2082   "Return the frequency corresponding to the expression on the stack."
2083   (interactive "P")
2084   (calc-slow-wrapper
2085    (calc-unary-op "freq" 'calcFunc-freq arg)))
2086
2087 (defun calc-midi (arg)
2088   "Return the MIDI number corresponding to the expression on the stack."
2089   (interactive "P")
2090   (calc-slow-wrapper
2091    (calc-unary-op "midi" 'calcFunc-midi arg)))
2092
2093 (defun calc-spn (arg)
2094   "Return the scientific pitch notation corresponding to the expression on the stack."
2095   (interactive "P")
2096   (calc-slow-wrapper
2097    (calc-unary-op "spn" 'calcFunc-spn arg)))
2098
2099
2100 (provide 'calc-units)
2101
2102 ;; Local variables:
2103 ;; coding: utf-8
2104 ;; End:
2105
2106 ;;; calc-units.el ends here