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 (defun calc-quick-units ()
 360   (interactive)
 361   (calc-slow-wrapper
 362    (let* ((num (- last-command-event ?0))
 363           (pos (if (= num 0) 10 num))
 364           (units (calc-var-value 'var-Units))
 365           (expr (calc-top-n 1)))
 366      (unless (and (>= num 0) (<= num 9))
 367        (error "Bad unit number"))
 368      (unless (math-vectorp units)
 369        (error "No \"quick units\" are defined"))
 370      (unless (< pos (length units))
 371        (error "Unit number %d not defined" pos))
 372      (if (math-units-in-expr-p expr nil)
 373          (calc-enter-result 1 (format "cun%d" num)
 374                             (math-convert-units expr (nth pos units)))
 375        (calc-enter-result 1 (format "*un%d" num)
 376                           (math-simplify-units
 377                            (math-mul expr (nth pos units))))))))
 378
 379 (defun math-get-standard-units (expr)
 380   "Return the standard units in EXPR."
 381   (math-simplify-units
 382    (math-extract-units
 383     (math-to-standard-units expr nil))))
 384
 385 (defun math-get-units (expr)
 386   "Return the units in EXPR."
 387   (math-simplify-units
 388    (math-extract-units expr)))
 389
 390 (defun math-make-unit-string (expr)
 391   "Return EXPR in string form.
 392 If EXPR is nil, return nil."
 393   (if expr
 394       (let ((cexpr (math-compose-expr expr 0)))
 395         (replace-regexp-in-string
 396          " / " "/"
 397          (if (stringp cexpr)
 398              cexpr
 399            (math-composition-to-string cexpr))))))
 400
 401 (defvar math-default-units-table
 402   (make-hash-table :test 'equal)
 403   "A table storing previously converted units.")
 404
 405 (defun math-get-default-units (expr)
 406   "Get default units to use when converting the units in EXPR."
 407   (let* ((units (math-get-units expr))
 408          (standard-units (math-get-standard-units expr))
 409          (default-units (gethash
 410                          standard-units
 411                          math-default-units-table)))
 412     (if (equal units (car default-units))
 413         (math-make-unit-string (cadr default-units))
 414       (math-make-unit-string (car default-units)))))
 415
 416 (defun math-put-default-units (expr)
 417   "Put the units in EXPR in the default units table."
 418   (let ((units (math-get-units expr)))
 419     (unless (eq units 1)
 420       (let* ((standard-units (math-get-standard-units expr))
 421          (default-units (gethash
 422                          standard-units
 423                          math-default-units-table)))
 424         (cond
 425          ((not default-units)
 426           (puthash standard-units (list units) math-default-units-table))
 427          ((not (equal units (car default-units)))
 428           (puthash standard-units
 429                    (list units (car default-units))
 430                    math-default-units-table)))))))
 431
 432
 433 (defun calc-convert-units (&optional old-units new-units)
 434   (interactive)
 435   (calc-slow-wrapper
 436    (let ((expr (calc-top-n 1))
 437          (uoldname nil)
 438          unew
 439          units
 440          defunits)
 441      (unless (math-units-in-expr-p expr t)
 442        (let ((uold (or old-units
 443                        (progn
 444                          (setq uoldname (read-string "Old units: "))
 445                          (if (equal uoldname "")
 446                              (progn
 447                                (setq uoldname "1")
 448                                1)
 449                            (if (string-match "\\` */" uoldname)
 450                                (setq uoldname (concat "1" uoldname)))
 451                            (math-read-expr uoldname))))))
 452          (when (eq (car-safe uold) 'error)
 453            (error "Bad format in units expression: %s" (nth 1 uold)))
 454          (setq expr (math-mul expr uold))))
 455      (unless new-units
 456        (setq defunits (math-get-default-units expr))
 457        (setq new-units
 458              (read-string (concat
 459                            (if uoldname
 460                                (concat "Old units: "
 461                                        uoldname
 462                                        ", new units")
 463                             "New units")
 464                            (if defunits
 465                                (concat
 466                                 " (default "
 467                                 defunits
 468                                 "): ")
 469                              ": "))))
 470
 471        (if (and
 472             (string= new-units "")
 473             defunits)
 474            (setq new-units defunits)))
 475      (when (string-match "\\` */" new-units)
 476        (setq new-units (concat "1" new-units)))
 477      (setq units (math-read-expr new-units))
 478      (when (eq (car-safe units) 'error)
 479        (error "Bad format in units expression: %s" (nth 2 units)))
 480      (math-put-default-units units)
 481      (let ((unew (math-units-in-expr-p units t))
 482            (std (and (eq (car-safe units) 'var)
 483                      (assq (nth 1 units) math-standard-units-systems))))
 484        (if std
 485            (calc-enter-result 1 "cvun" (math-simplify-units
 486                                         (math-to-standard-units expr
 487                                                                 (nth 1 std))))
 488          (unless unew
 489            (error "No units specified"))
 490          (calc-enter-result 1 "cvun"
 491                             (math-convert-units
 492                              expr units
 493                              (and uoldname (not (equal uoldname "1"))))))))))
 494
 495 (defun calc-autorange-units (arg)
 496   (interactive "P")
 497   (calc-wrapper
 498    (calc-change-mode 'calc-autorange-units arg nil t)
 499    (message (if calc-autorange-units
 500                 "Adjusting target unit prefix automatically"
 501               "Using target units exactly"))))
 502
 503 (defun calc-convert-temperature (&optional old-units new-units)
 504   (interactive)
 505   (calc-slow-wrapper
 506    (let ((expr (calc-top-n 1))
 507          (uold nil)
 508          (uoldname nil)
 509          unew
 510          defunits)
 511      (setq uold (or old-units
 512                     (let ((units (math-single-units-in-expr-p expr)))
 513                       (if units
 514                           (if (consp units)
 515                               (list 'var (car units)
 516                                     (intern (concat "var-"
 517                                                     (symbol-name
 518                                                      (car units)))))
 519                             (error "Not a pure temperature expression"))
 520                         (math-read-expr
 521                          (setq uoldname (read-string
 522                                          "Old temperature units: ")))))))
 523      (when (eq (car-safe uold) 'error)
 524        (error "Bad format in units expression: %s" (nth 2 uold)))
 525      (or (math-units-in-expr-p expr nil)
 526          (setq expr (math-mul expr uold)))
 527      (setq defunits (math-get-default-units expr))
 528      (setq unew (or new-units
 529                     (read-string
 530                      (concat
 531                       (if uoldname
 532                           (concat "Old temperature units: "
 533                                   uoldname
 534                                   ", new units")
 535                         "New temperature units")
 536                       (if defunits
 537                           (concat " (default "
 538                                   defunits
 539                                   "): ")
 540                         ": ")))))
 541      (setq unew (math-read-expr (if (string= unew "") defunits unew)))
 542      (when (eq (car-safe unew) 'error)
 543        (error "Bad format in units expression: %s" (nth 2 unew)))
 544      (math-put-default-units unew)
 545      (let ((ntemp (calc-normalize
 546                    (math-simplify-units
 547                     (math-convert-temperature expr uold unew
 548                                               uoldname)))))
 549        (if (Math-zerop ntemp)
 550            (setq ntemp (list '* ntemp unew)))
 551        (let ((calc-simplify-mode 'none))
 552          (calc-enter-result 1 "cvtm" ntemp))))))
 553
 554 (defun calc-remove-units ()
 555   (interactive)
 556   (calc-slow-wrapper
 557    (calc-enter-result 1 "rmun" (math-simplify-units
 558                                 (math-remove-units (calc-top-n 1))))))
 559
 560 (defun calc-extract-units ()
 561   (interactive)
 562   (calc-slow-wrapper
 563    (calc-enter-result 1 "rmun" (math-simplify-units
 564                                 (math-extract-units (calc-top-n 1))))))
 565
 566 ;; The variables calc-num-units and calc-den-units are local to
 567 ;; calc-explain-units, but are used by calc-explain-units-rec,
 568 ;; which is called by calc-explain-units.
 569 (defvar calc-num-units)
 570 (defvar calc-den-units)
 571
 572 (defun calc-explain-units ()
 573   (interactive)
 574   (calc-wrapper
 575    (let ((calc-num-units nil)
 576          (calc-den-units nil))
 577      (calc-explain-units-rec (calc-top-n 1) 1)
 578      (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units)
 579           (setq calc-den-units (concat "(" calc-den-units ")")))
 580      (if calc-num-units
 581          (if calc-den-units
 582              (message "%s per %s" calc-num-units calc-den-units)
 583            (message "%s" calc-num-units))
 584        (if calc-den-units
 585            (message "1 per %s" calc-den-units)
 586          (message "No units in expression"))))))
 587
 588 (defun calc-explain-units-rec (expr pow)
 589   (let ((u (math-check-unit-name expr))
 590         pos)
 591     (if (and u (not (math-zerop pow)))
 592         (let ((name (or (nth 2 u) (symbol-name (car u)))))
 593           (if (eq (aref name 0) ?\*)
 594               (setq name (substring name 1)))
 595           (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 596               (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name)
 597                   (while (setq pos (string-match "[ ()]" name))
 598                     (setq name (concat (substring name 0 pos)
 599                                        (if (eq (aref name pos) 32) "-" "")
 600                                        (substring name (1+ pos)))))
 601                 (setq name (concat "(" name ")"))))
 602           (or (eq (nth 1 expr) (car u))
 603               (setq name (concat (nth 2 (assq (aref (symbol-name
 604                                                      (nth 1 expr)) 0)
 605                                               math-unit-prefixes))
 606                                  (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name)
 607                                           (not (memq (car u) '(mHg gf))))
 608                                      (concat "-" name)
 609                                    (downcase name)))))
 610           (cond ((or (math-equal-int pow 1)
 611                      (math-equal-int pow -1)))
 612                 ((or (math-equal-int pow 2)
 613                      (math-equal-int pow -2))
 614                  (if (equal (nth 4 u) '((m . 1)))
 615                      (setq name (concat "Square-" name))
 616                    (setq name (concat name "-squared"))))
 617                 ((or (math-equal-int pow 3)
 618                      (math-equal-int pow -3))
 619                  (if (equal (nth 4 u) '((m . 1)))
 620                      (setq name (concat "Cubic-" name))
 621                    (setq name (concat name "-cubed"))))
 622                 (t
 623                  (setq name (concat name "^"
 624                                     (math-format-number (math-abs pow))))))
 625           (if (math-posp pow)
 626               (setq calc-num-units (if calc-num-units
 627                                   (concat calc-num-units " " name)
 628                                 name))
 629             (setq calc-den-units (if calc-den-units
 630                                 (concat calc-den-units " " name)
 631                               name))))
 632       (cond ((eq (car-safe expr) '*)
 633              (calc-explain-units-rec (nth 1 expr) pow)
 634              (calc-explain-units-rec (nth 2 expr) pow))
 635             ((eq (car-safe expr) '/)
 636              (calc-explain-units-rec (nth 1 expr) pow)
 637              (calc-explain-units-rec (nth 2 expr) (- pow)))
 638             ((memq (car-safe expr) '(neg + -))
 639              (calc-explain-units-rec (nth 1 expr) pow))
 640             ((and (eq (car-safe expr) '^)
 641                   (math-realp (nth 2 expr)))
 642              (calc-explain-units-rec (nth 1 expr)
 643                                      (math-mul pow (nth 2 expr))))))))
 644
 645 (defun calc-simplify-units ()
 646   (interactive)
 647   (calc-slow-wrapper
 648    (calc-with-default-simplification
 649     (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
 650
 651 (defun calc-view-units-table (n)
 652   (interactive "P")
 653   (and n (setq math-units-table-buffer-valid nil))
 654   (let ((win (get-buffer-window "*Units Table*")))
 655     (if (and win
 656              math-units-table
 657              math-units-table-buffer-valid)
 658         (progn
 659           (bury-buffer (window-buffer win))
 660           (let ((curwin (selected-window)))
 661             (select-window win)
 662             (switch-to-buffer nil)
 663             (select-window curwin)))
 664       (math-build-units-table-buffer nil))))
 665
 666 (defun calc-enter-units-table (n)
 667   (interactive "P")
 668   (and n (setq math-units-table-buffer-valid nil))
 669   (math-build-units-table-buffer t)
 670   (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator")))
 671
 672 (defun calc-define-unit (uname desc &optional disp)
 673   (interactive "SDefine unit name: \nsDescription: \nP")
 674   (if disp (setq disp (read-string "Display definition: ")))
 675   (calc-wrapper
 676    (let ((form (calc-top-n 1))
 677          (unit (assq uname math-additional-units)))
 678      (or unit
 679          (setq math-additional-units
 680                (cons (setq unit (list uname nil nil nil nil))
 681                      math-additional-units)
 682                math-units-table nil))
 683      (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var)
 684                                        (eq (nth 1 form) uname)))
 685                              (not (math-equal-int form 1))
 686                              (math-format-flat-expr form 0)))
 687      (setcar (cdr (cdr unit)) (and (not (equal desc ""))
 688                                    desc))
 689      (if disp
 690          (setcar (cdr (cdr (cdr (cdr unit)))) disp))))
 691   (calc-invalidate-units-table))
 692
 693 (defun calc-undefine-unit (uname)
 694   (interactive "SUndefine unit name: ")
 695   (calc-wrapper
 696    (let ((unit (assq uname math-additional-units)))
 697      (or unit
 698          (if (assq uname math-standard-units)
 699              (error "\"%s\" is a predefined unit name" uname)
 700            (error "Unit name \"%s\" not found" uname)))
 701      (setq math-additional-units (delq unit math-additional-units)
 702            math-units-table nil)))
 703   (calc-invalidate-units-table))
 704
 705 (defun calc-invalidate-units-table ()
 706   (setq math-units-table nil)
 707   (let ((buf (get-buffer "*Units Table*")))
 708     (and buf
 709          (with-current-buffer buf
 710            (save-excursion
 711              (goto-char (point-min))
 712              (if (looking-at "Calculator Units Table")
 713                  (let ((inhibit-read-only t))
 714                    (insert "(Obsolete) "))))))))
 715
 716 (defun calc-get-unit-definition (uname)
 717   (interactive "SGet definition for unit: ")
 718   (calc-wrapper
 719    (math-build-units-table)
 720    (let ((unit (assq uname math-units-table)))
 721      (or unit
 722          (error "Unit name \"%s\" not found" uname))
 723      (let ((msg (nth 2 unit)))
 724        (if (stringp msg)
 725            (if (string-match "^\\*" msg)
 726                (setq msg (substring msg 1)))
 727          (setq msg (symbol-name uname)))
 728        (if (nth 1 unit)
 729            (progn
 730              (calc-enter-result 0 "ugdf" (nth 1 unit))
 731              (message "Derived unit: %s" msg))
 732          (calc-enter-result 0 "ugdf" (list 'var uname
 733                                            (intern
 734                                             (concat "var-"
 735                                                     (symbol-name uname)))))
 736          (message "Base unit: %s" msg))))))
 737
 738 (defun calc-permanent-units ()
 739   (interactive)
 740   (calc-wrapper
 741    (let (pos)
 742      (set-buffer (find-file-noselect (substitute-in-file-name
 743                                       calc-settings-file)))
 744      (goto-char (point-min))
 745      (if (and (search-forward ";;; Custom units stored by Calc" nil t)
 746               (progn
 747                 (beginning-of-line)
 748                 (setq pos (point))
 749                 (search-forward "\n;;; End of custom units" nil t)))
 750          (progn
 751            (beginning-of-line)
 752            (forward-line 1)
 753            (delete-region pos (point)))
 754        (goto-char (point-max))
 755        (insert "\n\n")
 756        (forward-char -1))
 757      (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
 758      (if math-additional-units
 759          (progn
 760            (insert "(setq math-additional-units '(\n")
 761            (let ((list math-additional-units))
 762              (while list
 763                (insert "  (" (symbol-name (car (car list))) " "
 764                        (if (nth 1 (car list))
 765                            (if (stringp (nth 1 (car list)))
 766                                (prin1-to-string (nth 1 (car list)))
 767                              (prin1-to-string (math-format-flat-expr
 768                                                (nth 1 (car list)) 0)))
 769                          "nil")
 770                        " "
 771                        (prin1-to-string (nth 2 (car list)))
 772                        ")\n")
 773                (setq list (cdr list))))
 774            (insert "))\n"))
 775        (insert ";;; (no custom units defined)\n"))
 776      (insert ";;; End of custom units\n")
 777      (save-buffer))))
 778
 779
 780 ;; The variable math-cu-unit-list is local to math-build-units-table,
 781 ;; but is used by math-compare-unit-names, which is called (indirectly)
 782 ;; by math-build-units-table.
 783 ;; math-cu-unit-list is also local to math-convert-units, but is used
 784 ;; by math-convert-units-rec, which is called by math-convert-units.
 785 (defvar math-cu-unit-list)
 786
 787 (defun math-build-units-table ()
 788   (or math-units-table
 789       (let* ((combined-units (append math-additional-units
 790                                      math-standard-units))
 791              (math-cu-unit-list (mapcar 'car combined-units))
 792              tab)
 793         (message "Building units table...")
 794         (setq math-units-table-buffer-valid nil)
 795         (setq tab (mapcar (function
 796                            (lambda (x)
 797                              (list (car x)
 798                                    (and (nth 1 x)
 799                                         (if (stringp (nth 1 x))
 800                                             (let ((exp (math-read-plain-expr
 801                                                         (nth 1 x))))
 802                                               (if (eq (car-safe exp) 'error)
 803                                                   (error "Format error in definition of %s in units table: %s"
 804                                                          (car x) (nth 2 exp))
 805                                                 exp))
 806                                           (nth 1 x)))
 807                                    (nth 2 x)
 808                                    (nth 3 x)
 809                                    (and (not (nth 1 x))
 810                                         (list (cons (car x) 1)))
 811                                    (nth 4 x))))
 812                           combined-units))
 813         (let ((math-units-table tab))
 814           (mapc 'math-find-base-units tab))
 815         (message "Building units table...done")
 816         (setq math-units-table tab))))
 817
 818 ;; The variables math-fbu-base and math-fbu-entry are local to
 819 ;; math-find-base-units, but are used by math-find-base-units-rec,
 820 ;; which is called by math-find-base-units.
 821 (defvar math-fbu-base)
 822 (defvar math-fbu-entry)
 823
 824 (defun math-find-base-units (math-fbu-entry)
 825   (if (eq (nth 4 math-fbu-entry) 'boom)
 826       (error "Circular definition involving unit %s" (car math-fbu-entry)))
 827   (or (nth 4 math-fbu-entry)
 828       (let (math-fbu-base)
 829         (setcar (nthcdr 4 math-fbu-entry) 'boom)
 830         (math-find-base-units-rec (nth 1 math-fbu-entry) 1)
 831         '(or math-fbu-base
 832             (error "Dimensionless definition for unit %s" (car math-fbu-entry)))
 833         (while (eq (cdr (car math-fbu-base)) 0)
 834           (setq math-fbu-base (cdr math-fbu-base)))
 835         (let ((b math-fbu-base))
 836           (while (cdr b)
 837             (if (eq (cdr (car (cdr b))) 0)
 838                 (setcdr b (cdr (cdr b)))
 839               (setq b (cdr b)))))
 840         (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names))
 841         (setcar (nthcdr 4 math-fbu-entry) math-fbu-base)
 842         math-fbu-base)))
 843
 844 (defun math-compare-unit-names (a b)
 845   (memq (car b) (cdr (memq (car a) math-cu-unit-list))))
 846
 847 (defun math-find-base-units-rec (expr pow)
 848   (let ((u (math-check-unit-name expr)))
 849     (cond (u
 850            (let ((ulist (math-find-base-units u)))
 851              (while ulist
 852                (let ((p (* (cdr (car ulist)) pow))
 853                      (old (assq (car (car ulist)) math-fbu-base)))
 854                  (if old
 855                      (setcdr old (+ (cdr old) p))
 856                    (setq math-fbu-base
 857                          (cons (cons (car (car ulist)) p) math-fbu-base))))
 858                (setq ulist (cdr ulist)))))
 859           ((math-scalarp expr))
 860           ((and (eq (car expr) '^)
 861                 (integerp (nth 2 expr)))
 862            (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr))))
 863           ((eq (car expr) '*)
 864            (math-find-base-units-rec (nth 1 expr) pow)
 865            (math-find-base-units-rec (nth 2 expr) pow))
 866           ((eq (car expr) '/)
 867            (math-find-base-units-rec (nth 1 expr) pow)
 868            (math-find-base-units-rec (nth 2 expr) (- pow)))
 869           ((eq (car expr) 'neg)
 870            (math-find-base-units-rec (nth 1 expr) pow))
 871           ((eq (car expr) '+)
 872            (math-find-base-units-rec (nth 1 expr) pow))
 873           ((eq (car expr) 'var)
 874            (or (eq (nth 1 expr) 'pi)
 875                (error "Unknown name %s in defining expression for unit %s"
 876                       (nth 1 expr) (car math-fbu-entry))))
 877           ((equal expr '(calcFunc-ln 10)))
 878           (t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
 879
 880
 881 (defun math-units-in-expr-p (expr sub-exprs)
 882   (and (consp expr)
 883        (if (eq (car expr) 'var)
 884            (math-check-unit-name expr)
 885          (and (or sub-exprs
 886                   (memq (car expr) '(* / ^)))
 887               (or (math-units-in-expr-p (nth 1 expr) sub-exprs)
 888                   (math-units-in-expr-p (nth 2 expr) sub-exprs))))))
 889
 890 (defun math-only-units-in-expr-p (expr)
 891   (and (consp expr)
 892        (if (eq (car expr) 'var)
 893            (math-check-unit-name expr)
 894          (if (memq (car expr) '(* /))
 895              (and (math-only-units-in-expr-p (nth 1 expr))
 896                   (math-only-units-in-expr-p (nth 2 expr)))
 897            (and (eq (car expr) '^)
 898                 (and (math-only-units-in-expr-p (nth 1 expr))
 899                      (math-realp (nth 2 expr))))))))
 900
 901 (defun math-single-units-in-expr-p (expr)
 902   (cond ((math-scalarp expr) nil)
 903         ((eq (car expr) 'var)
 904          (math-check-unit-name expr))
 905         ((eq (car expr) '*)
 906          (let ((u1 (math-single-units-in-expr-p (nth 1 expr)))
 907                (u2 (math-single-units-in-expr-p (nth 2 expr))))
 908            (or (and u1 u2 'wrong)
 909                u1
 910                u2)))
 911         ((eq (car expr) '/)
 912          (if (math-units-in-expr-p (nth 2 expr) nil)
 913              'wrong
 914            (math-single-units-in-expr-p (nth 1 expr))))
 915         (t 'wrong)))
 916
 917 (defun math-check-unit-name (v)
 918   (and (eq (car-safe v) 'var)
 919        (or (assq (nth 1 v) (or math-units-table (math-build-units-table)))
 920            (let ((name (symbol-name (nth 1 v))))
 921              (and (> (length name) 1)
 922                   (assq (aref name 0) math-unit-prefixes)
 923                   (or (assq (intern (substring name 1)) math-units-table)
 924                       (and (eq (aref name 0) ?M)
 925                            (> (length name) 3)
 926                            (eq (aref name 1) ?e)
 927                            (eq (aref name 2) ?g)
 928                            (assq (intern (substring name 3))
 929                                  math-units-table))))))))
 930
 931 ;; The variable math-which-standard is local to math-to-standard-units,
 932 ;; but is used by math-to-standard-rec, which is called by
 933 ;; math-to-standard-units.
 934 (defvar math-which-standard)
 935
 936 (defun math-to-standard-units (expr math-which-standard)
 937   (math-to-standard-rec expr))
 938
 939 (defun math-to-standard-rec (expr)
 940   (if (eq (car-safe expr) 'var)
 941       (let ((u (math-check-unit-name expr))
 942             (base (nth 1 expr)))
 943         (if u
 944             (progn
 945               (if (nth 1 u)
 946                   (setq expr (math-to-standard-rec (nth 1 u)))
 947                 (let ((st (assq (car u) math-which-standard)))
 948                   (if st
 949                       (setq expr (nth 1 st))
 950                     (setq expr (list 'var (car u)
 951                                      (intern (concat "var-"
 952                                                      (symbol-name
 953                                                       (car u)))))))))
 954               (or (null u)
 955                   (eq base (car u))
 956                   (setq expr (list '*
 957                                    (nth 1 (assq (aref (symbol-name base) 0)
 958                                                 math-unit-prefixes))
 959                                    expr)))
 960               expr)
 961           (if (eq base 'pi)
 962               (math-pi)
 963             expr)))
 964     (if (or
 965          (Math-primp expr)
 966          (and (eq (car-safe expr) 'calcFunc-subscr)
 967               (eq (car-safe (nth 1 expr)) 'var)))
 968         expr
 969       (cons (car expr)
 970             (mapcar 'math-to-standard-rec (cdr expr))))))
 971
 972 (defun math-apply-units (expr units ulist &optional pure)
 973   (setq expr (math-simplify-units expr))
 974   (if ulist
 975       (let ((new 0)
 976             value)
 977         (or (math-numberp expr)
 978             (error "Incompatible units"))
 979         (while (cdr ulist)
 980           (setq value (math-div expr (nth 1 (car ulist)))
 981                 value (math-floor (let ((calc-internal-prec
 982                                          (1- calc-internal-prec)))
 983                                     (math-normalize value)))
 984                 new (math-add new (math-mul value (car (car ulist))))
 985                 expr (math-sub expr (math-mul value (nth 1 (car ulist))))
 986                 ulist (cdr ulist)))
 987         (math-add new (math-mul (math-div expr (nth 1 (car ulist)))
 988                                 (car (car ulist)))))
 989     (if pure
 990         expr
 991       (math-simplify-units (list '* expr units)))))
 992
 993 (defvar math-decompose-units-cache nil)
 994 (defun math-decompose-units (units)
 995   (let ((u (math-check-unit-name units)))
 996     (and u (eq (car-safe (nth 1 u)) '+)
 997          (setq units (nth 1 u))))
 998   (setq units (calcFunc-expand units))
 999   (and (eq (car-safe units) '+)
1000        (let ((entry (list units calc-internal-prec calc-prefer-frac)))
1001          (or (equal entry (car math-decompose-units-cache))
1002              (let ((ulist nil)
1003                    (utemp units)
1004                    qty unit)
1005                (while (eq (car-safe utemp) '+)
1006                  (setq ulist (cons (math-decompose-unit-part (nth 2 utemp))
1007                                    ulist)
1008                        utemp (nth 1 utemp)))
1009                (setq ulist (cons (math-decompose-unit-part utemp) ulist)
1010                      utemp ulist)
1011                (while (setq utemp (cdr utemp))
1012                  (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist)))
1013                    (error "Inconsistent units in sum")))
1014                (setq math-decompose-units-cache
1015                      (cons entry
1016                            (sort ulist
1017                                  (function
1018                                   (lambda (x y)
1019                                     (not (Math-lessp (nth 1 x)
1020                                                      (nth 1 y))))))))))
1021          (cdr math-decompose-units-cache))))
1022
1023 (defun math-decompose-unit-part (unit)
1024   (cons unit
1025         (math-is-multiple (math-simplify-units (math-to-standard-units
1026                                                 unit nil))
1027                           t)))
1028
1029 ;; The variable math-fcu-u is local to math-find-compatible-unit,
1030 ;; but is used by math-find-compatible-rec which is called by
1031 ;; math-find-compatible-unit.
1032 (defvar math-fcu-u)
1033
1034 (defun math-find-compatible-unit (expr unit)
1035   (let ((math-fcu-u (math-check-unit-name unit)))
1036     (if math-fcu-u
1037         (math-find-compatible-unit-rec expr 1))))
1038
1039 (defun math-find-compatible-unit-rec (expr pow)
1040   (cond ((eq (car-safe expr) '*)
1041          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1042              (math-find-compatible-unit-rec (nth 2 expr) pow)))
1043         ((eq (car-safe expr) '/)
1044          (or (math-find-compatible-unit-rec (nth 1 expr) pow)
1045              (math-find-compatible-unit-rec (nth 2 expr) (- pow))))
1046         ((and (eq (car-safe expr) '^)
1047               (integerp (nth 2 expr)))
1048          (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr))))
1049         (t
1050          (let ((u2 (math-check-unit-name expr)))
1051            (if (equal (nth 4 math-fcu-u) (nth 4 u2))
1052                (cons expr pow))))))
1053
1054 ;; The variables math-cu-new-units and math-cu-pure are local to
1055 ;; math-convert-units, but are used by math-convert-units-rec,
1056 ;; which is called by math-convert-units.
1057 (defvar math-cu-new-units)
1058 (defvar math-cu-pure)
1059
1060 (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure)
1061   (if (eq (car-safe math-cu-new-units) 'var)
1062       (let ((unew (assq (nth 1 math-cu-new-units)
1063                         (math-build-units-table))))
1064         (if (eq (car-safe (nth 1 unew)) '+)
1065             (setq math-cu-new-units (nth 1 unew)))))
1066   (math-with-extra-prec 2
1067     (let ((compat (and (not math-cu-pure)
1068                        (math-find-compatible-unit expr math-cu-new-units)))
1069           (math-cu-unit-list nil)
1070           (math-combining-units nil))
1071       (if compat
1072           (math-simplify-units
1073            (math-mul (math-mul (math-simplify-units
1074                                 (math-div expr (math-pow (car compat)
1075                                                          (cdr compat))))
1076                                (math-pow math-cu-new-units (cdr compat)))
1077                      (math-simplify-units
1078                       (math-to-standard-units
1079                        (math-pow (math-div (car compat) math-cu-new-units)
1080                                  (cdr compat))
1081                        nil))))
1082         (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units))
1083           (setq math-cu-new-units (nth 2 (car math-cu-unit-list))))
1084         (when (eq (car-safe expr) '+)
1085           (setq expr (math-simplify-units expr)))
1086         (if (math-units-in-expr-p expr t)
1087             (math-convert-units-rec expr)
1088           (math-apply-units (math-to-standard-units
1089                              (list '/ expr math-cu-new-units) nil)
1090                             math-cu-new-units math-cu-unit-list math-cu-pure))))))
1091
1092 (defun math-convert-units-rec (expr)
1093   (if (math-units-in-expr-p expr nil)
1094       (math-apply-units (math-to-standard-units
1095                          (list '/ expr math-cu-new-units) nil)
1096                         math-cu-new-units math-cu-unit-list math-cu-pure)
1097     (if (Math-primp expr)
1098         expr
1099       (cons (car expr)
1100             (mapcar 'math-convert-units-rec (cdr expr))))))
1101
1102 (defun math-convert-temperature (expr old new &optional pure)
1103   (let* ((units (math-single-units-in-expr-p expr))
1104          (uold (if old
1105                    (if (or (null units)
1106                            (equal (nth 1 old) (car units)))
1107                        (math-check-unit-name old)
1108                      (error "Inconsistent temperature units"))
1109                  units))
1110          (unew (math-check-unit-name new)))
1111     (unless (and (consp unew) (nth 3 unew))
1112       (error "Not a valid temperature unit"))
1113     (unless (and (consp uold) (nth 3 uold))
1114       (error "Not a pure temperature expression"))
1115     (let ((v (car uold)))
1116       (setq expr (list '/ expr (list 'var v
1117                                      (intern (concat "var-"
1118                                                      (symbol-name v)))))))
1119     (or (eq (nth 3 uold) (nth 3 unew))
1120         (cond ((eq (nth 3 uold) 'K)
1121                (setq expr (list '- expr '(/ 27315 100)))
1122                (if (eq (nth 3 unew) 'F)
1123                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))))
1124               ((eq (nth 3 uold) 'C)
1125                (if (eq (nth 3 unew) 'F)
1126                    (setq expr (list '+ (list '* expr '(/ 9 5)) 32))
1127                  (setq expr (list '+ expr '(/ 27315 100)))))
1128               (t
1129                (setq expr (list '* (list '- expr 32) '(/ 5 9)))
1130                (if (eq (nth 3 unew) 'K)
1131                    (setq expr (list '+ expr '(/ 27315 100)))))))
1132     (if pure
1133         expr
1134       (list '* expr new))))
1135
1136
1137
1138 (defun math-simplify-units (a)
1139   (let ((math-simplifying-units t)
1140         (calc-matrix-mode 'scalar))
1141     (math-simplify a)))
1142 (defalias 'calcFunc-usimplify 'math-simplify-units)
1143
1144 ;; The function created by math-defsimplify uses the variable
1145 ;; math-simplify-expr, and so is used by functions in math-defsimplify
1146 (defvar math-simplify-expr)
1147
1148 (math-defsimplify (+ -)
1149   (and math-simplifying-units
1150        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1151        (let* ((units (math-extract-units (nth 1 math-simplify-expr)))
1152               (ratio (math-simplify (math-to-standard-units
1153                                      (list '/ (nth 2 math-simplify-expr) units) nil))))
1154          (if (math-units-in-expr-p ratio nil)
1155              (progn
1156                (calc-record-why "*Inconsistent units" math-simplify-expr)
1157                math-simplify-expr)
1158            (list '* (math-add (math-remove-units (nth 1 math-simplify-expr))
1159                               (if (eq (car math-simplify-expr) '-)
1160                                   (math-neg ratio) ratio))
1161                  units)))))
1162
1163 (math-defsimplify *
1164   (math-simplify-units-prod))
1165
1166 (defun math-simplify-units-prod ()
1167   (and math-simplifying-units
1168        calc-autorange-units
1169        (Math-realp (nth 1 math-simplify-expr))
1170        (let* ((num (math-float (nth 1 math-simplify-expr)))
1171               (xpon (calcFunc-xpon num))
1172               (unitp (cdr (cdr math-simplify-expr)))
1173               (unit (car unitp))
1174               (pow (if (eq (car math-simplify-expr) '*) 1 -1))
1175               u)
1176          (and (eq (car-safe unit) '*)
1177               (setq unitp (cdr unit)
1178                     unit (car unitp)))
1179          (and (eq (car-safe unit) '^)
1180               (integerp (nth 2 unit))
1181               (setq pow (* pow (nth 2 unit))
1182                     unitp (cdr unit)
1183                     unit (car unitp)))
1184          (and (setq u (math-check-unit-name unit))
1185               (integerp xpon)
1186               (or (< xpon 0)
1187                   (>= xpon (if (eq (car u) 'm) 1 3)))
1188               (let* ((uxpon 0)
1189                      (pref (if (< pow 0)
1190                                (reverse math-unit-prefixes)
1191                              math-unit-prefixes))
1192                      (p pref)
1193                      pxpon pname)
1194                 (or (eq (car u) (nth 1 unit))
1195                     (setq uxpon (* pow
1196                                    (nth 2 (nth 1 (assq
1197                                                   (aref (symbol-name
1198                                                          (nth 1 unit)) 0)
1199                                                   math-unit-prefixes))))))
1200                 (setq xpon (+ xpon uxpon))
1201                 (while (and p
1202                             (or (memq (car (car p)) '(?d ?D ?h ?H))
1203                                 (and (eq (car (car p)) ?c)
1204                                      (not (eq (car u) 'm)))
1205                                 (< xpon (setq pxpon (* (nth 2 (nth 1 (car p)))
1206                                                        pow)))
1207                                 (progn
1208                                   (setq pname (math-build-var-name
1209                                                (if (eq (car (car p)) 0)
1210                                                    (car u)
1211                                                  (concat (char-to-string
1212                                                           (car (car p)))
1213                                                          (symbol-name
1214                                                           (car u))))))
1215                                   (and (/= (car (car p)) 0)
1216                                        (assq (nth 1 pname)
1217                                              math-units-table)))))
1218                   (setq p (cdr p)))
1219                 (and p
1220                      (/= pxpon uxpon)
1221                      (or (not (eq p pref))
1222                          (< xpon (+ pxpon (* (math-abs pow) 3))))
1223                      (progn
1224                        (setcar (cdr math-simplify-expr)
1225                                (let ((calc-prefer-frac nil))
1226                                  (calcFunc-scf (nth 1 math-simplify-expr)
1227                                                (- uxpon pxpon))))
1228                        (setcar unitp pname)
1229                        math-simplify-expr)))))))
1230
1231 (defvar math-try-cancel-units)
1232
1233 (math-defsimplify /
1234   (and math-simplifying-units
1235        (let ((np (cdr math-simplify-expr))
1236              (math-try-cancel-units 0)
1237              n nn)
1238          (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
1239                      (cdr (nth 2 math-simplify-expr))
1240                    (nthcdr 2 math-simplify-expr)))
1241          (if (math-realp (car n))
1242              (progn
1243                (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
1244                                             (let ((calc-prefer-frac nil))
1245                                               (math-div 1 (car n)))))
1246                (setcar n 1)))
1247          (while (eq (car-safe (setq n (car np))) '*)
1248            (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr)))
1249            (setq np (cdr (cdr n))))
1250          (math-simplify-units-divisor np (cdr (cdr math-simplify-expr)))
1251          (if (eq math-try-cancel-units 0)
1252              (let* ((math-simplifying-units nil)
1253                     (base (math-simplify
1254                            (math-to-standard-units math-simplify-expr nil))))
1255                (if (Math-numberp base)
1256                    (setq math-simplify-expr base))))
1257          (if (eq (car-safe math-simplify-expr) '/)
1258              (math-simplify-units-prod))
1259          math-simplify-expr)))
1260
1261 (defun math-simplify-units-divisor (np dp)
1262   (let ((n (car np))
1263         d dd temp)
1264     (while (eq (car-safe (setq d (car dp))) '*)
1265       (when (setq temp (math-simplify-units-quotient n (nth 1 d)))
1266         (setcar np (setq n temp))
1267         (setcar (cdr d) 1))
1268       (setq dp (cdr (cdr d))))
1269     (when (setq temp (math-simplify-units-quotient n d))
1270       (setcar np (setq n temp))
1271       (setcar dp 1))))
1272
1273 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1274 (defun math-simplify-units-quotient (n d)
1275   (let ((pow1 1)
1276         (pow2 1))
1277     (when (and (eq (car-safe n) '^)
1278                (integerp (nth 2 n)))
1279       (setq pow1 (nth 2 n) n (nth 1 n)))
1280     (when (and (eq (car-safe d) '^)
1281                (integerp (nth 2 d)))
1282       (setq pow2 (nth 2 d) d (nth 1 d)))
1283     (let ((un (math-check-unit-name n))
1284           (ud (math-check-unit-name d)))
1285       (and un ud
1286            (if (and (equal (nth 4 un) (nth 4 ud))
1287                     (eq pow1 pow2))
1288                (if (eq pow1 1)
1289                    (math-to-standard-units (list '/ n d) nil)
1290                  (list '^ (math-to-standard-units (list '/ n d) nil) pow1))
1291              (let (ud1)
1292                (setq un (nth 4 un)
1293                      ud (nth 4 ud))
1294                (while un
1295                  (setq ud1 ud)
1296                  (while ud1
1297                    (and (eq (car (car un)) (car (car ud1)))
1298                         (setq math-try-cancel-units
1299                               (+ math-try-cancel-units
1300                                  (- (* (cdr (car un)) pow1)
1301                                     (* (cdr (car ud)) pow2)))))
1302                    (setq ud1 (cdr ud1)))
1303                  (setq un (cdr un)))
1304                nil))))))
1305
1306 (math-defsimplify ^
1307   (and math-simplifying-units
1308        (math-realp (nth 2 math-simplify-expr))
1309        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1310            (list (car (nth 1 math-simplify-expr))
1311                  (list '^ (nth 1 (nth 1 math-simplify-expr))
1312                        (nth 2 math-simplify-expr))
1313                  (list '^ (nth 2 (nth 1 math-simplify-expr))
1314                        (nth 2 math-simplify-expr)))
1315          (math-simplify-units-pow (nth 1 math-simplify-expr)
1316                                   (nth 2 math-simplify-expr)))))
1317
1318 (math-defsimplify calcFunc-sqrt
1319   (and math-simplifying-units
1320        (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1321            (list (car (nth 1 math-simplify-expr))
1322                  (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr)))
1323                  (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))
1324          (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2)))))
1325
1326 (math-defsimplify (calcFunc-floor
1327                    calcFunc-ceil
1328                    calcFunc-round
1329                    calcFunc-rounde
1330                    calcFunc-roundu
1331                    calcFunc-trunc
1332                    calcFunc-float
1333                    calcFunc-frac
1334                    calcFunc-abs
1335                    calcFunc-clean)
1336   (and math-simplifying-units
1337        (= (length math-simplify-expr) 2)
1338        (if (math-only-units-in-expr-p (nth 1 math-simplify-expr))
1339            (nth 1 math-simplify-expr)
1340          (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
1341                   (or (math-only-units-in-expr-p
1342                        (nth 1 (nth 1 math-simplify-expr)))
1343                       (math-only-units-in-expr-p
1344                        (nth 2 (nth 1 math-simplify-expr)))))
1345              (list (car (nth 1 math-simplify-expr))
1346                    (cons (car math-simplify-expr)
1347                          (cons (nth 1 (nth 1 math-simplify-expr))
1348                                (cdr (cdr math-simplify-expr))))
1349                    (cons (car math-simplify-expr)
1350                          (cons (nth 2 (nth 1 math-simplify-expr))
1351                                (cdr (cdr math-simplify-expr)))))))))
1352
1353 (defun math-simplify-units-pow (a pow)
1354   (if (and (eq (car-safe a) '^)
1355            (math-check-unit-name (nth 1 a))
1356            (math-realp (nth 2 a)))
1357       (list '^ (nth 1 a) (math-mul pow (nth 2 a)))
1358     (let* ((u (math-check-unit-name a))
1359            (pf (math-to-simple-fraction pow))
1360            (d (and (eq (car-safe pf) 'frac) (nth 2 pf))))
1361       (and u d
1362            (math-units-are-multiple u d)
1363            (list '^ (math-to-standard-units a nil) pow)))))
1364
1365
1366 (defun math-units-are-multiple (u n)
1367   (setq u (nth 4 u))
1368   (while (and u (= (% (cdr (car u)) n) 0))
1369     (setq u (cdr u)))
1370   (null u))
1371
1372 (math-defsimplify calcFunc-sin
1373   (and math-simplifying-units
1374        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1375        (let ((rad (math-simplify-units
1376                    (math-evaluate-expr
1377                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1378              (calc-angle-mode 'rad))
1379          (and (eq (car-safe rad) '*)
1380               (math-realp (nth 1 rad))
1381               (eq (car-safe (nth 2 rad)) 'var)
1382               (eq (nth 1 (nth 2 rad)) 'rad)
1383               (list 'calcFunc-sin (nth 1 rad))))))
1384
1385 (math-defsimplify calcFunc-cos
1386   (and math-simplifying-units
1387        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1388        (let ((rad (math-simplify-units
1389                    (math-evaluate-expr
1390                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1391              (calc-angle-mode 'rad))
1392          (and (eq (car-safe rad) '*)
1393               (math-realp (nth 1 rad))
1394               (eq (car-safe (nth 2 rad)) 'var)
1395               (eq (nth 1 (nth 2 rad)) 'rad)
1396               (list 'calcFunc-cos (nth 1 rad))))))
1397
1398 (math-defsimplify calcFunc-tan
1399   (and math-simplifying-units
1400        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1401        (let ((rad (math-simplify-units
1402                    (math-evaluate-expr
1403                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1404              (calc-angle-mode 'rad))
1405          (and (eq (car-safe rad) '*)
1406               (math-realp (nth 1 rad))
1407               (eq (car-safe (nth 2 rad)) 'var)
1408               (eq (nth 1 (nth 2 rad)) 'rad)
1409               (list 'calcFunc-tan (nth 1 rad))))))
1410
1411 (math-defsimplify calcFunc-sec
1412   (and math-simplifying-units
1413        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1414        (let ((rad (math-simplify-units
1415                    (math-evaluate-expr
1416                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1417              (calc-angle-mode 'rad))
1418          (and (eq (car-safe rad) '*)
1419               (math-realp (nth 1 rad))
1420               (eq (car-safe (nth 2 rad)) 'var)
1421               (eq (nth 1 (nth 2 rad)) 'rad)
1422               (list 'calcFunc-sec (nth 1 rad))))))
1423
1424 (math-defsimplify calcFunc-csc
1425   (and math-simplifying-units
1426        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1427        (let ((rad (math-simplify-units
1428                    (math-evaluate-expr
1429                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1430              (calc-angle-mode 'rad))
1431          (and (eq (car-safe rad) '*)
1432               (math-realp (nth 1 rad))
1433               (eq (car-safe (nth 2 rad)) 'var)
1434               (eq (nth 1 (nth 2 rad)) 'rad)
1435               (list 'calcFunc-csc (nth 1 rad))))))
1436
1437 (math-defsimplify calcFunc-cot
1438   (and math-simplifying-units
1439        (math-units-in-expr-p (nth 1 math-simplify-expr) nil)
1440        (let ((rad (math-simplify-units
1441                    (math-evaluate-expr
1442                     (math-to-standard-units (nth 1 math-simplify-expr) nil))))
1443              (calc-angle-mode 'rad))
1444          (and (eq (car-safe rad) '*)
1445               (math-realp (nth 1 rad))
1446               (eq (car-safe (nth 2 rad)) 'var)
1447               (eq (nth 1 (nth 2 rad)) 'rad)
1448               (list 'calcFunc-cot (nth 1 rad))))))
1449
1450
1451 (defun math-remove-units (expr)
1452   (if (math-check-unit-name expr)
1453       1
1454     (if (Math-primp expr)
1455         expr
1456       (cons (car expr)
1457             (mapcar 'math-remove-units (cdr expr))))))
1458
1459 (defun math-extract-units (expr)
1460   (if (memq (car-safe expr) '(* /))
1461       (cons (car expr)
1462             (mapcar 'math-extract-units (cdr expr)))
1463     (if (math-check-unit-name expr) expr 1)))
1464
1465 (defun math-build-units-table-buffer (enter-buffer)
1466   (if (not (and math-units-table math-units-table-buffer-valid
1467                 (get-buffer "*Units Table*")))
1468       (let ((buf (get-buffer-create "*Units Table*"))
1469             (uptr (math-build-units-table))
1470             (calc-language (if (eq calc-language 'big) nil calc-language))
1471             (calc-float-format '(float 0))
1472             (calc-group-digits nil)
1473             (calc-number-radix 10)
1474             (calc-twos-complement-mode nil)
1475             (calc-point-char ".")
1476             (std nil)
1477             u name shadowed)
1478         (save-excursion
1479           (message "Formatting units table...")
1480           (set-buffer buf)
1481           (let ((inhibit-read-only t))
1482             (erase-buffer)
1483             (insert "Calculator Units Table:\n\n")
1484             (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n")
1485             (insert "Unit    Type  Definition                  Description\n\n")
1486             (while uptr
1487               (setq u (car uptr)
1488                     name (nth 2 u))
1489               (when (eq (car u) 'm)
1490                 (setq std t))
1491               (setq shadowed (and std (assq (car u) math-additional-units)))
1492               (when (and name
1493                          (> (length name) 1)
1494                          (eq (aref name 0) ?\*))
1495                 (unless (eq uptr math-units-table)
1496                   (insert "\n"))
1497                 (setq name (substring name 1)))
1498               (insert " ")
1499               (and shadowed (insert "("))
1500               (insert (symbol-name (car u)))
1501               (and shadowed (insert ")"))
1502               (if (nth 3 u)
1503                   (progn
1504                     (indent-to 10)
1505                     (insert (symbol-name (nth 3 u))))
1506                 (or std
1507                     (progn
1508                       (indent-to 10)
1509                       (insert "U"))))
1510               (indent-to 14)
1511               (and shadowed (insert "("))
1512               (if (nth 5 u)
1513                   (insert (nth 5 u))
1514                 (if (nth 1 u)
1515                     (insert (math-format-value (nth 1 u) 80))
1516                   (insert (symbol-name (car u)))))
1517               (and shadowed (insert ")"))
1518               (indent-to 41)
1519               (insert " ")
1520               (when name
1521                 (insert name))
1522               (if shadowed
1523                   (insert " (redefined above)")
1524                 (unless (nth 1 u)
1525                   (insert " (base unit)")))
1526               (insert "\n")
1527               (setq uptr (cdr uptr)))
1528             (insert "\n\nUnit Prefix Table:\n\n")
1529             (setq uptr math-unit-prefixes)
1530             (while uptr
1531               (setq u (car uptr))
1532               (insert " " (char-to-string (car u)))
1533               (if (equal (nth 1 u) (nth 1 (nth 1 uptr)))
1534                   (insert " " (char-to-string (car (car (setq uptr (cdr uptr)))))
1535                           "   ")
1536                 (insert "     "))
1537               (insert "10^" (int-to-string (nth 2 (nth 1 u))))
1538               (indent-to 15)
1539               (insert "   " (nth 2 u) "\n")
1540               (while (eq (car (car (setq uptr (cdr uptr)))) 0)))
1541             (insert "\n\n")
1542             (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
1543                      "names will not use the `tex' prefix; the unit name for a\n"
1544                      "TeX point will be `pt' instead of `texpt', for example.\n"
1545                      "To avoid conflicts, the unit names for pint and parsec will\n"
1546                      "be `pint' and `parsec' instead of `pt' and `pc'."))
1547           (view-mode)
1548           (message "Formatting units table...done"))
1549         (setq math-units-table-buffer-valid t)
1550         (let ((oldbuf (current-buffer)))
1551           (set-buffer buf)
1552           (goto-char (point-min))
1553           (set-buffer oldbuf))
1554         (if enter-buffer
1555             (pop-to-buffer buf)
1556           (display-buffer buf)))
1557     (if enter-buffer
1558         (pop-to-buffer (get-buffer "*Units Table*"))
1559       (display-buffer (get-buffer "*Units Table*")))))
1560
1561 ;;; Logarithmic units functions
1562
1563 (defvar math-logunits '((var dB var-dB)
1564                         (var Np var-Np)))
1565
1566 (defun math-conditional-apply (fn &rest args)
1567   "Evaluate f(args) unless in symbolic mode.
1568 In symbolic mode, return the list (fn args)."
1569   (if calc-symbolic-mode
1570       (cons fn args)
1571     (apply fn args)))
1572
1573 (defun math-conditional-pow (a b)
1574   "Evaluate a^b unless in symbolic mode.
1575 In symbolic mode, return the list (^ a b)."
1576   (if calc-symbolic-mode
1577       (list '^ a b)
1578     (math-pow a b)))
1579
1580 (defun math-extract-logunits (expr)
1581   (if (memq (car-safe expr) '(* /))
1582       (cons (car expr)
1583             (mapcar 'math-extract-logunits (cdr expr)))
1584     (if (memq (car-safe expr) '(^))
1585         (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
1586       (if (member expr math-logunits) expr 1))))
1587
1588 (defun math-logunits-add (a b neg power)
1589   (let ((aunit (math-simplify (math-extract-logunits a))))
1590     (if (not (eq (car-safe aunit) 'var))
1591         (calc-record-why "*Improper logarithmic unit" aunit)
1592       (let* ((units (math-extract-units a))
1593             (acoeff (math-simplify (math-remove-units a)))
1594             (bcoeff (math-simplify (math-to-standard-units
1595                                     (list '/ b units) nil))))
1596         (if (math-units-in-expr-p bcoeff nil)
1597             (calc-record-why "*Inconsistent units" nil)
1598           (if (and neg
1599                    (or (math-lessp acoeff bcoeff)
1600                        (math-equal acoeff bcoeff)))
1601               (calc-record-why "*Improper coefficients" nil)
1602             (math-mul
1603              (if (equal aunit '(var dB var-dB))
1604                  (let ((coef (if power 10 20)))
1605                    (math-mul coef
1606                              (math-conditional-apply 'calcFunc-log10
1607                               (if neg
1608                                   (math-sub
1609                                    (math-conditional-pow 10 (math-div acoeff coef))
1610                                    (math-conditional-pow 10 (math-div bcoeff coef)))
1611                                 (math-add
1612                                  (math-conditional-pow 10 (math-div acoeff coef))
1613                                  (math-conditional-pow 10 (math-div bcoeff coef)))))))
1614                (let ((coef (if power 2 1)))
1615                  (math-div
1616                   (math-conditional-apply 'calcFunc-ln
1617                    (if neg
1618                        (math-sub
1619                         (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1620                         (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
1621                      (math-add
1622                       (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
1623                       (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
1624                   coef)))
1625              units)))))))
1626
1627 (defun calcFunc-lufadd (a b)
1628   (math-logunits-add a b nil nil))
1629
1630 (defun calcFunc-lupadd (a b)
1631   (math-logunits-add a b nil t))
1632
1633 (defun calcFunc-lufsub (a b)
1634   (math-logunits-add a b t nil))
1635
1636 (defun calcFunc-lupsub (a b)
1637   (math-logunits-add a b t t))
1638
1639 (defun calc-lu-plus (arg)
1640   (interactive "P")
1641   (calc-slow-wrapper
1642    (if (calc-is-inverse)
1643        (if (calc-is-hyperbolic)
1644            (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1645          (calc-binary-op "lu-" 'calcFunc-lupsub arg))
1646      (if (calc-is-hyperbolic)
1647          (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1648        (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
1649
1650 (defun calc-lu-minus (arg)
1651   (interactive "P")
1652   (calc-slow-wrapper
1653    (if (calc-is-inverse)
1654        (if (calc-is-hyperbolic)
1655            (calc-binary-op "lu+" 'calcFunc-lufadd arg)
1656          (calc-binary-op "lu+" 'calcFunc-lupadd arg))
1657      (if (calc-is-hyperbolic)
1658          (calc-binary-op "lu-" 'calcFunc-lufsub arg)
1659        (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
1660
1661 (defun math-logunits-mul (a b power)
1662   (let (logunit coef units number)
1663     (cond
1664      ((and
1665        (setq logunit (math-simplify (math-extract-logunits a)))
1666        (eq (car-safe logunit) 'var)
1667        (eq (math-simplify (math-extract-units b)) 1))
1668       (setq coef (math-simplify (math-remove-units a))
1669             units (math-extract-units a)
1670             number b))
1671      ((and
1672        (setq logunit (math-simplify (math-extract-logunits b)))
1673        (eq (car-safe logunit) 'var)
1674        (eq (math-simplify (math-extract-units a)) 1))
1675       (setq coef (math-simplify (math-remove-units b))
1676             units (math-extract-units b)
1677             number a))
1678      (t (setq logunit nil)))
1679     (if logunit
1680         (cond
1681          ((equal logunit '(var dB var-dB))
1682           (math-simplify
1683            (math-mul
1684             (math-add
1685              coef
1686              (math-mul (if power 10 20)
1687                        (math-conditional-apply 'calcFunc-log10 number)))
1688             units)))
1689          (t
1690           (math-simplify
1691            (math-mul
1692             (math-add
1693              coef
1694              (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
1695             units))))
1696       (calc-record-why "*Improper units" nil))))
1697
1698 (defun math-logunits-divide (a b power)
1699   (let ((logunit (math-simplify (math-extract-logunits a))))
1700     (if (not (eq (car-safe logunit) 'var))
1701         (calc-record-why "*Improper logarithmic unit" logunit)
1702       (if (math-units-in-expr-p b nil)
1703           (calc-record-why "*Improper units quantity" b)
1704         (let* ((units (math-extract-units a))
1705                (coef (math-simplify (math-remove-units a))))
1706           (cond
1707            ((equal logunit '(var dB var-dB))
1708             (math-simplify
1709              (math-mul
1710               (math-sub
1711                coef
1712                (math-mul (if power 10 20)
1713                          (math-conditional-apply 'calcFunc-log10 b)))
1714               units)))
1715          (t
1716           (math-simplify
1717            (math-mul
1718             (math-sub
1719              coef
1720              (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
1721             units)))))))))
1722
1723 (defun calcFunc-lufmul (a b)
1724   (math-logunits-mul a b nil))
1725
1726 (defun calcFunc-lupmul (a b)
1727   (math-logunits-mul a b t))
1728
1729 (defun calc-lu-times (arg)
1730   (interactive "P")
1731   (calc-slow-wrapper
1732    (if (calc-is-inverse)
1733        (if (calc-is-hyperbolic)
1734            (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1735          (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
1736      (if (calc-is-hyperbolic)
1737          (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1738        (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
1739
1740 (defun calcFunc-lufdiv (a b)
1741   (math-logunits-divide a b nil))
1742
1743 (defun calcFunc-lupdiv (a b)
1744   (math-logunits-divide a b t))
1745
1746 (defun calc-lu-divide (arg)
1747   (interactive "P")
1748   (calc-slow-wrapper
1749    (if (calc-is-inverse)
1750        (if (calc-is-hyperbolic)
1751            (calc-binary-op "lu*" 'calcFunc-lufmul arg)
1752          (calc-binary-op "lu*" 'calcFunc-lupmul arg))
1753      (if (calc-is-hyperbolic)
1754          (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
1755        (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
1756
1757 (defun math-logunits-quant (val ref power)
1758   (let* ((units (math-simplify (math-extract-units val)))
1759          (lunit (math-simplify (math-extract-logunits units))))
1760     (if (not (eq (car-safe lunit) 'var))
1761         (calc-record-why "*Improper logarithmic unit" lunit)
1762       (let ((runits (math-simplify (math-div units lunit)))
1763             (coeff (math-simplify (math-div val units))))
1764         (math-mul
1765          (if (equal lunit '(var dB var-dB))
1766              (math-mul
1767               ref
1768               (math-conditional-pow
1769                10
1770                (math-div
1771                 coeff
1772                 (if power 10 20))))
1773            (math-mul
1774             ref
1775             (math-conditional-apply 'calcFunc-exp
1776              (if power
1777                  (math-mul 2 coeff)
1778                coeff))))
1779          runits)))))
1780
1781 (defvar calc-lu-field-reference)
1782 (defvar calc-lu-power-reference)
1783
1784 (defun calcFunc-lufquant (val &optional ref)
1785   (unless ref
1786     (setq ref (math-read-expr calc-lu-field-reference)))
1787   (math-logunits-quant val ref nil))
1788
1789 (defun calcFunc-lupquant (val &optional ref)
1790   (unless ref
1791     (setq ref (math-read-expr calc-lu-power-reference)))
1792   (math-logunits-quant val ref t))
1793
1794 (defun calc-lu-quant (arg)
1795   (interactive "P")
1796   (calc-slow-wrapper
1797    (if (calc-is-hyperbolic)
1798        (if (calc-is-option)
1799            (calc-binary-op "lupq" 'calcFunc-lufquant arg)
1800          (calc-unary-op "lupq" 'calcFunc-lufquant arg))
1801      (if (calc-is-option)
1802          (calc-binary-op "lufq" 'calcFunc-lupquant arg)
1803        (calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
1804
1805 (defun math-logunits-level (val ref db power)
1806   "Compute the value of VAL in decibels or nepers."
1807       (let* ((ratio (math-simplify-units (math-div val ref)))
1808              (ratiou (math-simplify-units (math-remove-units ratio)))
1809              (units (math-simplify (math-extract-units ratio))))
1810         (math-mul
1811          (if db
1812              (math-mul
1813               (math-mul (if power 10 20)
1814                         (math-conditional-apply 'calcFunc-log10 ratiou))
1815               '(var dB var-dB))
1816            (math-mul
1817             (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
1818             '(var Np var-Np)))
1819          units)))
1820
1821 (defun calcFunc-dbfield (val &optional ref)
1822   (unless ref
1823     (setq ref (math-read-expr calc-lu-field-reference)))
1824   (math-logunits-level val ref t nil))
1825
1826 (defun calcFunc-dbpower (val &optional ref)
1827   (unless ref
1828     (setq ref (math-read-expr calc-lu-power-reference)))
1829   (math-logunits-level val ref t t))
1830
1831 (defun calcFunc-npfield (val &optional ref)
1832   (unless ref
1833     (setq ref (math-read-expr calc-lu-field-reference)))
1834   (math-logunits-level val ref nil nil))
1835
1836 (defun calcFunc-nppower (val &optional ref)
1837   (unless ref
1838     (setq ref (math-read-expr calc-lu-power-reference)))
1839   (math-logunits-level val ref nil t))
1840
1841 (defun calc-db (arg)
1842   (interactive "P")
1843   (calc-slow-wrapper
1844    (if (calc-is-hyperbolic)
1845        (if (calc-is-option)
1846            (calc-binary-op "ludb" 'calcFunc-dbfield arg)
1847          (calc-unary-op "ludb" 'calcFunc-dbfield arg))
1848      (if (calc-is-option)
1849          (calc-binary-op "ludb" 'calcFunc-dbpower arg)
1850        (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
1851
1852 (defun calc-np (arg)
1853   (interactive "P")
1854   (calc-slow-wrapper
1855    (if (calc-is-hyperbolic)
1856        (if (calc-is-option)
1857            (calc-binary-op "lunp" 'calcFunc-npfield arg)
1858          (calc-unary-op "lunp" 'calcFunc-npfield arg))
1859      (if (calc-is-option)
1860          (calc-binary-op "lunp" 'calcFunc-nppower arg)
1861        (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
1862
1863 ;;; Musical notes
1864
1865
1866 (defvar calc-note-threshold)
1867
1868 (defun math-midi-round (num)
1869   "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
1870   (let* ((n (math-round num))
1871          (diff (math-abs
1872                 (math-sub num n))))
1873     (if (< (math-compare diff
1874                          (math-div (math-read-expr calc-note-threshold) 100)) 0)
1875         n
1876       num)))
1877
1878 (defconst math-notes
1879   '(((var C var-C) . 0)
1880     ((var Csharp var-Csharp) . 1)
1881 ;    ((var C♯ var-C♯) . 1)
1882     ((var Dflat var-Dflat) . 1)
1883 ;    ((var D♭ var-D♭) . 1)
1884     ((var D var-D) . 2)
1885     ((var Dsharp var-Dsharp) . 3)
1886 ;    ((var D♯ var-D♯) . 3)
1887     ((var E var-E) . 4)
1888     ((var F var-F) . 5)
1889     ((var Fsharp var-Fsharp) . 6)
1890 ;    ((var F♯ var-F♯) . 6)
1891     ((var Gflat var-Gflat) . 6)
1892 ;    ((var G♭ var-G♭) . 6)
1893     ((var G var-G) . 7)
1894     ((var Gsharp var-Gsharp) . 8)
1895 ;    ((var G♯ var-G♯) . 8)
1896     ((var A var-A) . 9)
1897     ((var Asharp var-Asharp) . 10)
1898 ;    ((var A♯ var-A♯) . 10)
1899     ((var Bflat var-Bflat) . 10)
1900 ;    ((var B♭ var-B♭) . 10)
1901     ((var B var-B) . 11))
1902   "An alist of notes with their number of semitones above C.")
1903
1904 (defun math-freqp (freq)
1905   "Non-nil if FREQ is a positive number times the unit Hz.
1906 If non-nil, return the coefficient of Hz."
1907   (let ((freqcoef (math-simplify-units
1908                    (math-div freq '(var Hz var-Hz)))))
1909     (if (Math-posp freqcoef) freqcoef)))
1910
1911 (defun math-midip (num)
1912   "Non-nil if NUM is a possible MIDI note number.
1913 If non-nil, return NUM."
1914   (if (Math-numberp num) num))
1915
1916 (defun math-spnp (spn)
1917   "Non-nil if NUM is a scientific pitch note (note + cents).
1918 If non-nil, return a list consisting of the note and the cents coefficient."
1919   (let (note cents rnote rcents)
1920     (if (eq (car-safe spn) '+)
1921         (setq note (nth 1 spn)
1922               cents (nth 2 spn))
1923       (setq note spn
1924             cents nil))
1925     (cond
1926      ((and  ;; NOTE is a note, CENTS is nil or cents.
1927        (eq (car-safe note) 'calcFunc-subscr)
1928        (assoc (nth 1 note) math-notes)
1929        (integerp (nth 2 note))
1930        (setq rnote note)
1931        (or
1932         (not cents)
1933         (Math-numberp (setq rcents
1934                             (math-simplify
1935                              (math-div cents '(var cents var-cents)))))))
1936       (list rnote rcents))
1937      ((and  ;; CENTS is a note, NOTE is cents.
1938        (eq (car-safe cents) 'calcFunc-subscr)
1939        (assoc (nth 1 cents) math-notes)
1940        (integerp (nth 2 cents))
1941        (setq rnote cents)
1942        (or
1943         (not note)
1944         (Math-numberp (setq rcents
1945                             (math-simplify
1946                              (math-div note '(var cents var-cents)))))))
1947       (list rnote rcents)))))
1948
1949 (defun math-freq-to-midi (freq)
1950   "Return the midi note number corresponding to FREQ Hz."
1951   (let ((midi (math-add
1952                69
1953                (math-mul
1954                 12
1955                 (calcFunc-log
1956                  (math-div freq 440)
1957                  2)))))
1958     (math-midi-round midi)))
1959
1960 (defun math-spn-to-midi (spn)
1961   "Return the MIDI number corresponding to SPN."
1962   (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
1963          (octave (math-add (nth 2 (car spn)) 1))
1964          (cents (nth 1 spn))
1965          (midi  (math-add
1966                  (math-mul 12 octave)
1967                  note)))
1968     (if cents
1969         (math-add midi (math-div cents 100))
1970       midi)))
1971
1972 (defun math-midi-to-spn (midi)
1973   "Return the scientific pitch notation corresponding to midi number MIDI."
1974   (let (midin cents)
1975     (if (math-integerp midi)
1976         (setq midin midi
1977               cents nil)
1978       (setq midin (math-floor midi)
1979             cents (math-mul 100 (math-sub midi midin))))
1980     (let* ((nr ;; This should be (math-idivmod midin 12), but with
1981                ;; better behavior for negative midin.
1982             (if (Math-negp midin)
1983                 (let ((dm (math-idivmod (math-neg midin) 12)))
1984                   (if (= (cdr dm) 0)
1985                       (cons (math-neg (car dm)) 0)
1986                     (cons
1987                      (math-sub (math-neg (car dm)) 1)
1988                      (math-sub 12 (cdr dm)))))
1989               (math-idivmod midin 12)))
1990            (n (math-sub (car nr) 1))
1991            (note (car (rassoc (cdr nr) math-notes))))
1992       (if cents
1993           (list '+ (list 'calcFunc-subscr note n)
1994                    (list '* cents '(var cents var-cents)))
1995         (list 'calcFunc-subscr note n)))))
1996
1997 (defun math-freq-to-spn (freq)
1998   "Return the scientific pitch notation corresponding to FREQ Hz."
1999   (math-with-extra-prec 3
2000     (math-midi-to-spn (math-freq-to-midi freq))))
2001
2002 (defun math-midi-to-freq (midi)
2003   "Return the frequency of the note with midi number MIDI."
2004   (list '*
2005         (math-mul
2006          440
2007          (math-pow
2008           2
2009           (math-div
2010            (math-sub
2011             midi
2012             69)
2013            12)))
2014         '(var Hz var-Hz)))
2015
2016 (defun math-spn-to-freq (spn)
2017   "Return the frequency of the note with scientific pitch notation SPN."
2018   (math-midi-to-freq (math-spn-to-midi spn)))
2019
2020 (defun calcFunc-spn (expr)
2021   "Return EXPR written as scientific pitch notation + cents."
2022   ;; Get the coefficient of Hz
2023   (let (note)
2024     (cond
2025      ((setq note (math-freqp expr))
2026       (math-freq-to-spn note))
2027      ((setq note (math-midip expr))
2028       (math-midi-to-spn note))
2029      ((math-spnp expr)
2030       expr)
2031      (t
2032       (math-reject-arg expr "*Improper expression")))))
2033
2034 (defun calcFunc-midi (expr)
2035   "Return EXPR written as a MIDI number."
2036   (let (note)
2037     (cond
2038      ((setq note (math-freqp expr))
2039       (math-freq-to-midi note))
2040      ((setq note (math-spnp expr))
2041       (math-spn-to-midi note))
2042      ((math-midip expr)
2043       expr)
2044      (t
2045       (math-reject-arg expr "*Improper expression")))))
2046
2047 (defun calcFunc-freq (expr)
2048   "Return the frequency corresponding to EXPR."
2049   (let (note)
2050     (cond
2051      ((setq note (math-midip expr))
2052       (math-midi-to-freq note))
2053      ((setq note (math-spnp expr))
2054       (math-spn-to-freq note))
2055      ((math-freqp expr)
2056       expr)
2057      (t
2058       (math-reject-arg expr "*Improper expression")))))
2059
2060 (defun calc-freq (arg)
2061   "Return the frequency corresponding to the expression on the stack."
2062   (interactive "P")
2063   (calc-slow-wrapper
2064    (calc-unary-op "freq" 'calcFunc-freq arg)))
2065
2066 (defun calc-midi (arg)
2067   "Return the MIDI number corresponding to the expression on the stack."
2068   (interactive "P")
2069   (calc-slow-wrapper
2070    (calc-unary-op "midi" 'calcFunc-midi arg)))
2071
2072 (defun calc-spn (arg)
2073   "Return the scientific pitch notation corresponding to the expression on the stack."
2074   (interactive "P")
2075   (calc-slow-wrapper
2076    (calc-unary-op "spn" 'calcFunc-spn arg)))
2077
2078
2079 (provide 'calc-units)
2080
2081 ;; Local variables:
2082 ;; coding: utf-8
2083 ;; End:
2084
2085 ;;; calc-units.el ends here