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8cd8ee52 CW |
1 | ;;; calc-units.el --- unit conversion functions for Calc |
2 | ||
ab422c4d | 3 | ;; Copyright (C) 1990-1993, 2001-2013 Free Software Foundation, Inc. |
8cd8ee52 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
e8fff8ed | 6 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 EZ |
7 | |
8 | ;; This file is part of GNU Emacs. | |
9 | ||
662c9c64 | 10 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
7c671b23 | 11 | ;; it under the terms of the GNU General Public License as published by |
662c9c64 GM |
12 | ;; the Free Software Foundation, either version 3 of the License, or |
13 | ;; (at your option) any later version. | |
7c671b23 | 14 | |
136211a9 | 15 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
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 | |
662c9c64 | 21 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
136211a9 | 22 | |
8cd8ee52 | 23 | ;;; Commentary: |
136211a9 | 24 | |
8cd8ee52 | 25 | ;;; Code: |
136211a9 EZ |
26 | |
27 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 28 | |
7d02e8cd | 29 | (require 'calc-ext) |
136211a9 | 30 | (require 'calc-macs) |
c7388379 JB |
31 | (eval-when-compile |
32 | (require 'calc-alg)) | |
136211a9 | 33 | |
8cd8ee52 CW |
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) | |
ae6bc504 | 38 | ;;; Updated April 2002 by Jochen Küpper |
be59410c | 39 | |
a21f3259 JB |
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 | |
ae6bc504 | 44 | ;;; Measures, by François Cardarelli) |
a21f3259 | 45 | ;;; All conversions are exact unless otherwise noted. |
8cd8ee52 CW |
46 | |
47 | (defvar math-standard-units | |
48 | '( ;; Length | |
cf39c182 | 49 | ( m nil "*Meter" ) |
60afd99b | 50 | ( in "254*10^(-2) cm" "Inch" nil |
19bdc4d8 JB |
51 | "2.54 cm") |
52 | ( ft "12 in" "Foot") | |
cf39c182 JB |
53 | ( yd "3 ft" "Yard" ) |
54 | ( mi "5280 ft" "Mile" ) | |
60afd99b | 55 | ( au "149597870691. m" "Astronomical Unit" nil |
19bdc4d8 | 56 | "149597870691 m (*)") |
a21f3259 JB |
57 | ;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html) |
58 | ( lyr "c yr" "Light Year" ) | |
1265829e | 59 | ( pc "3.0856775854*10^16 m" "Parsec (**)" nil |
ac318df0 | 60 | "3.0856775854 10^16 m (*)") ;; (approx) ESUWM |
cf39c182 JB |
61 | ( nmi "1852 m" "Nautical Mile" ) |
62 | ( fath "6 ft" "Fathom" ) | |
ac318df0 | 63 | ( fur "660 ft" "Furlong") |
cf39c182 | 64 | ( mu "1 um" "Micron" ) |
ac318df0 | 65 | ( mil "(1/1000) in" "Mil" ) |
1265829e | 66 | ( point "(1/72) in" "Point (PostScript convention)" ) |
a21f3259 | 67 | ( Ang "10^(-10) m" "Angstrom" ) |
cf39c182 JB |
68 | ( mfi "mi+ft+in" "Miles + feet + inches" ) |
69 | ;; TeX lengths | |
1265829e JB |
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) (**)" ) | |
a1506d29 | 76 | |
be59410c | 77 | ;; Area |
cf39c182 JB |
78 | ( hect "10000 m^2" "*Hectare" ) |
79 | ( a "100 m^2" "Are") | |
ac318df0 | 80 | ( acre "(1/640) mi^2" "Acre" ) |
a21f3259 | 81 | ( b "10^(-28) m^2" "Barn" ) |
a1506d29 | 82 | |
be59410c | 83 | ;; Volume |
a21f3259 | 84 | ( L "10^(-3) m^3" "*Liter" ) |
cf39c182 JB |
85 | ( l "L" "Liter" ) |
86 | ( gal "4 qt" "US Gallon" ) | |
87 | ( qt "2 pt" "Quart" ) | |
1265829e | 88 | ( pt "2 cup" "Pint (**)" ) |
cf39c182 JB |
89 | ( cup "8 ozfl" "Cup" ) |
90 | ( ozfl "2 tbsp" "Fluid Ounce" ) | |
91 | ( floz "2 tbsp" "Fluid Ounce" ) | |
92 | ( tbsp "3 tsp" "Tablespoon" ) | |
7026903c JB |
93 | ;; ESUWM defines a US gallon as 231 in^3. |
94 | ;; That gives the following exact value for tsp. | |
60afd99b | 95 | ( tsp "492892159375*10^(-11) ml" "Teaspoon" nil |
19bdc4d8 | 96 | "4.92892159375 ml") |
ac318df0 JB |
97 | ( vol "tsp+tbsp+ozfl+cup+pt+qt+gal" "Gallons + ... + teaspoons" nil |
98 | "tsp+tbsp+ozfl+cup+pt+qt+gal") | |
a21f3259 | 99 | ( galC "galUK" "Canadian Gallon" ) |
60afd99b | 100 | ( galUK "454609*10^(-5) L" "UK Gallon" nil |
19bdc4d8 | 101 | "4.54609 L") ;; NIST |
a1506d29 | 102 | |
be59410c | 103 | ;; Time |
cf39c182 JB |
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" ) | |
ac318df0 JB |
111 | ( yr "36525*10^(-2) day" "Year (Julian)" nil |
112 | "365.25 day") | |
cf39c182 | 113 | ( Hz "1/s" "Hertz" ) |
be59410c CW |
114 | |
115 | ;; Speed | |
cf39c182 JB |
116 | ( mph "mi/hr" "*Miles per hour" ) |
117 | ( kph "km/hr" "Kilometers per hour" ) | |
118 | ( knot "nmi/hr" "Knot" ) | |
a21f3259 | 119 | ( c "299792458 m/s" "Speed of light" ) ;;; CODATA |
a1506d29 | 120 | |
be59410c | 121 | ;; Acceleration |
60afd99b | 122 | ( ga "980665*10^(-5) m/s^2" "*\"g\" acceleration" nil |
19bdc4d8 | 123 | "9.80665 m / s^2") ;; CODATA |
be59410c CW |
124 | |
125 | ;; Mass | |
cf39c182 JB |
126 | ( g nil "*Gram" ) |
127 | ( lb "16 oz" "Pound (mass)" ) | |
60afd99b | 128 | ( oz "28349523125*10^(-9) g" "Ounce (mass)" nil |
19bdc4d8 | 129 | "28.349523125 g") ;; ESUWM |
cf39c182 JB |
130 | ( ton "2000 lb" "Ton" ) |
131 | ( tpo "ton+lb+oz" "Tons + pounds + ounces (mass)" ) | |
132 | ( t "1000 kg" "Metric ton" ) | |
60afd99b | 133 | ( tonUK "10160469088*10^(-7) kg" "UK ton" nil |
19bdc4d8 | 134 | "1016.0469088 kg") ;; ESUWM |
cf39c182 | 135 | ( lbt "12 ozt" "Troy pound" ) |
60afd99b | 136 | ( ozt "311034768*10^(-7) g" "Troy ounce" nil |
ac318df0 | 137 | "31.10347680 g") ;; ESUWM, 1/12 exact value for lbt |
60afd99b | 138 | ( ct "(2/10) g" "Carat" nil |
19bdc4d8 | 139 | "0.2 g") ;; ESUWM |
60afd99b | 140 | ( u "1.660538782*10^(-27) kg" "Unified atomic mass" nil |
ac318df0 | 141 | "1.660538782 10^-27 kg (*)");;(approx) CODATA |
be59410c CW |
142 | |
143 | ;; Force | |
cf39c182 | 144 | ( N "m kg/s^2" "*Newton" ) |
a21f3259 | 145 | ( dyn "10^(-5) N" "Dyne" ) |
cf39c182 | 146 | ( gf "ga g" "Gram (force)" ) |
a21f3259 | 147 | ( lbf "ga lb" "Pound (force)" ) |
cf39c182 | 148 | ( kip "1000 lbf" "Kilopound (force)" ) |
60afd99b | 149 | ( pdl "138254954376*10^(-12) N" "Poundal" nil |
19bdc4d8 | 150 | "0.138254954376 N") ;; ESUWM |
be59410c CW |
151 | |
152 | ;; Energy | |
cf39c182 | 153 | ( J "N m" "*Joule" ) |
a21f3259 | 154 | ( erg "10^(-7) J" "Erg" ) |
60afd99b | 155 | ( cal "41868*10^(-4) J" "International Table Calorie" nil |
ac318df0 | 156 | "4.1868 J") ;; NIST |
60afd99b | 157 | ( calth "4184*10^(-3) J" "Thermochemical Calorie" nil |
ac318df0 JB |
158 | "4.184 J") ;; NIST |
159 | ( Cal "1000 cal" "Large Calorie") | |
60afd99b | 160 | ( Btu "105505585262*10^(-8) J" "International Table Btu" nil |
19bdc4d8 | 161 | "1055.05585262 J") ;; ESUWM |
cf39c182 JB |
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") | |
02bf5ab9 | 170 | ( Wh "W hr" "Watt hour") |
cf39c182 | 171 | ( Ws "W s" "Watt second") |
be59410c CW |
172 | |
173 | ;; Power | |
cf39c182 | 174 | ( W "J/s" "*Watt" ) |
ac318df0 JB |
175 | ( hp "550 ft lbf/s" "Horsepower") ;;ESUWM |
176 | ( hpm "75 m kgf/s" "Metric Horsepower") ;;ESUWM | |
be59410c CW |
177 | |
178 | ;; Temperature | |
cf39c182 JB |
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 ) | |
be59410c CW |
186 | |
187 | ;; Pressure | |
cf39c182 | 188 | ( Pa "N/m^2" "*Pascal" ) |
a21f3259 JB |
189 | ( bar "10^5 Pa" "Bar" ) |
190 | ( atm "101325 Pa" "Standard atmosphere" ) ;; CODATA | |
ac318df0 | 191 | ( Torr "(1/760) atm" "Torr") |
cf39c182 | 192 | ( mHg "1000 Torr" "Meter of mercury" ) |
60afd99b | 193 | ( inHg "254*10^(-1) mmHg" "Inch of mercury" nil |
19bdc4d8 | 194 | "25.4 mmHg") |
60afd99b | 195 | ( inH2O "2.490889*10^2 Pa" "Inch of water" nil |
ac318df0 | 196 | "2.490889 10^2 Pa (*)") ;;(approx) NIST |
a21f3259 | 197 | ( psi "lbf/in^2" "Pounds per square inch" ) |
be59410c CW |
198 | |
199 | ;; Viscosity | |
a21f3259 JB |
200 | ( P "(1/10) Pa s" "*Poise" ) |
201 | ( St "10^(-4) m^2/s" "Stokes" ) | |
be59410c CW |
202 | |
203 | ;; Electromagnetism | |
cf39c182 JB |
204 | ( A nil "*Ampere" ) |
205 | ( C "A s" "Coulomb" ) | |
206 | ( Fdy "ech Nav" "Faraday" ) | |
a21f3259 | 207 | ( e "ech" "Elementary charge" ) |
60afd99b | 208 | ( ech "1.602176487*10^(-19) C" "Elementary charge" nil |
ac318df0 | 209 | "1.602176487 10^-19 C (*)") ;;(approx) CODATA |
cf39c182 JB |
210 | ( V "W/A" "Volt" ) |
211 | ( ohm "V/A" "Ohm" ) | |
ae6bc504 | 212 | ( Ω "ohm" "Ohm" ) |
cf39c182 JB |
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" ) | |
a21f3259 | 218 | ( Gs "10^(-4) T" "Gauss" ) |
cf39c182 | 219 | ( Wb "V s" "Weber" ) |
be59410c CW |
220 | |
221 | ;; Luminous intensity | |
cf39c182 | 222 | ( cd nil "*Candela" ) |
a21f3259 | 223 | ( sb "10000 cd/m^2" "Stilb" ) |
cf39c182 JB |
224 | ( lm "cd sr" "Lumen" ) |
225 | ( lx "lm/m^2" "Lux" ) | |
a21f3259 | 226 | ( ph "10000 lx" "Phot" ) |
ac318df0 | 227 | ( fc "lm/ft^2" "Footcandle") ;; ESUWM |
a21f3259 | 228 | ( lam "10000 lm/m^2" "Lambert" ) |
ac318df0 | 229 | ( flam "(1/pi) cd/ft^2" "Footlambert") ;; ESUWM |
be59410c CW |
230 | |
231 | ;; Radioactivity | |
cf39c182 | 232 | ( Bq "1/s" "*Becquerel" ) |
a21f3259 | 233 | ( Ci "37*10^9 Bq" "Curie" ) ;; ESUWM |
cf39c182 JB |
234 | ( Gy "J/kg" "Gray" ) |
235 | ( Sv "Gy" "Sievert" ) | |
a21f3259 JB |
236 | ( R "258*10^(-6) C/kg" "Roentgen" ) ;; NIST |
237 | ( rd "(1/100) Gy" "Rad" ) | |
cf39c182 | 238 | ( rem "rd" "Rem" ) |
be59410c CW |
239 | |
240 | ;; Amount of substance | |
cf39c182 | 241 | ( mol nil "*Mole" ) |
be59410c CW |
242 | |
243 | ;; Plane angle | |
cf39c182 JB |
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" ) | |
be59410c CW |
252 | |
253 | ;; Solid angle | |
cf39c182 | 254 | ( sr nil "*Steradian" ) |
be59410c | 255 | |
cf39c182 | 256 | ;; Other physical quantities |
a21f3259 | 257 | ;; The values are from CODATA, and are approximate. |
60afd99b | 258 | ( h "6.62606896*10^(-34) J s" "*Planck's constant" nil |
ac318df0 JB |
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 | |
ae6bc504 | 262 | ( μ0 "mu0" "Permeability of vacuum") ;; Exact |
4929aa69 | 263 | ( eps0 "1 / (mu0 c^2)" "Permittivity of vacuum" ) |
ae6bc504 | 264 | ( ε0 "eps0" "Permittivity of vacuum" ) |
60afd99b | 265 | ( G "6.67428*10^(-11) m^3/(kg s^2)" "Gravitational constant" nil |
9b3e5667 | 266 | "6.67428 10^-11 m^3/(kg s^2) (*)") |
60afd99b | 267 | ( Nav "6.02214179*10^(23) / mol" "Avogadro's constant" nil |
ac318df0 | 268 | "6.02214179 10^23 / mol (*)") |
60afd99b | 269 | ( me "9.10938215*10^(-31) kg" "Electron rest mass" nil |
ac318df0 | 270 | "9.10938215 10^-31 kg (*)") |
60afd99b | 271 | ( mp "1.672621637*10^(-27) kg" "Proton rest mass" nil |
ac318df0 | 272 | "1.672621637 10^-27 kg (*)") |
60afd99b | 273 | ( mn "1.674927211*10^(-27) kg" "Neutron rest mass" nil |
ac318df0 | 274 | "1.674927211 10^-27 kg (*)") |
60afd99b | 275 | ( mmu "1.88353130*10^(-28) kg" "Muon rest mass" nil |
ac318df0 | 276 | "1.88353130 10^-28 kg (*)") |
ae6bc504 JB |
277 | ( mμ "mmu" "Muon rest mass" nil |
278 | "1.88353130 10^-28 kg (*)") | |
60afd99b | 279 | ( Ryd "10973731.568527 /m" "Rydberg's constant" nil |
19bdc4d8 | 280 | "10973731.568527 /m (*)") |
60afd99b | 281 | ( k "1.3806504*10^(-23) J/K" "Boltzmann's constant" nil |
ac318df0 | 282 | "1.3806504 10^-23 J/K (*)") |
60afd99b | 283 | ( alpha "7.2973525376*10^(-3)" "Fine structure constant" nil |
ac318df0 | 284 | "7.2973525376 10^-3 (*)") |
ae6bc504 JB |
285 | ( α "alpha" "Fine structure constant" nil |
286 | "7.2973525376 10^-3 (*)") | |
60afd99b | 287 | ( muB "927.400915*10^(-26) J/T" "Bohr magneton" nil |
ac318df0 | 288 | "927.400915 10^-26 J/T (*)") |
60afd99b | 289 | ( muN "5.05078324*10^(-27) J/T" "Nuclear magneton" nil |
ac318df0 | 290 | "5.05078324 10^-27 J/T (*)") |
60afd99b | 291 | ( mue "-928.476377*10^(-26) J/T" "Electron magnetic moment" nil |
ac318df0 | 292 | "-928.476377 10^-26 J/T (*)") |
60afd99b | 293 | ( mup "1.410606662*10^(-26) J/T" "Proton magnetic moment" nil |
ac318df0 | 294 | "1.410606662 10^-26 J/T (*)") |
60afd99b | 295 | ( R0 "8.314472 J/(mol K)" "Molar gas constant" nil |
19bdc4d8 | 296 | "8.314472 J/(mol K) (*)") |
60afd99b | 297 | ( V0 "22.710981*10^(-3) m^3/mol" "Standard volume of ideal gas" nil |
603823f5 JB |
298 | "22.710981 10^-3 m^3/mol (*)") |
299 | ;; Logarithmic units | |
300 | ( Np nil "*Neper") | |
301 | ( dB "(ln(10)/20) Np" "decibel"))) | |
8cd8ee52 CW |
302 | |
303 | ||
304 | (defvar math-additional-units nil | |
fb7ada5f | 305 | "Additional units table for user-defined units. |
60afd99b | 306 | Must be formatted like `math-standard-units'. |
11220394 | 307 | If you change this, be sure to set `math-units-table' to nil to ensure |
8cd8ee52 CW |
308 | that the combined units table will be rebuilt.") |
309 | ||
310 | (defvar math-unit-prefixes | |
a21f3259 JB |
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" ) | |
be19ef0b | 328 | ( ?μ (^ 10 -6) "Micro" ) |
a21f3259 JB |
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" ))) | |
8cd8ee52 CW |
335 | |
336 | (defvar math-standard-units-systems | |
337 | '( ( base nil ) | |
a21f3259 JB |
338 | ( si ( ( g '(/ (var kg var-kg) 1000) ) ) ) |
339 | ( mks ( ( g '(/ (var kg var-kg) 1000) ) ) ) | |
340 | ( cgs ( ( m '(* (var cm var-cm) 100 ) ) ) ))) | |
8cd8ee52 CW |
341 | |
342 | (defvar math-units-table nil | |
60afd99b JB |
343 | "Internal units table. |
344 | Derived from `math-standard-units' and `math-additional-units'. | |
8cd8ee52 CW |
345 | Entries are (SYMBOL EXPR DOC-STRING TEMP-TYPE BASE-UNITS).") |
346 | ||
347 | (defvar math-units-table-buffer-valid nil) | |
136211a9 EZ |
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) | |
c9aef719 | 357 | nil)))))) |
136211a9 | 358 | |
cd3466e6 JB |
359 | (defvar calc-ensure-consistent-units) |
360 | ||
136211a9 EZ |
361 | (defun calc-quick-units () |
362 | (interactive) | |
363 | (calc-slow-wrapper | |
e93c003e | 364 | (let* ((num (- last-command-event ?0)) |
136211a9 EZ |
365 | (pos (if (= num 0) 10 num)) |
366 | (units (calc-var-value 'var-Units)) | |
367 | (expr (calc-top-n 1))) | |
8cd8ee52 | 368 | (unless (and (>= num 0) (<= num 9)) |
91af11b2 | 369 | (error "Bad unit number")) |
8cd8ee52 | 370 | (unless (math-vectorp units) |
91af11b2 | 371 | (error "No \"quick units\" are defined")) |
8cd8ee52 | 372 | (unless (< pos (length units)) |
91af11b2 | 373 | (error "Unit number %d not defined" pos)) |
136211a9 | 374 | (if (math-units-in-expr-p expr nil) |
d14b0029 JB |
375 | (progn |
376 | (if calc-ensure-consistent-units | |
6b38973b | 377 | (math-check-unit-consistency expr (nth pos units))) |
d14b0029 JB |
378 | (calc-enter-result 1 (format "cun%d" num) |
379 | (math-convert-units expr (nth pos units)))) | |
136211a9 EZ |
380 | (calc-enter-result 1 (format "*un%d" num) |
381 | (math-simplify-units | |
c9aef719 | 382 | (math-mul expr (nth pos units)))))))) |
136211a9 | 383 | |
5360ea16 JB |
384 | (defun math-get-standard-units (expr) |
385 | "Return the standard units in EXPR." | |
386 | (math-simplify-units | |
387 | (math-extract-units | |
388 | (math-to-standard-units expr nil)))) | |
389 | ||
390 | (defun math-get-units (expr) | |
391 | "Return the units in EXPR." | |
392 | (math-simplify-units | |
393 | (math-extract-units expr))) | |
394 | ||
395 | (defun math-make-unit-string (expr) | |
396 | "Return EXPR in string form. | |
397 | If EXPR is nil, return nil." | |
398 | (if expr | |
399 | (let ((cexpr (math-compose-expr expr 0))) | |
09040c8d | 400 | (replace-regexp-in-string |
a21f3259 JB |
401 | " / " "/" |
402 | (if (stringp cexpr) | |
403 | cexpr | |
404 | (math-composition-to-string cexpr)))))) | |
5360ea16 | 405 | |
09040c8d | 406 | (defvar math-default-units-table |
7c3fb76f | 407 | (make-hash-table :test 'equal) |
5360ea16 JB |
408 | "A table storing previously converted units.") |
409 | ||
410 | (defun math-get-default-units (expr) | |
411 | "Get default units to use when converting the units in EXPR." | |
412 | (let* ((units (math-get-units expr)) | |
413 | (standard-units (math-get-standard-units expr)) | |
09040c8d | 414 | (default-units (gethash |
5360ea16 JB |
415 | standard-units |
416 | math-default-units-table))) | |
417 | (if (equal units (car default-units)) | |
418 | (math-make-unit-string (cadr default-units)) | |
419 | (math-make-unit-string (car default-units))))) | |
420 | ||
0fd09128 JB |
421 | (defun math-put-default-units (expr &optional comp std) |
422 | "Put the units in EXPR in the default units table. | |
423 | If COMP or STD is non-nil, put that in the units table instead." | |
424 | (let* ((new-units (or comp std (math-get-units expr))) | |
425 | (standard-units (math-get-standard-units | |
426 | (cond | |
427 | (comp (math-simplify-units expr)) | |
428 | (std expr) | |
429 | (t new-units)))) | |
430 | (default-units (gethash standard-units math-default-units-table))) | |
431 | (unless (eq standard-units 1) | |
432 | (cond | |
433 | ((not default-units) | |
434 | (puthash standard-units (list new-units) math-default-units-table)) | |
435 | ((not (equal new-units (car default-units))) | |
436 | (puthash standard-units | |
437 | (list new-units (car default-units)) | |
438 | math-default-units-table)))))) | |
5360ea16 | 439 | |
136211a9 EZ |
440 | (defun calc-convert-units (&optional old-units new-units) |
441 | (interactive) | |
442 | (calc-slow-wrapper | |
443 | (let ((expr (calc-top-n 1)) | |
444 | (uoldname nil) | |
7c3fb76f | 445 | (unitscancel nil) |
27971241 | 446 | unew |
5360ea16 JB |
447 | units |
448 | defunits) | |
7c3fb76f JB |
449 | (if (or (not (math-units-in-expr-p expr t)) |
450 | (setq unitscancel (eq (math-get-standard-units expr) 1))) | |
8cd8ee52 CW |
451 | (let ((uold (or old-units |
452 | (progn | |
7c3fb76f JB |
453 | (setq uoldname |
454 | (if unitscancel | |
455 | (read-string | |
456 | "(The expression is unitless when simplified) Old Units: ") | |
457 | (read-string "Old units: "))) | |
8cd8ee52 CW |
458 | (if (equal uoldname "") |
459 | (progn | |
460 | (setq uoldname "1") | |
461 | 1) | |
462 | (if (string-match "\\` */" uoldname) | |
463 | (setq uoldname (concat "1" uoldname))) | |
464 | (math-read-expr uoldname)))))) | |
465 | (when (eq (car-safe uold) 'error) | |
466 | (error "Bad format in units expression: %s" (nth 1 uold))) | |
467 | (setq expr (math-mul expr uold)))) | |
0fd09128 | 468 | (setq defunits (math-get-default-units expr)) |
7c3fb76f JB |
469 | (unless new-units |
470 | (setq new-units | |
471 | (read-string (concat | |
472 | (if uoldname | |
473 | (concat "Old units: " | |
474 | uoldname | |
475 | ", new units") | |
476 | "New units") | |
477 | (if defunits | |
478 | (concat | |
479 | " (default " | |
480 | defunits | |
481 | "): ") | |
482 | ": ")))) | |
483 | (if (and | |
484 | (string= new-units "") | |
485 | defunits) | |
486 | (setq new-units defunits))) | |
487 | (when (string-match "\\` */" new-units) | |
488 | (setq new-units (concat "1" new-units))) | |
489 | (setq units (math-read-expr new-units)) | |
490 | (when (eq (car-safe units) 'error) | |
491 | (error "Bad format in units expression: %s" (nth 2 units))) | |
492 | (if calc-ensure-consistent-units | |
493 | (math-check-unit-consistency expr units)) | |
494 | (let ((unew (math-units-in-expr-p units t)) | |
495 | (std (and (eq (car-safe units) 'var) | |
496 | (assq (nth 1 units) math-standard-units-systems))) | |
497 | (comp (eq (car-safe units) '+))) | |
498 | (unless (or unew std) | |
499 | (error "No units specified")) | |
500 | (let ((res | |
501 | (if std | |
502 | (math-simplify-units (math-to-standard-units expr (nth 1 std))) | |
503 | (math-convert-units expr units (and uoldname (not (equal uoldname "1"))))))) | |
504 | (math-put-default-units res (if comp units)) | |
505 | (calc-enter-result 1 "cvun" res)))))) | |
136211a9 EZ |
506 | |
507 | (defun calc-autorange-units (arg) | |
508 | (interactive "P") | |
509 | (calc-wrapper | |
510 | (calc-change-mode 'calc-autorange-units arg nil t) | |
511 | (message (if calc-autorange-units | |
8cd8ee52 CW |
512 | "Adjusting target unit prefix automatically" |
513 | "Using target units exactly")))) | |
136211a9 EZ |
514 | |
515 | (defun calc-convert-temperature (&optional old-units new-units) | |
516 | (interactive) | |
517 | (calc-slow-wrapper | |
518 | (let ((expr (calc-top-n 1)) | |
519 | (uold nil) | |
520 | (uoldname nil) | |
5360ea16 JB |
521 | unew |
522 | defunits) | |
136211a9 EZ |
523 | (setq uold (or old-units |
524 | (let ((units (math-single-units-in-expr-p expr))) | |
525 | (if units | |
526 | (if (consp units) | |
527 | (list 'var (car units) | |
528 | (intern (concat "var-" | |
529 | (symbol-name | |
530 | (car units))))) | |
531 | (error "Not a pure temperature expression")) | |
532 | (math-read-expr | |
533 | (setq uoldname (read-string | |
534 | "Old temperature units: "))))))) | |
8cd8ee52 CW |
535 | (when (eq (car-safe uold) 'error) |
536 | (error "Bad format in units expression: %s" (nth 2 uold))) | |
136211a9 EZ |
537 | (or (math-units-in-expr-p expr nil) |
538 | (setq expr (math-mul expr uold))) | |
5360ea16 | 539 | (setq defunits (math-get-default-units expr)) |
136211a9 | 540 | (setq unew (or new-units |
fa786329 JB |
541 | (read-string |
542 | (concat | |
543 | (if uoldname | |
544 | (concat "Old temperature units: " | |
545 | uoldname | |
546 | ", new units") | |
547 | "New temperature units") | |
548 | (if defunits | |
549 | (concat " (default " | |
550 | defunits | |
551 | "): ") | |
552 | ": "))))) | |
553 | (setq unew (math-read-expr (if (string= unew "") defunits unew))) | |
8cd8ee52 CW |
554 | (when (eq (car-safe unew) 'error) |
555 | (error "Bad format in units expression: %s" (nth 2 unew))) | |
5360ea16 | 556 | (math-put-default-units unew) |
a34f800f JB |
557 | (let ((ntemp (calc-normalize |
558 | (math-simplify-units | |
559 | (math-convert-temperature expr uold unew | |
560 | uoldname))))) | |
561 | (if (Math-zerop ntemp) | |
562 | (setq ntemp (list '* ntemp unew))) | |
563 | (let ((calc-simplify-mode 'none)) | |
564 | (calc-enter-result 1 "cvtm" ntemp)))))) | |
136211a9 EZ |
565 | |
566 | (defun calc-remove-units () | |
567 | (interactive) | |
568 | (calc-slow-wrapper | |
569 | (calc-enter-result 1 "rmun" (math-simplify-units | |
c9aef719 | 570 | (math-remove-units (calc-top-n 1)))))) |
136211a9 EZ |
571 | |
572 | (defun calc-extract-units () | |
573 | (interactive) | |
574 | (calc-slow-wrapper | |
d14b0029 | 575 | (calc-enter-result 1 "exun" (math-simplify-units |
c9aef719 | 576 | (math-extract-units (calc-top-n 1)))))) |
136211a9 | 577 | |
09040c8d | 578 | ;; The variables calc-num-units and calc-den-units are local to |
27971241 JB |
579 | ;; calc-explain-units, but are used by calc-explain-units-rec, |
580 | ;; which is called by calc-explain-units. | |
581 | (defvar calc-num-units) | |
582 | (defvar calc-den-units) | |
583 | ||
136211a9 EZ |
584 | (defun calc-explain-units () |
585 | (interactive) | |
586 | (calc-wrapper | |
27971241 JB |
587 | (let ((calc-num-units nil) |
588 | (calc-den-units nil)) | |
136211a9 | 589 | (calc-explain-units-rec (calc-top-n 1) 1) |
27971241 JB |
590 | (and calc-den-units (string-match "^[^(].* .*[^)]$" calc-den-units) |
591 | (setq calc-den-units (concat "(" calc-den-units ")"))) | |
592 | (if calc-num-units | |
593 | (if calc-den-units | |
594 | (message "%s per %s" calc-num-units calc-den-units) | |
595 | (message "%s" calc-num-units)) | |
596 | (if calc-den-units | |
597 | (message "1 per %s" calc-den-units) | |
c9aef719 | 598 | (message "No units in expression")))))) |
136211a9 EZ |
599 | |
600 | (defun calc-explain-units-rec (expr pow) | |
601 | (let ((u (math-check-unit-name expr)) | |
602 | pos) | |
603 | (if (and u (not (math-zerop pow))) | |
604 | (let ((name (or (nth 2 u) (symbol-name (car u))))) | |
605 | (if (eq (aref name 0) ?\*) | |
606 | (setq name (substring name 1))) | |
ae6bc504 JB |
607 | (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name) |
608 | (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" name) | |
136211a9 EZ |
609 | (while (setq pos (string-match "[ ()]" name)) |
610 | (setq name (concat (substring name 0 pos) | |
611 | (if (eq (aref name pos) 32) "-" "") | |
612 | (substring name (1+ pos))))) | |
613 | (setq name (concat "(" name ")")))) | |
614 | (or (eq (nth 1 expr) (car u)) | |
615 | (setq name (concat (nth 2 (assq (aref (symbol-name | |
616 | (nth 1 expr)) 0) | |
617 | math-unit-prefixes)) | |
ae6bc504 | 618 | (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name) |
136211a9 EZ |
619 | (not (memq (car u) '(mHg gf)))) |
620 | (concat "-" name) | |
621 | (downcase name))))) | |
622 | (cond ((or (math-equal-int pow 1) | |
623 | (math-equal-int pow -1))) | |
624 | ((or (math-equal-int pow 2) | |
625 | (math-equal-int pow -2)) | |
626 | (if (equal (nth 4 u) '((m . 1))) | |
627 | (setq name (concat "Square-" name)) | |
628 | (setq name (concat name "-squared")))) | |
629 | ((or (math-equal-int pow 3) | |
630 | (math-equal-int pow -3)) | |
631 | (if (equal (nth 4 u) '((m . 1))) | |
632 | (setq name (concat "Cubic-" name)) | |
633 | (setq name (concat name "-cubed")))) | |
634 | (t | |
635 | (setq name (concat name "^" | |
636 | (math-format-number (math-abs pow)))))) | |
637 | (if (math-posp pow) | |
27971241 JB |
638 | (setq calc-num-units (if calc-num-units |
639 | (concat calc-num-units " " name) | |
136211a9 | 640 | name)) |
27971241 JB |
641 | (setq calc-den-units (if calc-den-units |
642 | (concat calc-den-units " " name) | |
136211a9 EZ |
643 | name)))) |
644 | (cond ((eq (car-safe expr) '*) | |
645 | (calc-explain-units-rec (nth 1 expr) pow) | |
646 | (calc-explain-units-rec (nth 2 expr) pow)) | |
647 | ((eq (car-safe expr) '/) | |
648 | (calc-explain-units-rec (nth 1 expr) pow) | |
649 | (calc-explain-units-rec (nth 2 expr) (- pow))) | |
650 | ((memq (car-safe expr) '(neg + -)) | |
651 | (calc-explain-units-rec (nth 1 expr) pow)) | |
652 | ((and (eq (car-safe expr) '^) | |
653 | (math-realp (nth 2 expr))) | |
654 | (calc-explain-units-rec (nth 1 expr) | |
c9aef719 | 655 | (math-mul pow (nth 2 expr)))))))) |
136211a9 EZ |
656 | |
657 | (defun calc-simplify-units () | |
658 | (interactive) | |
659 | (calc-slow-wrapper | |
660 | (calc-with-default-simplification | |
c9aef719 | 661 | (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1)))))) |
136211a9 EZ |
662 | |
663 | (defun calc-view-units-table (n) | |
664 | (interactive "P") | |
665 | (and n (setq math-units-table-buffer-valid nil)) | |
666 | (let ((win (get-buffer-window "*Units Table*"))) | |
667 | (if (and win | |
668 | math-units-table | |
669 | math-units-table-buffer-valid) | |
670 | (progn | |
671 | (bury-buffer (window-buffer win)) | |
672 | (let ((curwin (selected-window))) | |
673 | (select-window win) | |
674 | (switch-to-buffer nil) | |
675 | (select-window curwin))) | |
c9aef719 | 676 | (math-build-units-table-buffer nil)))) |
136211a9 EZ |
677 | |
678 | (defun calc-enter-units-table (n) | |
679 | (interactive "P") | |
680 | (and n (setq math-units-table-buffer-valid nil)) | |
681 | (math-build-units-table-buffer t) | |
5c08522d | 682 | (message "%s" (substitute-command-keys "Type \\[calc] to return to the Calculator"))) |
136211a9 | 683 | |
19bdc4d8 JB |
684 | (defun calc-define-unit (uname desc &optional disp) |
685 | (interactive "SDefine unit name: \nsDescription: \nP") | |
686 | (if disp (setq disp (read-string "Display definition: "))) | |
136211a9 EZ |
687 | (calc-wrapper |
688 | (let ((form (calc-top-n 1)) | |
689 | (unit (assq uname math-additional-units))) | |
690 | (or unit | |
691 | (setq math-additional-units | |
19bdc4d8 | 692 | (cons (setq unit (list uname nil nil nil nil)) |
136211a9 EZ |
693 | math-additional-units) |
694 | math-units-table nil)) | |
695 | (setcar (cdr unit) (and (not (and (eq (car-safe form) 'var) | |
696 | (eq (nth 1 form) uname))) | |
697 | (not (math-equal-int form 1)) | |
698 | (math-format-flat-expr form 0))) | |
699 | (setcar (cdr (cdr unit)) (and (not (equal desc "")) | |
19bdc4d8 JB |
700 | desc)) |
701 | (if disp | |
702 | (setcar (cdr (cdr (cdr (cdr unit)))) disp)))) | |
c9aef719 | 703 | (calc-invalidate-units-table)) |
136211a9 EZ |
704 | |
705 | (defun calc-undefine-unit (uname) | |
706 | (interactive "SUndefine unit name: ") | |
707 | (calc-wrapper | |
708 | (let ((unit (assq uname math-additional-units))) | |
709 | (or unit | |
710 | (if (assq uname math-standard-units) | |
711 | (error "\"%s\" is a predefined unit name" uname) | |
712 | (error "Unit name \"%s\" not found" uname))) | |
713 | (setq math-additional-units (delq unit math-additional-units) | |
714 | math-units-table nil))) | |
c9aef719 | 715 | (calc-invalidate-units-table)) |
136211a9 EZ |
716 | |
717 | (defun calc-invalidate-units-table () | |
718 | (setq math-units-table nil) | |
719 | (let ((buf (get-buffer "*Units Table*"))) | |
720 | (and buf | |
6df9b6d7 | 721 | (with-current-buffer buf |
136211a9 EZ |
722 | (save-excursion |
723 | (goto-char (point-min)) | |
724 | (if (looking-at "Calculator Units Table") | |
ed8060d9 | 725 | (let ((inhibit-read-only t)) |
c9aef719 | 726 | (insert "(Obsolete) ")))))))) |
136211a9 EZ |
727 | |
728 | (defun calc-get-unit-definition (uname) | |
729 | (interactive "SGet definition for unit: ") | |
730 | (calc-wrapper | |
731 | (math-build-units-table) | |
732 | (let ((unit (assq uname math-units-table))) | |
733 | (or unit | |
734 | (error "Unit name \"%s\" not found" uname)) | |
735 | (let ((msg (nth 2 unit))) | |
736 | (if (stringp msg) | |
737 | (if (string-match "^\\*" msg) | |
738 | (setq msg (substring msg 1))) | |
739 | (setq msg (symbol-name uname))) | |
740 | (if (nth 1 unit) | |
741 | (progn | |
742 | (calc-enter-result 0 "ugdf" (nth 1 unit)) | |
743 | (message "Derived unit: %s" msg)) | |
744 | (calc-enter-result 0 "ugdf" (list 'var uname | |
745 | (intern | |
746 | (concat "var-" | |
747 | (symbol-name uname))))) | |
c9aef719 | 748 | (message "Base unit: %s" msg)))))) |
136211a9 EZ |
749 | |
750 | (defun calc-permanent-units () | |
751 | (interactive) | |
752 | (calc-wrapper | |
753 | (let (pos) | |
754 | (set-buffer (find-file-noselect (substitute-in-file-name | |
755 | calc-settings-file))) | |
756 | (goto-char (point-min)) | |
757 | (if (and (search-forward ";;; Custom units stored by Calc" nil t) | |
758 | (progn | |
759 | (beginning-of-line) | |
760 | (setq pos (point)) | |
761 | (search-forward "\n;;; End of custom units" nil t))) | |
762 | (progn | |
763 | (beginning-of-line) | |
764 | (forward-line 1) | |
765 | (delete-region pos (point))) | |
766 | (goto-char (point-max)) | |
767 | (insert "\n\n") | |
768 | (forward-char -1)) | |
769 | (insert ";;; Custom units stored by Calc on " (current-time-string) "\n") | |
770 | (if math-additional-units | |
771 | (progn | |
772 | (insert "(setq math-additional-units '(\n") | |
773 | (let ((list math-additional-units)) | |
774 | (while list | |
775 | (insert " (" (symbol-name (car (car list))) " " | |
776 | (if (nth 1 (car list)) | |
777 | (if (stringp (nth 1 (car list))) | |
778 | (prin1-to-string (nth 1 (car list))) | |
779 | (prin1-to-string (math-format-flat-expr | |
780 | (nth 1 (car list)) 0))) | |
781 | "nil") | |
782 | " " | |
783 | (prin1-to-string (nth 2 (car list))) | |
784 | ")\n") | |
785 | (setq list (cdr list)))) | |
786 | (insert "))\n")) | |
787 | (insert ";;; (no custom units defined)\n")) | |
788 | (insert ";;; End of custom units\n") | |
c9aef719 | 789 | (save-buffer)))) |
136211a9 EZ |
790 | |
791 | ||
27971241 JB |
792 | ;; The variable math-cu-unit-list is local to math-build-units-table, |
793 | ;; but is used by math-compare-unit-names, which is called (indirectly) | |
794 | ;; by math-build-units-table. | |
795 | ;; math-cu-unit-list is also local to math-convert-units, but is used | |
796 | ;; by math-convert-units-rec, which is called by math-convert-units. | |
797 | (defvar math-cu-unit-list) | |
136211a9 | 798 | |
136211a9 EZ |
799 | (defun math-build-units-table () |
800 | (or math-units-table | |
801 | (let* ((combined-units (append math-additional-units | |
802 | math-standard-units)) | |
27971241 | 803 | (math-cu-unit-list (mapcar 'car combined-units)) |
136211a9 EZ |
804 | tab) |
805 | (message "Building units table...") | |
806 | (setq math-units-table-buffer-valid nil) | |
807 | (setq tab (mapcar (function | |
808 | (lambda (x) | |
809 | (list (car x) | |
810 | (and (nth 1 x) | |
811 | (if (stringp (nth 1 x)) | |
812 | (let ((exp (math-read-plain-expr | |
813 | (nth 1 x)))) | |
814 | (if (eq (car-safe exp) 'error) | |
815 | (error "Format error in definition of %s in units table: %s" | |
816 | (car x) (nth 2 exp)) | |
817 | exp)) | |
818 | (nth 1 x))) | |
819 | (nth 2 x) | |
820 | (nth 3 x) | |
821 | (and (not (nth 1 x)) | |
19bdc4d8 JB |
822 | (list (cons (car x) 1))) |
823 | (nth 4 x)))) | |
136211a9 EZ |
824 | combined-units)) |
825 | (let ((math-units-table tab)) | |
09040c8d | 826 | (mapc 'math-find-base-units tab)) |
136211a9 | 827 | (message "Building units table...done") |
c9aef719 | 828 | (setq math-units-table tab)))) |
136211a9 | 829 | |
27971241 JB |
830 | ;; The variables math-fbu-base and math-fbu-entry are local to |
831 | ;; math-find-base-units, but are used by math-find-base-units-rec, | |
832 | ;; which is called by math-find-base-units. | |
833 | (defvar math-fbu-base) | |
834 | (defvar math-fbu-entry) | |
835 | ||
3effaa28 JB |
836 | (defun math-find-base-units (math-fbu-entry) |
837 | (if (eq (nth 4 math-fbu-entry) 'boom) | |
838 | (error "Circular definition involving unit %s" (car math-fbu-entry))) | |
839 | (or (nth 4 math-fbu-entry) | |
840 | (let (math-fbu-base) | |
841 | (setcar (nthcdr 4 math-fbu-entry) 'boom) | |
842 | (math-find-base-units-rec (nth 1 math-fbu-entry) 1) | |
843 | '(or math-fbu-base | |
844 | (error "Dimensionless definition for unit %s" (car math-fbu-entry))) | |
845 | (while (eq (cdr (car math-fbu-base)) 0) | |
846 | (setq math-fbu-base (cdr math-fbu-base))) | |
847 | (let ((b math-fbu-base)) | |
136211a9 EZ |
848 | (while (cdr b) |
849 | (if (eq (cdr (car (cdr b))) 0) | |
850 | (setcdr b (cdr (cdr b))) | |
851 | (setq b (cdr b))))) | |
3effaa28 JB |
852 | (setq math-fbu-base (sort math-fbu-base 'math-compare-unit-names)) |
853 | (setcar (nthcdr 4 math-fbu-entry) math-fbu-base) | |
854 | math-fbu-base))) | |
136211a9 EZ |
855 | |
856 | (defun math-compare-unit-names (a b) | |
27971241 | 857 | (memq (car b) (cdr (memq (car a) math-cu-unit-list)))) |
136211a9 EZ |
858 | |
859 | (defun math-find-base-units-rec (expr pow) | |
860 | (let ((u (math-check-unit-name expr))) | |
861 | (cond (u | |
862 | (let ((ulist (math-find-base-units u))) | |
863 | (while ulist | |
864 | (let ((p (* (cdr (car ulist)) pow)) | |
3effaa28 | 865 | (old (assq (car (car ulist)) math-fbu-base))) |
136211a9 EZ |
866 | (if old |
867 | (setcdr old (+ (cdr old) p)) | |
09040c8d | 868 | (setq math-fbu-base |
3effaa28 | 869 | (cons (cons (car (car ulist)) p) math-fbu-base)))) |
136211a9 EZ |
870 | (setq ulist (cdr ulist))))) |
871 | ((math-scalarp expr)) | |
872 | ((and (eq (car expr) '^) | |
873 | (integerp (nth 2 expr))) | |
874 | (math-find-base-units-rec (nth 1 expr) (* pow (nth 2 expr)))) | |
875 | ((eq (car expr) '*) | |
876 | (math-find-base-units-rec (nth 1 expr) pow) | |
877 | (math-find-base-units-rec (nth 2 expr) pow)) | |
878 | ((eq (car expr) '/) | |
879 | (math-find-base-units-rec (nth 1 expr) pow) | |
880 | (math-find-base-units-rec (nth 2 expr) (- pow))) | |
881 | ((eq (car expr) 'neg) | |
882 | (math-find-base-units-rec (nth 1 expr) pow)) | |
883 | ((eq (car expr) '+) | |
884 | (math-find-base-units-rec (nth 1 expr) pow)) | |
885 | ((eq (car expr) 'var) | |
886 | (or (eq (nth 1 expr) 'pi) | |
887 | (error "Unknown name %s in defining expression for unit %s" | |
3effaa28 | 888 | (nth 1 expr) (car math-fbu-entry)))) |
603823f5 | 889 | ((equal expr '(calcFunc-ln 10))) |
3effaa28 | 890 | (t (error "Malformed defining expression for unit %s" (car math-fbu-entry)))))) |
136211a9 EZ |
891 | |
892 | ||
893 | (defun math-units-in-expr-p (expr sub-exprs) | |
894 | (and (consp expr) | |
895 | (if (eq (car expr) 'var) | |
896 | (math-check-unit-name expr) | |
897 | (and (or sub-exprs | |
898 | (memq (car expr) '(* / ^))) | |
899 | (or (math-units-in-expr-p (nth 1 expr) sub-exprs) | |
c9aef719 | 900 | (math-units-in-expr-p (nth 2 expr) sub-exprs)))))) |
136211a9 EZ |
901 | |
902 | (defun math-only-units-in-expr-p (expr) | |
903 | (and (consp expr) | |
904 | (if (eq (car expr) 'var) | |
905 | (math-check-unit-name expr) | |
906 | (if (memq (car expr) '(* /)) | |
907 | (and (math-only-units-in-expr-p (nth 1 expr)) | |
908 | (math-only-units-in-expr-p (nth 2 expr))) | |
909 | (and (eq (car expr) '^) | |
910 | (and (math-only-units-in-expr-p (nth 1 expr)) | |
c9aef719 | 911 | (math-realp (nth 2 expr)))))))) |
136211a9 EZ |
912 | |
913 | (defun math-single-units-in-expr-p (expr) | |
914 | (cond ((math-scalarp expr) nil) | |
915 | ((eq (car expr) 'var) | |
916 | (math-check-unit-name expr)) | |
917 | ((eq (car expr) '*) | |
918 | (let ((u1 (math-single-units-in-expr-p (nth 1 expr))) | |
919 | (u2 (math-single-units-in-expr-p (nth 2 expr)))) | |
920 | (or (and u1 u2 'wrong) | |
921 | u1 | |
922 | u2))) | |
923 | ((eq (car expr) '/) | |
924 | (if (math-units-in-expr-p (nth 2 expr) nil) | |
925 | 'wrong | |
926 | (math-single-units-in-expr-p (nth 1 expr)))) | |
c9aef719 | 927 | (t 'wrong))) |
136211a9 | 928 | |
76bc2ec7 JB |
929 | (defun math-consistent-units-p (expr newunits) |
930 | "Non-nil if EXPR and NEWUNITS have consistent units." | |
931 | (or | |
932 | (and (eq (car-safe newunits) 'var) | |
933 | (assq (nth 1 newunits) math-standard-units-systems)) | |
934 | (math-numberp (math-get-units (list '/ expr newunits))))) | |
d14b0029 JB |
935 | |
936 | (defun math-check-unit-consistency (expr units) | |
937 | "Give an error if EXPR and UNITS do not have consistent units." | |
938 | (unless (math-consistent-units-p expr units) | |
939 | (error "New units (%s) are inconsistent with current units (%s)" | |
940 | (math-format-value units) | |
941 | (math-format-value (math-get-units expr))))) | |
942 | ||
136211a9 EZ |
943 | (defun math-check-unit-name (v) |
944 | (and (eq (car-safe v) 'var) | |
945 | (or (assq (nth 1 v) (or math-units-table (math-build-units-table))) | |
946 | (let ((name (symbol-name (nth 1 v)))) | |
947 | (and (> (length name) 1) | |
948 | (assq (aref name 0) math-unit-prefixes) | |
949 | (or (assq (intern (substring name 1)) math-units-table) | |
950 | (and (eq (aref name 0) ?M) | |
951 | (> (length name) 3) | |
952 | (eq (aref name 1) ?e) | |
953 | (eq (aref name 2) ?g) | |
954 | (assq (intern (substring name 3)) | |
c9aef719 | 955 | math-units-table)))))))) |
136211a9 | 956 | |
27971241 JB |
957 | ;; The variable math-which-standard is local to math-to-standard-units, |
958 | ;; but is used by math-to-standard-rec, which is called by | |
959 | ;; math-to-standard-units. | |
960 | (defvar math-which-standard) | |
136211a9 | 961 | |
27971241 | 962 | (defun math-to-standard-units (expr math-which-standard) |
c9aef719 | 963 | (math-to-standard-rec expr)) |
136211a9 EZ |
964 | |
965 | (defun math-to-standard-rec (expr) | |
966 | (if (eq (car-safe expr) 'var) | |
967 | (let ((u (math-check-unit-name expr)) | |
968 | (base (nth 1 expr))) | |
969 | (if u | |
970 | (progn | |
971 | (if (nth 1 u) | |
972 | (setq expr (math-to-standard-rec (nth 1 u))) | |
27971241 | 973 | (let ((st (assq (car u) math-which-standard))) |
136211a9 EZ |
974 | (if st |
975 | (setq expr (nth 1 st)) | |
976 | (setq expr (list 'var (car u) | |
977 | (intern (concat "var-" | |
978 | (symbol-name | |
979 | (car u))))))))) | |
980 | (or (null u) | |
981 | (eq base (car u)) | |
982 | (setq expr (list '* | |
983 | (nth 1 (assq (aref (symbol-name base) 0) | |
984 | math-unit-prefixes)) | |
985 | expr))) | |
986 | expr) | |
987 | (if (eq base 'pi) | |
988 | (math-pi) | |
989 | expr))) | |
d6ffd3f8 JB |
990 | (if (or |
991 | (Math-primp expr) | |
992 | (and (eq (car-safe expr) 'calcFunc-subscr) | |
993 | (eq (car-safe (nth 1 expr)) 'var))) | |
136211a9 EZ |
994 | expr |
995 | (cons (car expr) | |
c9aef719 | 996 | (mapcar 'math-to-standard-rec (cdr expr)))))) |
136211a9 EZ |
997 | |
998 | (defun math-apply-units (expr units ulist &optional pure) | |
2e2b4fbe | 999 | (setq expr (math-simplify-units expr)) |
136211a9 EZ |
1000 | (if ulist |
1001 | (let ((new 0) | |
1002 | value) | |
136211a9 EZ |
1003 | (or (math-numberp expr) |
1004 | (error "Incompatible units")) | |
1005 | (while (cdr ulist) | |
1006 | (setq value (math-div expr (nth 1 (car ulist))) | |
1007 | value (math-floor (let ((calc-internal-prec | |
1008 | (1- calc-internal-prec))) | |
1009 | (math-normalize value))) | |
1010 | new (math-add new (math-mul value (car (car ulist)))) | |
1011 | expr (math-sub expr (math-mul value (nth 1 (car ulist)))) | |
1012 | ulist (cdr ulist))) | |
1013 | (math-add new (math-mul (math-div expr (nth 1 (car ulist))) | |
1014 | (car (car ulist))))) | |
2e2b4fbe JB |
1015 | (if pure |
1016 | expr | |
1017 | (math-simplify-units (list '* expr units))))) | |
136211a9 | 1018 | |
8cd8ee52 | 1019 | (defvar math-decompose-units-cache nil) |
136211a9 EZ |
1020 | (defun math-decompose-units (units) |
1021 | (let ((u (math-check-unit-name units))) | |
1022 | (and u (eq (car-safe (nth 1 u)) '+) | |
1023 | (setq units (nth 1 u)))) | |
1024 | (setq units (calcFunc-expand units)) | |
1025 | (and (eq (car-safe units) '+) | |
1026 | (let ((entry (list units calc-internal-prec calc-prefer-frac))) | |
1027 | (or (equal entry (car math-decompose-units-cache)) | |
1028 | (let ((ulist nil) | |
1029 | (utemp units) | |
1030 | qty unit) | |
1031 | (while (eq (car-safe utemp) '+) | |
1032 | (setq ulist (cons (math-decompose-unit-part (nth 2 utemp)) | |
1033 | ulist) | |
1034 | utemp (nth 1 utemp))) | |
1035 | (setq ulist (cons (math-decompose-unit-part utemp) ulist) | |
1036 | utemp ulist) | |
1037 | (while (setq utemp (cdr utemp)) | |
8cd8ee52 CW |
1038 | (unless (equal (nth 2 (car utemp)) (nth 2 (car ulist))) |
1039 | (error "Inconsistent units in sum"))) | |
136211a9 EZ |
1040 | (setq math-decompose-units-cache |
1041 | (cons entry | |
1042 | (sort ulist | |
1043 | (function | |
1044 | (lambda (x y) | |
1045 | (not (Math-lessp (nth 1 x) | |
1046 | (nth 1 y)))))))))) | |
c9aef719 | 1047 | (cdr math-decompose-units-cache)))) |
136211a9 EZ |
1048 | |
1049 | (defun math-decompose-unit-part (unit) | |
1050 | (cons unit | |
1051 | (math-is-multiple (math-simplify-units (math-to-standard-units | |
1052 | unit nil)) | |
c9aef719 | 1053 | t))) |
136211a9 | 1054 | |
27971241 JB |
1055 | ;; The variable math-fcu-u is local to math-find-compatible-unit, |
1056 | ;; but is used by math-find-compatible-rec which is called by | |
1057 | ;; math-find-compatible-unit. | |
1058 | (defvar math-fcu-u) | |
1059 | ||
136211a9 | 1060 | (defun math-find-compatible-unit (expr unit) |
27971241 JB |
1061 | (let ((math-fcu-u (math-check-unit-name unit))) |
1062 | (if math-fcu-u | |
c9aef719 | 1063 | (math-find-compatible-unit-rec expr 1)))) |
136211a9 EZ |
1064 | |
1065 | (defun math-find-compatible-unit-rec (expr pow) | |
1066 | (cond ((eq (car-safe expr) '*) | |
1067 | (or (math-find-compatible-unit-rec (nth 1 expr) pow) | |
1068 | (math-find-compatible-unit-rec (nth 2 expr) pow))) | |
1069 | ((eq (car-safe expr) '/) | |
1070 | (or (math-find-compatible-unit-rec (nth 1 expr) pow) | |
1071 | (math-find-compatible-unit-rec (nth 2 expr) (- pow)))) | |
1072 | ((and (eq (car-safe expr) '^) | |
1073 | (integerp (nth 2 expr))) | |
1074 | (math-find-compatible-unit-rec (nth 1 expr) (* pow (nth 2 expr)))) | |
1075 | (t | |
1076 | (let ((u2 (math-check-unit-name expr))) | |
27971241 | 1077 | (if (equal (nth 4 math-fcu-u) (nth 4 u2)) |
c9aef719 | 1078 | (cons expr pow)))))) |
136211a9 | 1079 | |
09040c8d JB |
1080 | ;; The variables math-cu-new-units and math-cu-pure are local to |
1081 | ;; math-convert-units, but are used by math-convert-units-rec, | |
27971241 JB |
1082 | ;; which is called by math-convert-units. |
1083 | (defvar math-cu-new-units) | |
1084 | (defvar math-cu-pure) | |
1085 | ||
1086 | (defun math-convert-units (expr math-cu-new-units &optional math-cu-pure) | |
65b62d0a JB |
1087 | (if (eq (car-safe math-cu-new-units) 'var) |
1088 | (let ((unew (assq (nth 1 math-cu-new-units) | |
1089 | (math-build-units-table)))) | |
1090 | (if (eq (car-safe (nth 1 unew)) '+) | |
1091 | (setq math-cu-new-units (nth 1 unew))))) | |
136211a9 | 1092 | (math-with-extra-prec 2 |
09040c8d | 1093 | (let ((compat (and (not math-cu-pure) |
27971241 JB |
1094 | (math-find-compatible-unit expr math-cu-new-units))) |
1095 | (math-cu-unit-list nil) | |
136211a9 EZ |
1096 | (math-combining-units nil)) |
1097 | (if compat | |
1098 | (math-simplify-units | |
1099 | (math-mul (math-mul (math-simplify-units | |
1100 | (math-div expr (math-pow (car compat) | |
1101 | (cdr compat)))) | |
27971241 | 1102 | (math-pow math-cu-new-units (cdr compat))) |
136211a9 EZ |
1103 | (math-simplify-units |
1104 | (math-to-standard-units | |
27971241 | 1105 | (math-pow (math-div (car compat) math-cu-new-units) |
136211a9 EZ |
1106 | (cdr compat)) |
1107 | nil)))) | |
27971241 JB |
1108 | (when (setq math-cu-unit-list (math-decompose-units math-cu-new-units)) |
1109 | (setq math-cu-new-units (nth 2 (car math-cu-unit-list)))) | |
8cd8ee52 CW |
1110 | (when (eq (car-safe expr) '+) |
1111 | (setq expr (math-simplify-units expr))) | |
136211a9 EZ |
1112 | (if (math-units-in-expr-p expr t) |
1113 | (math-convert-units-rec expr) | |
1114 | (math-apply-units (math-to-standard-units | |
27971241 JB |
1115 | (list '/ expr math-cu-new-units) nil) |
1116 | math-cu-new-units math-cu-unit-list math-cu-pure)))))) | |
136211a9 EZ |
1117 | |
1118 | (defun math-convert-units-rec (expr) | |
1119 | (if (math-units-in-expr-p expr nil) | |
09040c8d | 1120 | (math-apply-units (math-to-standard-units |
27971241 JB |
1121 | (list '/ expr math-cu-new-units) nil) |
1122 | math-cu-new-units math-cu-unit-list math-cu-pure) | |
136211a9 EZ |
1123 | (if (Math-primp expr) |
1124 | expr | |
1125 | (cons (car expr) | |
c9aef719 | 1126 | (mapcar 'math-convert-units-rec (cdr expr)))))) |
136211a9 EZ |
1127 | |
1128 | (defun math-convert-temperature (expr old new &optional pure) | |
1129 | (let* ((units (math-single-units-in-expr-p expr)) | |
1130 | (uold (if old | |
1131 | (if (or (null units) | |
1132 | (equal (nth 1 old) (car units))) | |
1133 | (math-check-unit-name old) | |
1134 | (error "Inconsistent temperature units")) | |
1135 | units)) | |
1136 | (unew (math-check-unit-name new))) | |
8cd8ee52 CW |
1137 | (unless (and (consp unew) (nth 3 unew)) |
1138 | (error "Not a valid temperature unit")) | |
1139 | (unless (and (consp uold) (nth 3 uold)) | |
1140 | (error "Not a pure temperature expression")) | |
136211a9 EZ |
1141 | (let ((v (car uold))) |
1142 | (setq expr (list '/ expr (list 'var v | |
1143 | (intern (concat "var-" | |
1144 | (symbol-name v))))))) | |
1145 | (or (eq (nth 3 uold) (nth 3 unew)) | |
1146 | (cond ((eq (nth 3 uold) 'K) | |
e6cd99dc | 1147 | (setq expr (list '- expr '(/ 27315 100))) |
136211a9 | 1148 | (if (eq (nth 3 unew) 'F) |
e6cd99dc | 1149 | (setq expr (list '+ (list '* expr '(/ 9 5)) 32)))) |
136211a9 EZ |
1150 | ((eq (nth 3 uold) 'C) |
1151 | (if (eq (nth 3 unew) 'F) | |
e6cd99dc JB |
1152 | (setq expr (list '+ (list '* expr '(/ 9 5)) 32)) |
1153 | (setq expr (list '+ expr '(/ 27315 100))))) | |
136211a9 | 1154 | (t |
e6cd99dc | 1155 | (setq expr (list '* (list '- expr 32) '(/ 5 9))) |
136211a9 | 1156 | (if (eq (nth 3 unew) 'K) |
e6cd99dc | 1157 | (setq expr (list '+ expr '(/ 27315 100))))))) |
136211a9 EZ |
1158 | (if pure |
1159 | expr | |
c9aef719 | 1160 | (list '* expr new)))) |
136211a9 EZ |
1161 | |
1162 | ||
1163 | ||
1164 | (defun math-simplify-units (a) | |
1165 | (let ((math-simplifying-units t) | |
1166 | (calc-matrix-mode 'scalar)) | |
c9aef719 | 1167 | (math-simplify a))) |
8cd8ee52 | 1168 | (defalias 'calcFunc-usimplify 'math-simplify-units) |
136211a9 | 1169 | |
f095c6c9 JB |
1170 | ;; The function created by math-defsimplify uses the variable |
1171 | ;; math-simplify-expr, and so is used by functions in math-defsimplify | |
1172 | (defvar math-simplify-expr) | |
1173 | ||
136211a9 EZ |
1174 | (math-defsimplify (+ -) |
1175 | (and math-simplifying-units | |
f095c6c9 JB |
1176 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) |
1177 | (let* ((units (math-extract-units (nth 1 math-simplify-expr))) | |
136211a9 | 1178 | (ratio (math-simplify (math-to-standard-units |
f095c6c9 | 1179 | (list '/ (nth 2 math-simplify-expr) units) nil)))) |
136211a9 EZ |
1180 | (if (math-units-in-expr-p ratio nil) |
1181 | (progn | |
f095c6c9 JB |
1182 | (calc-record-why "*Inconsistent units" math-simplify-expr) |
1183 | math-simplify-expr) | |
1184 | (list '* (math-add (math-remove-units (nth 1 math-simplify-expr)) | |
09040c8d | 1185 | (if (eq (car math-simplify-expr) '-) |
f095c6c9 | 1186 | (math-neg ratio) ratio)) |
c9aef719 | 1187 | units))))) |
136211a9 EZ |
1188 | |
1189 | (math-defsimplify * | |
c9aef719 | 1190 | (math-simplify-units-prod)) |
136211a9 EZ |
1191 | |
1192 | (defun math-simplify-units-prod () | |
1193 | (and math-simplifying-units | |
1194 | calc-autorange-units | |
f095c6c9 JB |
1195 | (Math-realp (nth 1 math-simplify-expr)) |
1196 | (let* ((num (math-float (nth 1 math-simplify-expr))) | |
136211a9 | 1197 | (xpon (calcFunc-xpon num)) |
f095c6c9 | 1198 | (unitp (cdr (cdr math-simplify-expr))) |
136211a9 | 1199 | (unit (car unitp)) |
f095c6c9 | 1200 | (pow (if (eq (car math-simplify-expr) '*) 1 -1)) |
136211a9 EZ |
1201 | u) |
1202 | (and (eq (car-safe unit) '*) | |
1203 | (setq unitp (cdr unit) | |
1204 | unit (car unitp))) | |
1205 | (and (eq (car-safe unit) '^) | |
1206 | (integerp (nth 2 unit)) | |
1207 | (setq pow (* pow (nth 2 unit)) | |
1208 | unitp (cdr unit) | |
1209 | unit (car unitp))) | |
1210 | (and (setq u (math-check-unit-name unit)) | |
1211 | (integerp xpon) | |
1212 | (or (< xpon 0) | |
1213 | (>= xpon (if (eq (car u) 'm) 1 3))) | |
1214 | (let* ((uxpon 0) | |
1215 | (pref (if (< pow 0) | |
1216 | (reverse math-unit-prefixes) | |
1217 | math-unit-prefixes)) | |
1218 | (p pref) | |
1219 | pxpon pname) | |
1220 | (or (eq (car u) (nth 1 unit)) | |
1221 | (setq uxpon (* pow | |
1222 | (nth 2 (nth 1 (assq | |
1223 | (aref (symbol-name | |
1224 | (nth 1 unit)) 0) | |
1225 | math-unit-prefixes)))))) | |
1226 | (setq xpon (+ xpon uxpon)) | |
1227 | (while (and p | |
1228 | (or (memq (car (car p)) '(?d ?D ?h ?H)) | |
1229 | (and (eq (car (car p)) ?c) | |
1230 | (not (eq (car u) 'm))) | |
1231 | (< xpon (setq pxpon (* (nth 2 (nth 1 (car p))) | |
1232 | pow))) | |
1233 | (progn | |
1234 | (setq pname (math-build-var-name | |
1235 | (if (eq (car (car p)) 0) | |
1236 | (car u) | |
1237 | (concat (char-to-string | |
1238 | (car (car p))) | |
1239 | (symbol-name | |
1240 | (car u)))))) | |
1241 | (and (/= (car (car p)) 0) | |
1242 | (assq (nth 1 pname) | |
1243 | math-units-table))))) | |
1244 | (setq p (cdr p))) | |
1245 | (and p | |
1246 | (/= pxpon uxpon) | |
1247 | (or (not (eq p pref)) | |
1248 | (< xpon (+ pxpon (* (math-abs pow) 3)))) | |
1249 | (progn | |
f095c6c9 | 1250 | (setcar (cdr math-simplify-expr) |
136211a9 | 1251 | (let ((calc-prefer-frac nil)) |
f095c6c9 | 1252 | (calcFunc-scf (nth 1 math-simplify-expr) |
136211a9 EZ |
1253 | (- uxpon pxpon)))) |
1254 | (setcar unitp pname) | |
f095c6c9 | 1255 | math-simplify-expr))))))) |
136211a9 | 1256 | |
27971241 JB |
1257 | (defvar math-try-cancel-units) |
1258 | ||
136211a9 EZ |
1259 | (math-defsimplify / |
1260 | (and math-simplifying-units | |
f095c6c9 | 1261 | (let ((np (cdr math-simplify-expr)) |
27971241 | 1262 | (math-try-cancel-units 0) |
136211a9 | 1263 | n nn) |
f095c6c9 JB |
1264 | (setq n (if (eq (car-safe (nth 2 math-simplify-expr)) '*) |
1265 | (cdr (nth 2 math-simplify-expr)) | |
1266 | (nthcdr 2 math-simplify-expr))) | |
136211a9 EZ |
1267 | (if (math-realp (car n)) |
1268 | (progn | |
f095c6c9 | 1269 | (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr) |
136211a9 EZ |
1270 | (let ((calc-prefer-frac nil)) |
1271 | (math-div 1 (car n))))) | |
1272 | (setcar n 1))) | |
1273 | (while (eq (car-safe (setq n (car np))) '*) | |
f095c6c9 | 1274 | (math-simplify-units-divisor (cdr n) (cdr (cdr math-simplify-expr))) |
136211a9 | 1275 | (setq np (cdr (cdr n)))) |
f095c6c9 | 1276 | (math-simplify-units-divisor np (cdr (cdr math-simplify-expr))) |
27971241 | 1277 | (if (eq math-try-cancel-units 0) |
136211a9 | 1278 | (let* ((math-simplifying-units nil) |
09040c8d | 1279 | (base (math-simplify |
f095c6c9 | 1280 | (math-to-standard-units math-simplify-expr nil)))) |
136211a9 | 1281 | (if (Math-numberp base) |
f095c6c9 JB |
1282 | (setq math-simplify-expr base)))) |
1283 | (if (eq (car-safe math-simplify-expr) '/) | |
136211a9 | 1284 | (math-simplify-units-prod)) |
f095c6c9 | 1285 | math-simplify-expr))) |
136211a9 EZ |
1286 | |
1287 | (defun math-simplify-units-divisor (np dp) | |
1288 | (let ((n (car np)) | |
1289 | d dd temp) | |
1290 | (while (eq (car-safe (setq d (car dp))) '*) | |
8cd8ee52 CW |
1291 | (when (setq temp (math-simplify-units-quotient n (nth 1 d))) |
1292 | (setcar np (setq n temp)) | |
1293 | (setcar (cdr d) 1)) | |
136211a9 | 1294 | (setq dp (cdr (cdr d)))) |
8cd8ee52 CW |
1295 | (when (setq temp (math-simplify-units-quotient n d)) |
1296 | (setcar np (setq n temp)) | |
1297 | (setcar dp 1)))) | |
136211a9 EZ |
1298 | |
1299 | ;; Simplify, e.g., "in / cm" to "2.54" in a units expression. | |
1300 | (defun math-simplify-units-quotient (n d) | |
1301 | (let ((pow1 1) | |
1302 | (pow2 1)) | |
8cd8ee52 CW |
1303 | (when (and (eq (car-safe n) '^) |
1304 | (integerp (nth 2 n))) | |
1305 | (setq pow1 (nth 2 n) n (nth 1 n))) | |
1306 | (when (and (eq (car-safe d) '^) | |
1307 | (integerp (nth 2 d))) | |
1308 | (setq pow2 (nth 2 d) d (nth 1 d))) | |
136211a9 EZ |
1309 | (let ((un (math-check-unit-name n)) |
1310 | (ud (math-check-unit-name d))) | |
1311 | (and un ud | |
1312 | (if (and (equal (nth 4 un) (nth 4 ud)) | |
1313 | (eq pow1 pow2)) | |
0317ca78 JB |
1314 | (if (eq pow1 1) |
1315 | (math-to-standard-units (list '/ n d) nil) | |
1316 | (list '^ (math-to-standard-units (list '/ n d) nil) pow1)) | |
136211a9 EZ |
1317 | (let (ud1) |
1318 | (setq un (nth 4 un) | |
1319 | ud (nth 4 ud)) | |
1320 | (while un | |
1321 | (setq ud1 ud) | |
1322 | (while ud1 | |
1323 | (and (eq (car (car un)) (car (car ud1))) | |
27971241 JB |
1324 | (setq math-try-cancel-units |
1325 | (+ math-try-cancel-units | |
136211a9 EZ |
1326 | (- (* (cdr (car un)) pow1) |
1327 | (* (cdr (car ud)) pow2))))) | |
1328 | (setq ud1 (cdr ud1))) | |
1329 | (setq un (cdr un))) | |
c9aef719 | 1330 | nil)))))) |
136211a9 EZ |
1331 | |
1332 | (math-defsimplify ^ | |
1333 | (and math-simplifying-units | |
f095c6c9 JB |
1334 | (math-realp (nth 2 math-simplify-expr)) |
1335 | (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
1336 | (list (car (nth 1 math-simplify-expr)) | |
09040c8d | 1337 | (list '^ (nth 1 (nth 1 math-simplify-expr)) |
f095c6c9 | 1338 | (nth 2 math-simplify-expr)) |
09040c8d | 1339 | (list '^ (nth 2 (nth 1 math-simplify-expr)) |
f095c6c9 | 1340 | (nth 2 math-simplify-expr))) |
09040c8d | 1341 | (math-simplify-units-pow (nth 1 math-simplify-expr) |
f095c6c9 | 1342 | (nth 2 math-simplify-expr))))) |
136211a9 EZ |
1343 | |
1344 | (math-defsimplify calcFunc-sqrt | |
1345 | (and math-simplifying-units | |
f095c6c9 JB |
1346 | (if (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) |
1347 | (list (car (nth 1 math-simplify-expr)) | |
1348 | (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr))) | |
1349 | (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr)))) | |
1350 | (math-simplify-units-pow (nth 1 math-simplify-expr) '(frac 1 2))))) | |
136211a9 EZ |
1351 | |
1352 | (math-defsimplify (calcFunc-floor | |
1353 | calcFunc-ceil | |
1354 | calcFunc-round | |
1355 | calcFunc-rounde | |
1356 | calcFunc-roundu | |
1357 | calcFunc-trunc | |
1358 | calcFunc-float | |
1359 | calcFunc-frac | |
1360 | calcFunc-abs | |
1361 | calcFunc-clean) | |
1362 | (and math-simplifying-units | |
f095c6c9 JB |
1363 | (= (length math-simplify-expr) 2) |
1364 | (if (math-only-units-in-expr-p (nth 1 math-simplify-expr)) | |
1365 | (nth 1 math-simplify-expr) | |
1366 | (if (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
136211a9 | 1367 | (or (math-only-units-in-expr-p |
f095c6c9 | 1368 | (nth 1 (nth 1 math-simplify-expr))) |
136211a9 | 1369 | (math-only-units-in-expr-p |
f095c6c9 JB |
1370 | (nth 2 (nth 1 math-simplify-expr))))) |
1371 | (list (car (nth 1 math-simplify-expr)) | |
1372 | (cons (car math-simplify-expr) | |
1373 | (cons (nth 1 (nth 1 math-simplify-expr)) | |
1374 | (cdr (cdr math-simplify-expr)))) | |
1375 | (cons (car math-simplify-expr) | |
1376 | (cons (nth 2 (nth 1 math-simplify-expr)) | |
1377 | (cdr (cdr math-simplify-expr))))))))) | |
136211a9 EZ |
1378 | |
1379 | (defun math-simplify-units-pow (a pow) | |
1380 | (if (and (eq (car-safe a) '^) | |
1381 | (math-check-unit-name (nth 1 a)) | |
1382 | (math-realp (nth 2 a))) | |
1383 | (list '^ (nth 1 a) (math-mul pow (nth 2 a))) | |
1384 | (let* ((u (math-check-unit-name a)) | |
1385 | (pf (math-to-simple-fraction pow)) | |
1386 | (d (and (eq (car-safe pf) 'frac) (nth 2 pf)))) | |
1387 | (and u d | |
1388 | (math-units-are-multiple u d) | |
c9aef719 | 1389 | (list '^ (math-to-standard-units a nil) pow))))) |
136211a9 EZ |
1390 | |
1391 | ||
1392 | (defun math-units-are-multiple (u n) | |
1393 | (setq u (nth 4 u)) | |
1394 | (while (and u (= (% (cdr (car u)) n) 0)) | |
1395 | (setq u (cdr u))) | |
c9aef719 | 1396 | (null u)) |
136211a9 EZ |
1397 | |
1398 | (math-defsimplify calcFunc-sin | |
1399 | (and math-simplifying-units | |
f095c6c9 | 1400 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) |
136211a9 EZ |
1401 | (let ((rad (math-simplify-units |
1402 | (math-evaluate-expr | |
f095c6c9 | 1403 | (math-to-standard-units (nth 1 math-simplify-expr) nil)))) |
136211a9 EZ |
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) | |
c9aef719 | 1409 | (list 'calcFunc-sin (nth 1 rad)))))) |
136211a9 EZ |
1410 | |
1411 | (math-defsimplify calcFunc-cos | |
1412 | (and math-simplifying-units | |
f095c6c9 | 1413 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) |
136211a9 EZ |
1414 | (let ((rad (math-simplify-units |
1415 | (math-evaluate-expr | |
f095c6c9 | 1416 | (math-to-standard-units (nth 1 math-simplify-expr) nil)))) |
136211a9 EZ |
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) | |
c9aef719 | 1422 | (list 'calcFunc-cos (nth 1 rad)))))) |
136211a9 EZ |
1423 | |
1424 | (math-defsimplify calcFunc-tan | |
1425 | (and math-simplifying-units | |
f095c6c9 | 1426 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) |
136211a9 EZ |
1427 | (let ((rad (math-simplify-units |
1428 | (math-evaluate-expr | |
f095c6c9 | 1429 | (math-to-standard-units (nth 1 math-simplify-expr) nil)))) |
136211a9 EZ |
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) | |
c9aef719 | 1435 | (list 'calcFunc-tan (nth 1 rad)))))) |
136211a9 | 1436 | |
40b444ac JB |
1437 | (math-defsimplify calcFunc-sec |
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-sec (nth 1 rad)))))) | |
1449 | ||
1450 | (math-defsimplify calcFunc-csc | |
1451 | (and math-simplifying-units | |
1452 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) | |
1453 | (let ((rad (math-simplify-units | |
1454 | (math-evaluate-expr | |
1455 | (math-to-standard-units (nth 1 math-simplify-expr) nil)))) | |
1456 | (calc-angle-mode 'rad)) | |
1457 | (and (eq (car-safe rad) '*) | |
1458 | (math-realp (nth 1 rad)) | |
1459 | (eq (car-safe (nth 2 rad)) 'var) | |
1460 | (eq (nth 1 (nth 2 rad)) 'rad) | |
1461 | (list 'calcFunc-csc (nth 1 rad)))))) | |
1462 | ||
1463 | (math-defsimplify calcFunc-cot | |
1464 | (and math-simplifying-units | |
1465 | (math-units-in-expr-p (nth 1 math-simplify-expr) nil) | |
1466 | (let ((rad (math-simplify-units | |
1467 | (math-evaluate-expr | |
1468 | (math-to-standard-units (nth 1 math-simplify-expr) nil)))) | |
1469 | (calc-angle-mode 'rad)) | |
1470 | (and (eq (car-safe rad) '*) | |
1471 | (math-realp (nth 1 rad)) | |
1472 | (eq (car-safe (nth 2 rad)) 'var) | |
1473 | (eq (nth 1 (nth 2 rad)) 'rad) | |
1474 | (list 'calcFunc-cot (nth 1 rad)))))) | |
1475 | ||
136211a9 EZ |
1476 | |
1477 | (defun math-remove-units (expr) | |
1478 | (if (math-check-unit-name expr) | |
1479 | 1 | |
1480 | (if (Math-primp expr) | |
1481 | expr | |
1482 | (cons (car expr) | |
c9aef719 | 1483 | (mapcar 'math-remove-units (cdr expr)))))) |
136211a9 EZ |
1484 | |
1485 | (defun math-extract-units (expr) | |
4c9e9550 JB |
1486 | (cond |
1487 | ((memq (car-safe expr) '(* /)) | |
1488 | (cons (car expr) | |
1489 | (mapcar 'math-extract-units (cdr expr)))) | |
1490 | ((and | |
1491 | (eq (car-safe expr) '^) | |
1492 | (math-check-unit-name (nth 1 expr))) | |
1493 | expr) | |
1494 | ((math-check-unit-name expr) expr) | |
1495 | (t 1))) | |
136211a9 EZ |
1496 | |
1497 | (defun math-build-units-table-buffer (enter-buffer) | |
1498 | (if (not (and math-units-table math-units-table-buffer-valid | |
1499 | (get-buffer "*Units Table*"))) | |
1500 | (let ((buf (get-buffer-create "*Units Table*")) | |
1501 | (uptr (math-build-units-table)) | |
1502 | (calc-language (if (eq calc-language 'big) nil calc-language)) | |
1503 | (calc-float-format '(float 0)) | |
1504 | (calc-group-digits nil) | |
1505 | (calc-number-radix 10) | |
7b999abb | 1506 | (calc-twos-complement-mode nil) |
136211a9 EZ |
1507 | (calc-point-char ".") |
1508 | (std nil) | |
1509 | u name shadowed) | |
1510 | (save-excursion | |
1511 | (message "Formatting units table...") | |
1512 | (set-buffer buf) | |
ed8060d9 JB |
1513 | (let ((inhibit-read-only t)) |
1514 | (erase-buffer) | |
1515 | (insert "Calculator Units Table:\n\n") | |
ac318df0 | 1516 | (insert "(All definitions are exact unless marked with an asterisk (*).)\n\n") |
ed8060d9 JB |
1517 | (insert "Unit Type Definition Description\n\n") |
1518 | (while uptr | |
1519 | (setq u (car uptr) | |
1520 | name (nth 2 u)) | |
1521 | (when (eq (car u) 'm) | |
1522 | (setq std t)) | |
1523 | (setq shadowed (and std (assq (car u) math-additional-units))) | |
1524 | (when (and name | |
1525 | (> (length name) 1) | |
1526 | (eq (aref name 0) ?\*)) | |
1527 | (unless (eq uptr math-units-table) | |
1528 | (insert "\n")) | |
1529 | (setq name (substring name 1))) | |
1530 | (insert " ") | |
1531 | (and shadowed (insert "(")) | |
1532 | (insert (symbol-name (car u))) | |
1533 | (and shadowed (insert ")")) | |
1534 | (if (nth 3 u) | |
1535 | (progn | |
1536 | (indent-to 10) | |
1537 | (insert (symbol-name (nth 3 u)))) | |
1538 | (or std | |
1539 | (progn | |
1540 | (indent-to 10) | |
1541 | (insert "U")))) | |
1542 | (indent-to 14) | |
1543 | (and shadowed (insert "(")) | |
19bdc4d8 JB |
1544 | (if (nth 5 u) |
1545 | (insert (nth 5 u)) | |
1546 | (if (nth 1 u) | |
1547 | (insert (math-format-value (nth 1 u) 80)) | |
1548 | (insert (symbol-name (car u))))) | |
ed8060d9 JB |
1549 | (and shadowed (insert ")")) |
1550 | (indent-to 41) | |
1551 | (insert " ") | |
1552 | (when name | |
1553 | (insert name)) | |
1554 | (if shadowed | |
1555 | (insert " (redefined above)") | |
1556 | (unless (nth 1 u) | |
1557 | (insert " (base unit)"))) | |
1558 | (insert "\n") | |
1559 | (setq uptr (cdr uptr))) | |
1560 | (insert "\n\nUnit Prefix Table:\n\n") | |
1561 | (setq uptr math-unit-prefixes) | |
1562 | (while uptr | |
1563 | (setq u (car uptr)) | |
1564 | (insert " " (char-to-string (car u))) | |
1565 | (if (equal (nth 1 u) (nth 1 (nth 1 uptr))) | |
1566 | (insert " " (char-to-string (car (car (setq uptr (cdr uptr))))) | |
1567 | " ") | |
1568 | (insert " ")) | |
1569 | (insert "10^" (int-to-string (nth 2 (nth 1 u)))) | |
1570 | (indent-to 15) | |
1571 | (insert " " (nth 2 u) "\n") | |
1572 | (while (eq (car (car (setq uptr (cdr uptr)))) 0))) | |
1265829e JB |
1573 | (insert "\n\n") |
1574 | (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n" | |
1575 | "names will not use the `tex' prefix; the unit name for a\n" | |
1576 | "TeX point will be `pt' instead of `texpt', for example.\n" | |
1577 | "To avoid conflicts, the unit names for pint and parsec will\n" | |
1578 | "be `pint' and `parsec' instead of `pt' and `pc'.")) | |
ed8060d9 | 1579 | (view-mode) |
136211a9 EZ |
1580 | (message "Formatting units table...done")) |
1581 | (setq math-units-table-buffer-valid t) | |
1582 | (let ((oldbuf (current-buffer))) | |
1583 | (set-buffer buf) | |
1584 | (goto-char (point-min)) | |
1585 | (set-buffer oldbuf)) | |
1586 | (if enter-buffer | |
1587 | (pop-to-buffer buf) | |
1588 | (display-buffer buf))) | |
1589 | (if enter-buffer | |
1590 | (pop-to-buffer (get-buffer "*Units Table*")) | |
c9aef719 | 1591 | (display-buffer (get-buffer "*Units Table*"))))) |
136211a9 | 1592 | |
603823f5 JB |
1593 | ;;; Logarithmic units functions |
1594 | ||
1595 | (defvar math-logunits '((var dB var-dB) | |
1596 | (var Np var-Np))) | |
1597 | ||
771fc75e JB |
1598 | (defun math-conditional-apply (fn &rest args) |
1599 | "Evaluate f(args) unless in symbolic mode. | |
1600 | In symbolic mode, return the list (fn args)." | |
1601 | (if calc-symbolic-mode | |
1602 | (cons fn args) | |
1603 | (apply fn args))) | |
1604 | ||
1605 | (defun math-conditional-pow (a b) | |
1606 | "Evaluate a^b unless in symbolic mode. | |
1607 | In symbolic mode, return the list (^ a b)." | |
1608 | (if calc-symbolic-mode | |
1609 | (list '^ a b) | |
1610 | (math-pow a b))) | |
1611 | ||
603823f5 JB |
1612 | (defun math-extract-logunits (expr) |
1613 | (if (memq (car-safe expr) '(* /)) | |
1614 | (cons (car expr) | |
1615 | (mapcar 'math-extract-logunits (cdr expr))) | |
1616 | (if (memq (car-safe expr) '(^)) | |
1617 | (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr)) | |
1618 | (if (member expr math-logunits) expr 1)))) | |
1619 | ||
ec6ad6f2 | 1620 | (defun math-logunits-add (a b neg power) |
603823f5 JB |
1621 | (let ((aunit (math-simplify (math-extract-logunits a)))) |
1622 | (if (not (eq (car-safe aunit) 'var)) | |
1623 | (calc-record-why "*Improper logarithmic unit" aunit) | |
1624 | (let* ((units (math-extract-units a)) | |
1625 | (acoeff (math-simplify (math-remove-units a))) | |
1626 | (bcoeff (math-simplify (math-to-standard-units | |
1627 | (list '/ b units) nil)))) | |
1628 | (if (math-units-in-expr-p bcoeff nil) | |
1629 | (calc-record-why "*Inconsistent units" nil) | |
1630 | (if (and neg | |
1631 | (or (math-lessp acoeff bcoeff) | |
1632 | (math-equal acoeff bcoeff))) | |
1633 | (calc-record-why "*Improper coefficients" nil) | |
da6062e6 | 1634 | (math-mul |
603823f5 | 1635 | (if (equal aunit '(var dB var-dB)) |
6f16becc JB |
1636 | (let ((coef (if power 10 20))) |
1637 | (math-mul coef | |
771fc75e | 1638 | (math-conditional-apply 'calcFunc-log10 |
6f16becc JB |
1639 | (if neg |
1640 | (math-sub | |
771fc75e JB |
1641 | (math-conditional-pow 10 (math-div acoeff coef)) |
1642 | (math-conditional-pow 10 (math-div bcoeff coef))) | |
6f16becc | 1643 | (math-add |
771fc75e JB |
1644 | (math-conditional-pow 10 (math-div acoeff coef)) |
1645 | (math-conditional-pow 10 (math-div bcoeff coef))))))) | |
6f16becc JB |
1646 | (let ((coef (if power 2 1))) |
1647 | (math-div | |
771fc75e | 1648 | (math-conditional-apply 'calcFunc-ln |
6f16becc JB |
1649 | (if neg |
1650 | (math-sub | |
771fc75e JB |
1651 | (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff)) |
1652 | (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff))) | |
6f16becc | 1653 | (math-add |
771fc75e JB |
1654 | (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff)) |
1655 | (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff))))) | |
6f16becc | 1656 | coef))) |
603823f5 JB |
1657 | units))))))) |
1658 | ||
d71990a1 | 1659 | (defun calcFunc-lufadd (a b) |
ec6ad6f2 | 1660 | (math-logunits-add a b nil nil)) |
603823f5 | 1661 | |
d71990a1 | 1662 | (defun calcFunc-lupadd (a b) |
ec6ad6f2 | 1663 | (math-logunits-add a b nil t)) |
603823f5 | 1664 | |
d71990a1 | 1665 | (defun calcFunc-lufsub (a b) |
ec6ad6f2 | 1666 | (math-logunits-add a b t nil)) |
6f16becc | 1667 | |
d71990a1 | 1668 | (defun calcFunc-lupsub (a b) |
ec6ad6f2 | 1669 | (math-logunits-add a b t t)) |
6f16becc | 1670 | |
d71990a1 | 1671 | (defun calc-lu-plus (arg) |
603823f5 JB |
1672 | (interactive "P") |
1673 | (calc-slow-wrapper | |
1674 | (if (calc-is-inverse) | |
6f16becc | 1675 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1676 | (calc-binary-op "lu-" 'calcFunc-lufsub arg) |
1677 | (calc-binary-op "lu-" 'calcFunc-lupsub arg)) | |
6f16becc | 1678 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1679 | (calc-binary-op "lu+" 'calcFunc-lufadd arg) |
1680 | (calc-binary-op "lu+" 'calcFunc-lupadd arg))))) | |
6f16becc | 1681 | |
d71990a1 | 1682 | (defun calc-lu-minus (arg) |
6f16becc JB |
1683 | (interactive "P") |
1684 | (calc-slow-wrapper | |
1685 | (if (calc-is-inverse) | |
1686 | (if (calc-is-hyperbolic) | |
d71990a1 JB |
1687 | (calc-binary-op "lu+" 'calcFunc-lufadd arg) |
1688 | (calc-binary-op "lu+" 'calcFunc-lupadd arg)) | |
6f16becc | 1689 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1690 | (calc-binary-op "lu-" 'calcFunc-lufsub arg) |
1691 | (calc-binary-op "lu-" 'calcFunc-lupsub arg))))) | |
6f16becc | 1692 | |
ec6ad6f2 | 1693 | (defun math-logunits-mul (a b power) |
6f16becc JB |
1694 | (let (logunit coef units number) |
1695 | (cond | |
1696 | ((and | |
1697 | (setq logunit (math-simplify (math-extract-logunits a))) | |
1698 | (eq (car-safe logunit) 'var) | |
1699 | (eq (math-simplify (math-extract-units b)) 1)) | |
1700 | (setq coef (math-simplify (math-remove-units a)) | |
1701 | units (math-extract-units a) | |
1702 | number b)) | |
1703 | ((and | |
1704 | (setq logunit (math-simplify (math-extract-logunits b))) | |
1705 | (eq (car-safe logunit) 'var) | |
1706 | (eq (math-simplify (math-extract-units a)) 1)) | |
1707 | (setq coef (math-simplify (math-remove-units b)) | |
1708 | units (math-extract-units b) | |
1709 | number a)) | |
1710 | (t (setq logunit nil))) | |
1711 | (if logunit | |
1712 | (cond | |
1713 | ((equal logunit '(var dB var-dB)) | |
1714 | (math-simplify | |
1715 | (math-mul | |
1716 | (math-add | |
da6062e6 | 1717 | coef |
6f16becc | 1718 | (math-mul (if power 10 20) |
771fc75e | 1719 | (math-conditional-apply 'calcFunc-log10 number))) |
6f16becc JB |
1720 | units))) |
1721 | (t | |
1722 | (math-simplify | |
1723 | (math-mul | |
1724 | (math-add | |
da6062e6 | 1725 | coef |
771fc75e | 1726 | (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1))) |
6f16becc JB |
1727 | units)))) |
1728 | (calc-record-why "*Improper units" nil)))) | |
1729 | ||
1730 | (defun math-logunits-divide (a b power) | |
1731 | (let ((logunit (math-simplify (math-extract-logunits a)))) | |
1732 | (if (not (eq (car-safe logunit) 'var)) | |
1733 | (calc-record-why "*Improper logarithmic unit" logunit) | |
1734 | (if (math-units-in-expr-p b nil) | |
1735 | (calc-record-why "*Improper units quantity" b) | |
1736 | (let* ((units (math-extract-units a)) | |
1737 | (coef (math-simplify (math-remove-units a)))) | |
1738 | (cond | |
1739 | ((equal logunit '(var dB var-dB)) | |
1740 | (math-simplify | |
1741 | (math-mul | |
1742 | (math-sub | |
da6062e6 | 1743 | coef |
6f16becc | 1744 | (math-mul (if power 10 20) |
771fc75e | 1745 | (math-conditional-apply 'calcFunc-log10 b))) |
6f16becc JB |
1746 | units))) |
1747 | (t | |
1748 | (math-simplify | |
1749 | (math-mul | |
1750 | (math-sub | |
da6062e6 | 1751 | coef |
771fc75e | 1752 | (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1))) |
6f16becc JB |
1753 | units))))))))) |
1754 | ||
d71990a1 | 1755 | (defun calcFunc-lufmul (a b) |
ec6ad6f2 | 1756 | (math-logunits-mul a b nil)) |
6f16becc | 1757 | |
d71990a1 | 1758 | (defun calcFunc-lupmul (a b) |
ec6ad6f2 | 1759 | (math-logunits-mul a b t)) |
6f16becc | 1760 | |
d71990a1 | 1761 | (defun calc-lu-times (arg) |
603823f5 JB |
1762 | (interactive "P") |
1763 | (calc-slow-wrapper | |
1764 | (if (calc-is-inverse) | |
6f16becc | 1765 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1766 | (calc-binary-op "lu/" 'calcFunc-lufdiv arg) |
1767 | (calc-binary-op "lu/" 'calcFunc-lupdiv arg)) | |
6f16becc | 1768 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1769 | (calc-binary-op "lu*" 'calcFunc-lufmul arg) |
1770 | (calc-binary-op "lu*" 'calcFunc-lupmul arg))))) | |
603823f5 | 1771 | |
d71990a1 | 1772 | (defun calcFunc-lufdiv (a b) |
6f16becc | 1773 | (math-logunits-divide a b nil)) |
603823f5 | 1774 | |
d71990a1 | 1775 | (defun calcFunc-lupdiv (a b) |
6f16becc | 1776 | (math-logunits-divide a b t)) |
603823f5 | 1777 | |
d71990a1 | 1778 | (defun calc-lu-divide (arg) |
6f16becc JB |
1779 | (interactive "P") |
1780 | (calc-slow-wrapper | |
1781 | (if (calc-is-inverse) | |
1782 | (if (calc-is-hyperbolic) | |
d71990a1 JB |
1783 | (calc-binary-op "lu*" 'calcFunc-lufmul arg) |
1784 | (calc-binary-op "lu*" 'calcFunc-lupmul arg)) | |
6f16becc | 1785 | (if (calc-is-hyperbolic) |
d71990a1 JB |
1786 | (calc-binary-op "lu/" 'calcFunc-lufdiv arg) |
1787 | (calc-binary-op "lu/" 'calcFunc-lupdiv arg))))) | |
6f16becc JB |
1788 | |
1789 | (defun math-logunits-quant (val ref power) | |
226590f8 JB |
1790 | (let* ((units (math-simplify (math-extract-units val))) |
1791 | (lunit (math-simplify (math-extract-logunits units)))) | |
603823f5 JB |
1792 | (if (not (eq (car-safe lunit) 'var)) |
1793 | (calc-record-why "*Improper logarithmic unit" lunit) | |
226590f8 JB |
1794 | (let ((runits (math-simplify (math-div units lunit))) |
1795 | (coeff (math-simplify (math-div val units)))) | |
1796 | (math-mul | |
1797 | (if (equal lunit '(var dB var-dB)) | |
da6062e6 | 1798 | (math-mul |
226590f8 | 1799 | ref |
da6062e6 | 1800 | (math-conditional-pow |
226590f8 JB |
1801 | 10 |
1802 | (math-div | |
1803 | coeff | |
1804 | (if power 10 20)))) | |
da6062e6 | 1805 | (math-mul |
226590f8 | 1806 | ref |
771fc75e | 1807 | (math-conditional-apply 'calcFunc-exp |
da6062e6 | 1808 | (if power |
226590f8 JB |
1809 | (math-mul 2 coeff) |
1810 | coeff)))) | |
1811 | runits))))) | |
603823f5 | 1812 | |
d71990a1 JB |
1813 | (defvar calc-lu-field-reference) |
1814 | (defvar calc-lu-power-reference) | |
603823f5 | 1815 | |
580b66d8 | 1816 | (defun calcFunc-lufquant (val &optional ref) |
603823f5 | 1817 | (unless ref |
d71990a1 | 1818 | (setq ref (math-read-expr calc-lu-field-reference))) |
6f16becc | 1819 | (math-logunits-quant val ref nil)) |
603823f5 | 1820 | |
580b66d8 | 1821 | (defun calcFunc-lupquant (val &optional ref) |
603823f5 | 1822 | (unless ref |
d71990a1 | 1823 | (setq ref (math-read-expr calc-lu-power-reference))) |
6f16becc JB |
1824 | (math-logunits-quant val ref t)) |
1825 | ||
d71990a1 | 1826 | (defun calc-lu-quant (arg) |
6f16becc JB |
1827 | (interactive "P") |
1828 | (calc-slow-wrapper | |
1829 | (if (calc-is-hyperbolic) | |
1830 | (if (calc-is-option) | |
580b66d8 JB |
1831 | (calc-binary-op "lupq" 'calcFunc-lufquant arg) |
1832 | (calc-unary-op "lupq" 'calcFunc-lufquant arg)) | |
6f16becc | 1833 | (if (calc-is-option) |
580b66d8 JB |
1834 | (calc-binary-op "lufq" 'calcFunc-lupquant arg) |
1835 | (calc-unary-op "lufq" 'calcFunc-lupquant arg))))) | |
6f16becc JB |
1836 | |
1837 | (defun math-logunits-level (val ref db power) | |
1838 | "Compute the value of VAL in decibels or nepers." | |
1839 | (let* ((ratio (math-simplify-units (math-div val ref))) | |
771fc75e | 1840 | (ratiou (math-simplify-units (math-remove-units ratio))) |
6f16becc JB |
1841 | (units (math-simplify (math-extract-units ratio)))) |
1842 | (math-mul | |
1843 | (if db | |
1844 | (math-mul | |
1845 | (math-mul (if power 10 20) | |
771fc75e | 1846 | (math-conditional-apply 'calcFunc-log10 ratiou)) |
6f16becc JB |
1847 | '(var dB var-dB)) |
1848 | (math-mul | |
771fc75e | 1849 | (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1)) |
6f16becc JB |
1850 | '(var Np var-Np))) |
1851 | units))) | |
1852 | ||
d71990a1 | 1853 | (defun calcFunc-dbfield (val &optional ref) |
6f16becc | 1854 | (unless ref |
d71990a1 | 1855 | (setq ref (math-read-expr calc-lu-field-reference))) |
6f16becc JB |
1856 | (math-logunits-level val ref t nil)) |
1857 | ||
d71990a1 | 1858 | (defun calcFunc-dbpower (val &optional ref) |
6f16becc | 1859 | (unless ref |
d71990a1 | 1860 | (setq ref (math-read-expr calc-lu-power-reference))) |
6f16becc JB |
1861 | (math-logunits-level val ref t t)) |
1862 | ||
d71990a1 | 1863 | (defun calcFunc-npfield (val &optional ref) |
6f16becc | 1864 | (unless ref |
d71990a1 | 1865 | (setq ref (math-read-expr calc-lu-field-reference))) |
6f16becc JB |
1866 | (math-logunits-level val ref nil nil)) |
1867 | ||
d71990a1 | 1868 | (defun calcFunc-nppower (val &optional ref) |
6f16becc | 1869 | (unless ref |
d71990a1 | 1870 | (setq ref (math-read-expr calc-lu-power-reference))) |
6f16becc JB |
1871 | (math-logunits-level val ref nil t)) |
1872 | ||
d71990a1 | 1873 | (defun calc-db (arg) |
6f16becc JB |
1874 | (interactive "P") |
1875 | (calc-slow-wrapper | |
1876 | (if (calc-is-hyperbolic) | |
1877 | (if (calc-is-option) | |
d71990a1 JB |
1878 | (calc-binary-op "ludb" 'calcFunc-dbfield arg) |
1879 | (calc-unary-op "ludb" 'calcFunc-dbfield arg)) | |
6f16becc | 1880 | (if (calc-is-option) |
d71990a1 JB |
1881 | (calc-binary-op "ludb" 'calcFunc-dbpower arg) |
1882 | (calc-unary-op "ludb" 'calcFunc-dbpower arg))))) | |
603823f5 | 1883 | |
d71990a1 | 1884 | (defun calc-np (arg) |
603823f5 JB |
1885 | (interactive "P") |
1886 | (calc-slow-wrapper | |
1887 | (if (calc-is-hyperbolic) | |
1888 | (if (calc-is-option) | |
d71990a1 JB |
1889 | (calc-binary-op "lunp" 'calcFunc-npfield arg) |
1890 | (calc-unary-op "lunp" 'calcFunc-npfield arg)) | |
603823f5 | 1891 | (if (calc-is-option) |
d71990a1 JB |
1892 | (calc-binary-op "lunp" 'calcFunc-nppower arg) |
1893 | (calc-unary-op "lunp" 'calcFunc-nppower arg))))) | |
603823f5 | 1894 | |
05a29101 JB |
1895 | ;;; Musical notes |
1896 | ||
1897 | ||
1898 | (defvar calc-note-threshold) | |
1899 | ||
1900 | (defun math-midi-round (num) | |
1901 | "Round NUM to an integer N if NUM is within calc-note-threshold cents of N." | |
1902 | (let* ((n (math-round num)) | |
1903 | (diff (math-abs | |
1904 | (math-sub num n)))) | |
da6062e6 | 1905 | (if (< (math-compare diff |
8f60c820 | 1906 | (math-div (math-read-expr calc-note-threshold) 100)) 0) |
05a29101 JB |
1907 | n |
1908 | num))) | |
1909 | ||
1910 | (defconst math-notes | |
1911 | '(((var C var-C) . 0) | |
1912 | ((var Csharp var-Csharp) . 1) | |
1913 | ; ((var C♯ var-C♯) . 1) | |
1914 | ((var Dflat var-Dflat) . 1) | |
1915 | ; ((var D♭ var-D♭) . 1) | |
1916 | ((var D var-D) . 2) | |
1917 | ((var Dsharp var-Dsharp) . 3) | |
1918 | ; ((var D♯ var-D♯) . 3) | |
1919 | ((var E var-E) . 4) | |
1920 | ((var F var-F) . 5) | |
1921 | ((var Fsharp var-Fsharp) . 6) | |
1922 | ; ((var F♯ var-F♯) . 6) | |
1923 | ((var Gflat var-Gflat) . 6) | |
1924 | ; ((var G♭ var-G♭) . 6) | |
1925 | ((var G var-G) . 7) | |
1926 | ((var Gsharp var-Gsharp) . 8) | |
1927 | ; ((var G♯ var-G♯) . 8) | |
1928 | ((var A var-A) . 9) | |
1929 | ((var Asharp var-Asharp) . 10) | |
1930 | ; ((var A♯ var-A♯) . 10) | |
1931 | ((var Bflat var-Bflat) . 10) | |
1932 | ; ((var B♭ var-B♭) . 10) | |
1933 | ((var B var-B) . 11)) | |
1934 | "An alist of notes with their number of semitones above C.") | |
1935 | ||
1936 | (defun math-freqp (freq) | |
1937 | "Non-nil if FREQ is a positive number times the unit Hz. | |
1938 | If non-nil, return the coefficient of Hz." | |
1939 | (let ((freqcoef (math-simplify-units | |
1940 | (math-div freq '(var Hz var-Hz))))) | |
1941 | (if (Math-posp freqcoef) freqcoef))) | |
1942 | ||
1943 | (defun math-midip (num) | |
1944 | "Non-nil if NUM is a possible MIDI note number. | |
1945 | If non-nil, return NUM." | |
1946 | (if (Math-numberp num) num)) | |
1947 | ||
1948 | (defun math-spnp (spn) | |
1949 | "Non-nil if NUM is a scientific pitch note (note + cents). | |
1950 | If non-nil, return a list consisting of the note and the cents coefficient." | |
1951 | (let (note cents rnote rcents) | |
1952 | (if (eq (car-safe spn) '+) | |
1953 | (setq note (nth 1 spn) | |
1954 | cents (nth 2 spn)) | |
1955 | (setq note spn | |
1956 | cents nil)) | |
1957 | (cond | |
1958 | ((and ;; NOTE is a note, CENTS is nil or cents. | |
1959 | (eq (car-safe note) 'calcFunc-subscr) | |
1960 | (assoc (nth 1 note) math-notes) | |
1961 | (integerp (nth 2 note)) | |
1962 | (setq rnote note) | |
da6062e6 | 1963 | (or |
05a29101 JB |
1964 | (not cents) |
1965 | (Math-numberp (setq rcents | |
da6062e6 | 1966 | (math-simplify |
05a29101 JB |
1967 | (math-div cents '(var cents var-cents))))))) |
1968 | (list rnote rcents)) | |
1969 | ((and ;; CENTS is a note, NOTE is cents. | |
1970 | (eq (car-safe cents) 'calcFunc-subscr) | |
1971 | (assoc (nth 1 cents) math-notes) | |
1972 | (integerp (nth 2 cents)) | |
1973 | (setq rnote cents) | |
da6062e6 | 1974 | (or |
05a29101 JB |
1975 | (not note) |
1976 | (Math-numberp (setq rcents | |
da6062e6 | 1977 | (math-simplify |
05a29101 JB |
1978 | (math-div note '(var cents var-cents))))))) |
1979 | (list rnote rcents))))) | |
1980 | ||
1981 | (defun math-freq-to-midi (freq) | |
1982 | "Return the midi note number corresponding to FREQ Hz." | |
1983 | (let ((midi (math-add | |
1984 | 69 | |
1985 | (math-mul | |
1986 | 12 | |
1987 | (calcFunc-log | |
1988 | (math-div freq 440) | |
1989 | 2))))) | |
1990 | (math-midi-round midi))) | |
1991 | ||
1992 | (defun math-spn-to-midi (spn) | |
1993 | "Return the MIDI number corresponding to SPN." | |
1994 | (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes))) | |
1995 | (octave (math-add (nth 2 (car spn)) 1)) | |
1996 | (cents (nth 1 spn)) | |
1997 | (midi (math-add | |
1998 | (math-mul 12 octave) | |
1999 | note))) | |
2000 | (if cents | |
2001 | (math-add midi (math-div cents 100)) | |
2002 | midi))) | |
2003 | ||
2004 | (defun math-midi-to-spn (midi) | |
2005 | "Return the scientific pitch notation corresponding to midi number MIDI." | |
2006 | (let (midin cents) | |
2007 | (if (math-integerp midi) | |
da6062e6 | 2008 | (setq midin midi |
05a29101 JB |
2009 | cents nil) |
2010 | (setq midin (math-floor midi) | |
2011 | cents (math-mul 100 (math-sub midi midin)))) | |
2012 | (let* ((nr ;; This should be (math-idivmod midin 12), but with | |
2013 | ;; better behavior for negative midin. | |
2014 | (if (Math-negp midin) | |
2015 | (let ((dm (math-idivmod (math-neg midin) 12))) | |
2016 | (if (= (cdr dm) 0) | |
2017 | (cons (math-neg (car dm)) 0) | |
2018 | (cons | |
2019 | (math-sub (math-neg (car dm)) 1) | |
2020 | (math-sub 12 (cdr dm))))) | |
2021 | (math-idivmod midin 12))) | |
2022 | (n (math-sub (car nr) 1)) | |
2023 | (note (car (rassoc (cdr nr) math-notes)))) | |
2024 | (if cents | |
da6062e6 | 2025 | (list '+ (list 'calcFunc-subscr note n) |
05a29101 JB |
2026 | (list '* cents '(var cents var-cents))) |
2027 | (list 'calcFunc-subscr note n))))) | |
2028 | ||
2029 | (defun math-freq-to-spn (freq) | |
2030 | "Return the scientific pitch notation corresponding to FREQ Hz." | |
2031 | (math-with-extra-prec 3 | |
2032 | (math-midi-to-spn (math-freq-to-midi freq)))) | |
2033 | ||
2034 | (defun math-midi-to-freq (midi) | |
2035 | "Return the frequency of the note with midi number MIDI." | |
2036 | (list '* | |
2037 | (math-mul | |
2038 | 440 | |
2039 | (math-pow | |
2040 | 2 | |
da6062e6 | 2041 | (math-div |
05a29101 JB |
2042 | (math-sub |
2043 | midi | |
2044 | 69) | |
2045 | 12))) | |
2046 | '(var Hz var-Hz))) | |
2047 | ||
2048 | (defun math-spn-to-freq (spn) | |
2049 | "Return the frequency of the note with scientific pitch notation SPN." | |
2050 | (math-midi-to-freq (math-spn-to-midi spn))) | |
2051 | ||
2052 | (defun calcFunc-spn (expr) | |
2053 | "Return EXPR written as scientific pitch notation + cents." | |
da6062e6 | 2054 | ;; Get the coefficient of Hz |
05a29101 JB |
2055 | (let (note) |
2056 | (cond | |
2057 | ((setq note (math-freqp expr)) | |
2058 | (math-freq-to-spn note)) | |
2059 | ((setq note (math-midip expr)) | |
2060 | (math-midi-to-spn note)) | |
2061 | ((math-spnp expr) | |
2062 | expr) | |
2063 | (t | |
2064 | (math-reject-arg expr "*Improper expression"))))) | |
2065 | ||
2066 | (defun calcFunc-midi (expr) | |
2067 | "Return EXPR written as a MIDI number." | |
2068 | (let (note) | |
2069 | (cond | |
2070 | ((setq note (math-freqp expr)) | |
2071 | (math-freq-to-midi note)) | |
2072 | ((setq note (math-spnp expr)) | |
2073 | (math-spn-to-midi note)) | |
2074 | ((math-midip expr) | |
2075 | expr) | |
2076 | (t | |
2077 | (math-reject-arg expr "*Improper expression"))))) | |
2078 | ||
2079 | (defun calcFunc-freq (expr) | |
2080 | "Return the frequency corresponding to EXPR." | |
2081 | (let (note) | |
2082 | (cond | |
2083 | ((setq note (math-midip expr)) | |
2084 | (math-midi-to-freq note)) | |
2085 | ((setq note (math-spnp expr)) | |
2086 | (math-spn-to-freq note)) | |
2087 | ((math-freqp expr) | |
2088 | expr) | |
2089 | (t | |
2090 | (math-reject-arg expr "*Improper expression"))))) | |
2091 | ||
2092 | (defun calc-freq (arg) | |
2093 | "Return the frequency corresponding to the expression on the stack." | |
2094 | (interactive "P") | |
2095 | (calc-slow-wrapper | |
2096 | (calc-unary-op "freq" 'calcFunc-freq arg))) | |
2097 | ||
2098 | (defun calc-midi (arg) | |
2099 | "Return the MIDI number corresponding to the expression on the stack." | |
2100 | (interactive "P") | |
2101 | (calc-slow-wrapper | |
2102 | (calc-unary-op "midi" 'calcFunc-midi arg))) | |
2103 | ||
2104 | (defun calc-spn (arg) | |
2105 | "Return the scientific pitch notation corresponding to the expression on the stack." | |
2106 | (interactive "P") | |
2107 | (calc-slow-wrapper | |
2108 | (calc-unary-op "spn" 'calcFunc-spn arg))) | |
2109 | ||
2110 | ||
7d02e8cd JB |
2111 | (provide 'calc-units) |
2112 | ||
be19ef0b GM |
2113 | ;; Local variables: |
2114 | ;; coding: utf-8 | |
2115 | ;; End: | |
2116 | ||
c9aef719 | 2117 | ;;; calc-units.el ends here |