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