1 ;;; calc-units.el --- unit conversion functions for Calc
3 ;; Copyright (C) 1990-1993, 2001-2011 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8 ;; This file is part of GNU Emacs.
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.
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.
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/>.
27 ;; This file is autoloaded from calc-ext.el.
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
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.
47 (defvar math-standard-units
50 ( in
"254*10^(-2) cm" "Inch" nil
54 ( mi
"5280 ft" "Mile" )
55 ( au
"149597870691. m" "Astronomical Unit" nil
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" )
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) (**)" )
78 ( hect
"10000 m^2" "*Hectare" )
80 ( acre
"(1/640) mi^2" "Acre" )
81 ( b
"10^(-28) m^2" "Barn" )
84 ( L
"10^(-3) m^3" "*Liter" )
86 ( gal
"4 qt" "US Gallon" )
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
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
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
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
122 ( ga
"980665*10^(-5) m/s^2" "*\"g\" acceleration" nil
123 "9.80665 m / s^2") ;; CODATA
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
140 ( u
"1.660538782*10^(-27) kg" "Unified atomic mass" nil
141 "1.660538782 10^-27 kg (*)");;(approx) CODATA
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
154 ( erg
"10^(-7) J" "Erg" )
155 ( cal
"41868*10^(-4) J" "International Table Calorie" nil
157 ( calth
"4184*10^(-3) J" "Thermochemical Calorie" nil
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")
175 ( hp
"550 ft lbf/s" "Horsepower") ;;ESUWM
176 ( hpm
"75 m kgf/s" "Metric Horsepower") ;;ESUWM
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
)
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
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" )
200 ( P
"(1/10) Pa s" "*Poise" )
201 ( St
"10^(-4) m^2/s" "Stokes" )
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
214 ( S
"A/V" "Siemens" )
217 ( T
"Wb/m^2" "Tesla" )
218 ( Gs
"10^(-4) T" "Gauss" )
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
232 ( Bq
"1/s" "*Becquerel" )
233 ( Ci
"37*10^9 Bq" "Curie" ) ;; ESUWM
235 ( Sv
"Gy" "Sievert" )
236 ( R
"258*10^(-6) C/kg" "Roentgen" ) ;; NIST
237 ( rd
"(1/100) Gy" "Rad" )
240 ;; Amount of substance
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" )
254 ( sr nil
"*Steradian" )
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 ( μ
0 "mu0" "Permeability of vacuum") ;; Exact
263 ( eps0
"1 / (mu0 c^2)" "Permittivity of vacuum" )
264 ( ε
0 "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 (*)")
301 ( dB
"(ln(10)/20) Np" "decibel")))
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.")
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" )
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" )))
336 (defvar math-standard-units-systems
338 ( si
( ( g
'(/ (var kg var-kg
) 1000) ) ) )
339 ( mks
( ( g
'(/ (var kg var-kg
) 1000) ) ) )
340 ( cgs
( ( m
'(* (var cm var-cm
) 100 ) ) ) )))
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).")
347 (defvar math-units-table-buffer-valid nil
)
351 (defun calc-base-units ()
354 (let ((calc-autorange-units nil
))
355 (calc-enter-result 1 "bsun" (math-simplify-units
356 (math-to-standard-units (calc-top-n 1)
359 (defun calc-quick-units ()
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
)
377 (math-mul expr
(nth pos units
))))))))
379 (defun math-get-standard-units (expr)
380 "Return the standard units in EXPR."
383 (math-to-standard-units expr nil
))))
385 (defun math-get-units (expr)
386 "Return the units in EXPR."
388 (math-extract-units expr
)))
390 (defun math-make-unit-string (expr)
391 "Return EXPR in string form.
392 If EXPR is nil, return nil."
394 (let ((cexpr (math-compose-expr expr
0)))
395 (replace-regexp-in-string
399 (math-composition-to-string cexpr
))))))
401 (defvar math-default-units-table
402 (make-hash-table :test
'equal
)
403 "A table storing previously converted units.")
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
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
)))))
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
422 math-default-units-table
)))
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
)))))
432 (defun calc-convert-units (&optional old-units new-units
)
435 (let ((expr (calc-top-n 1))
440 (unless (math-units-in-expr-p expr t
)
441 (let ((uold (or old-units
443 (setq uoldname
(read-string "Old units: "))
444 (if (equal uoldname
"")
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
))))
455 (setq defunits
(math-get-default-units expr
))
459 (concat "Old units: "
471 (string= new-units
"")
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
))))
484 (calc-enter-result 1 "cvun" (math-simplify-units
485 (math-to-standard-units expr
488 (error "No units specified"))
489 (calc-enter-result 1 "cvun"
492 (and uoldname
(not (equal uoldname
"1"))))))))))
494 (defun calc-autorange-units (arg)
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"))))
502 (defun calc-convert-temperature (&optional old-units new-units
)
505 (let ((expr (calc-top-n 1))
510 (setq uold
(or old-units
511 (let ((units (math-single-units-in-expr-p expr
)))
514 (list 'var
(car units
)
515 (intern (concat "var-"
518 (error "Not a pure temperature expression"))
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
531 (concat "Old temperature units: "
534 "New temperature units")
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
546 (math-convert-temperature expr uold unew
548 (if (Math-zerop ntemp
)
549 (setq ntemp
(list '* ntemp unew
)))
550 (let ((calc-simplify-mode 'none
))
551 (calc-enter-result 1 "cvtm" ntemp
))))))
553 (defun calc-remove-units ()
556 (calc-enter-result 1 "rmun" (math-simplify-units
557 (math-remove-units (calc-top-n 1))))))
559 (defun calc-extract-units ()
562 (calc-enter-result 1 "rmun" (math-simplify-units
563 (math-extract-units (calc-top-n 1))))))
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
)
571 (defun calc-explain-units ()
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 "^[^(].* .*[^)]$" calc-den-units
)
578 (setq calc-den-units
(concat "(" calc-den-units
")")))
581 (message "%s per %s" calc-num-units calc-den-units
)
582 (message "%s" calc-num-units
))
584 (message "1 per %s" calc-den-units
)
585 (message "No units in expression"))))))
587 (defun calc-explain-units-rec (expr pow
)
588 (let ((u (math-check-unit-name expr
))
590 (if (and u
(not (math-zerop pow
)))
591 (let ((name (or (nth 2 u
) (symbol-name (car u
)))))
592 (if (eq (aref name
0) ?\
*)
593 (setq name
(substring name
1)))
594 (if (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name
)
595 (if (string-match "^[a-zA-Zα-ωΑ-Ω0-9' ()]*$" 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
605 (if (and (string-match "[^a-zA-Zα-ωΑ-Ω0-9']" name
)
606 (not (memq (car u
) '(mHg gf
))))
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"))))
622 (setq name
(concat name
"^"
623 (math-format-number (math-abs pow
))))))
625 (setq calc-num-units
(if calc-num-units
626 (concat calc-num-units
" " name
)
628 (setq calc-den-units
(if calc-den-units
629 (concat calc-den-units
" " 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
))))))))
644 (defun calc-simplify-units ()
647 (calc-with-default-simplification
648 (calc-enter-result 1 "smun" (math-simplify-units (calc-top-n 1))))))
650 (defun calc-view-units-table (n)
652 (and n
(setq math-units-table-buffer-valid nil
))
653 (let ((win (get-buffer-window "*Units Table*")))
656 math-units-table-buffer-valid
)
658 (bury-buffer (window-buffer win
))
659 (let ((curwin (selected-window)))
661 (switch-to-buffer nil
)
662 (select-window curwin
)))
663 (math-build-units-table-buffer nil
))))
665 (defun calc-enter-units-table (n)
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")))
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: ")))
675 (let ((form (calc-top-n 1))
676 (unit (assq uname math-additional-units
)))
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
""))
689 (setcar (cdr (cdr (cdr (cdr unit
)))) disp
))))
690 (calc-invalidate-units-table))
692 (defun calc-undefine-unit (uname)
693 (interactive "SUndefine unit name: ")
695 (let ((unit (assq uname math-additional-units
)))
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))
704 (defun calc-invalidate-units-table ()
705 (setq math-units-table nil
)
706 (let ((buf (get-buffer "*Units Table*")))
708 (with-current-buffer buf
710 (goto-char (point-min))
711 (if (looking-at "Calculator Units Table")
712 (let ((inhibit-read-only t
))
713 (insert "(Obsolete) "))))))))
715 (defun calc-get-unit-definition (uname)
716 (interactive "SGet definition for unit: ")
718 (math-build-units-table)
719 (let ((unit (assq uname math-units-table
)))
721 (error "Unit name \"%s\" not found" uname
))
722 (let ((msg (nth 2 unit
)))
724 (if (string-match "^\\*" msg
)
725 (setq msg
(substring msg
1)))
726 (setq msg
(symbol-name uname
)))
729 (calc-enter-result 0 "ugdf" (nth 1 unit
))
730 (message "Derived unit: %s" msg
))
731 (calc-enter-result 0 "ugdf" (list 'var uname
734 (symbol-name uname
)))))
735 (message "Base unit: %s" msg
))))))
737 (defun calc-permanent-units ()
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
)
748 (search-forward "\n;;; End of custom units" nil t
)))
752 (delete-region pos
(point)))
753 (goto-char (point-max))
756 (insert ";;; Custom units stored by Calc on " (current-time-string) "\n")
757 (if math-additional-units
759 (insert "(setq math-additional-units '(\n")
760 (let ((list math-additional-units
))
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)))
770 (prin1-to-string (nth 2 (car list
)))
772 (setq list
(cdr list
))))
774 (insert ";;; (no custom units defined)\n"))
775 (insert ";;; End of custom units\n")
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
)
786 (defun math-build-units-table ()
788 (let* ((combined-units (append math-additional-units
789 math-standard-units
))
790 (math-cu-unit-list (mapcar 'car combined-units
))
792 (message "Building units table...")
793 (setq math-units-table-buffer-valid nil
)
794 (setq tab
(mapcar (function
798 (if (stringp (nth 1 x
))
799 (let ((exp (math-read-plain-expr
801 (if (eq (car-safe exp
) 'error
)
802 (error "Format error in definition of %s in units table: %s"
809 (list (cons (car x
) 1)))
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
))))
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
)
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
)
828 (setcar (nthcdr 4 math-fbu-entry
) 'boom
)
829 (math-find-base-units-rec (nth 1 math-fbu-entry
) 1)
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
))
836 (if (eq (cdr (car (cdr b
))) 0)
837 (setcdr b
(cdr (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
)
843 (defun math-compare-unit-names (a b
)
844 (memq (car b
) (cdr (memq (car a
) math-cu-unit-list
))))
846 (defun math-find-base-units-rec (expr pow
)
847 (let ((u (math-check-unit-name expr
)))
849 (let ((ulist (math-find-base-units u
)))
851 (let ((p (* (cdr (car ulist
)) pow
))
852 (old (assq (car (car ulist
)) math-fbu-base
)))
854 (setcdr old
(+ (cdr old
) p
))
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
))))
863 (math-find-base-units-rec (nth 1 expr
) pow
)
864 (math-find-base-units-rec (nth 2 expr
) pow
))
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
))
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
))))))
880 (defun math-units-in-expr-p (expr sub-exprs
)
882 (if (eq (car expr
) 'var
)
883 (math-check-unit-name expr
)
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
))))))
889 (defun math-only-units-in-expr-p (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
))))))))
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
))
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
)
911 (if (math-units-in-expr-p (nth 2 expr
) nil
)
913 (math-single-units-in-expr-p (nth 1 expr
))))
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
)
925 (eq (aref name
1) ?e
)
926 (eq (aref name
2) ?g
)
927 (assq (intern (substring name
3))
928 math-units-table
))))))))
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
)
935 (defun math-to-standard-units (expr math-which-standard
)
936 (math-to-standard-rec expr
))
938 (defun math-to-standard-rec (expr)
939 (if (eq (car-safe expr
) 'var
)
940 (let ((u (math-check-unit-name expr
))
945 (setq expr
(math-to-standard-rec (nth 1 u
)))
946 (let ((st (assq (car u
) math-which-standard
)))
948 (setq expr
(nth 1 st
))
949 (setq expr
(list 'var
(car u
)
950 (intern (concat "var-"
956 (nth 1 (assq (aref (symbol-name base
) 0)
965 (and (eq (car-safe expr
) 'calcFunc-subscr
)
966 (eq (car-safe (nth 1 expr
)) 'var
)))
969 (mapcar 'math-to-standard-rec
(cdr expr
))))))
971 (defun math-apply-units (expr units ulist
&optional pure
)
972 (setq expr
(math-simplify-units expr
))
976 (or (math-numberp expr
)
977 (error "Incompatible units"))
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
))))
986 (math-add new
(math-mul (math-div expr
(nth 1 (car ulist
)))
990 (math-simplify-units (list '* expr units
)))))
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
))
1004 (while (eq (car-safe utemp
) '+)
1005 (setq ulist
(cons (math-decompose-unit-part (nth 2 utemp
))
1007 utemp
(nth 1 utemp
)))
1008 (setq ulist
(cons (math-decompose-unit-part 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
1018 (not (Math-lessp (nth 1 x
)
1020 (cdr math-decompose-units-cache
))))
1022 (defun math-decompose-unit-part (unit)
1024 (math-is-multiple (math-simplify-units (math-to-standard-units
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.
1033 (defun math-find-compatible-unit (expr unit
)
1034 (let ((math-fcu-u (math-check-unit-name unit
)))
1036 (math-find-compatible-unit-rec expr
1))))
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
))))
1049 (let ((u2 (math-check-unit-name expr
)))
1050 (if (equal (nth 4 math-fcu-u
) (nth 4 u2
))
1051 (cons expr pow
))))))
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
)
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
))
1071 (math-simplify-units
1072 (math-mul (math-mul (math-simplify-units
1073 (math-div expr
(math-pow (car 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
)
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
))))))
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
)
1099 (mapcar 'math-convert-units-rec
(cdr expr
))))))
1101 (defun math-convert-temperature (expr old new
&optional pure
)
1102 (let* ((units (math-single-units-in-expr-p expr
))
1104 (if (or (null units
)
1105 (equal (nth 1 old
) (car units
)))
1106 (math-check-unit-name old
)
1107 (error "Inconsistent temperature 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)))))
1128 (setq expr
(list '* (list '- expr
32) '(/ 5 9)))
1129 (if (eq (nth 3 unew
) 'K
)
1130 (setq expr
(list '+ expr
'(/ 27315 100)))))))
1133 (list '* expr new
))))
1137 (defun math-simplify-units (a)
1138 (let ((math-simplifying-units t
)
1139 (calc-matrix-mode 'scalar
))
1141 (defalias 'calcFunc-usimplify
'math-simplify-units
)
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
)
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
)
1155 (calc-record-why "*Inconsistent units" 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
))
1163 (math-simplify-units-prod))
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
)))
1173 (pow (if (eq (car math-simplify-expr
) '*) 1 -
1))
1175 (and (eq (car-safe unit
) '*)
1176 (setq unitp
(cdr unit
)
1178 (and (eq (car-safe unit
) '^
)
1179 (integerp (nth 2 unit
))
1180 (setq pow
(* pow
(nth 2 unit
))
1183 (and (setq u
(math-check-unit-name unit
))
1186 (>= xpon
(if (eq (car u
) 'm
) 1 3)))
1189 (reverse math-unit-prefixes
)
1190 math-unit-prefixes
))
1193 (or (eq (car u
) (nth 1 unit
))
1198 math-unit-prefixes
))))))
1199 (setq xpon
(+ xpon uxpon
))
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
)))
1207 (setq pname
(math-build-var-name
1208 (if (eq (car (car p
)) 0)
1210 (concat (char-to-string
1214 (and (/= (car (car p
)) 0)
1216 math-units-table
)))))
1220 (or (not (eq p pref
))
1221 (< xpon
(+ pxpon
(* (math-abs pow
) 3))))
1223 (setcar (cdr math-simplify-expr
)
1224 (let ((calc-prefer-frac nil
))
1225 (calcFunc-scf (nth 1 math-simplify-expr
)
1227 (setcar unitp pname
)
1228 math-simplify-expr
)))))))
1230 (defvar math-try-cancel-units
)
1233 (and math-simplifying-units
1234 (let ((np (cdr math-simplify-expr
))
1235 (math-try-cancel-units 0)
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
))
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
)))))
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
)))
1260 (defun math-simplify-units-divisor (np dp
)
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
))
1267 (setq dp
(cdr (cdr d
))))
1268 (when (setq temp
(math-simplify-units-quotient n d
))
1269 (setcar np
(setq n temp
))
1272 ;; Simplify, e.g., "in / cm" to "2.54" in a units expression.
1273 (defun math-simplify-units-quotient (n d
)
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
)))
1285 (if (and (equal (nth 4 un
) (nth 4 ud
))
1288 (math-to-standard-units (list '/ n d
) nil
)
1289 (list '^
(math-to-standard-units (list '/ n d
) nil
) pow1
))
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
)))
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
)))))
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)))))
1325 (math-defsimplify (calcFunc-floor
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
)))))))))
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
))))
1361 (math-units-are-multiple u d
)
1362 (list '^
(math-to-standard-units a nil
) pow
)))))
1365 (defun math-units-are-multiple (u n
)
1367 (while (and u
(= (%
(cdr (car u
)) n
) 0))
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
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
))))))
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
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
))))))
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
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
))))))
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
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
))))))
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
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
))))))
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
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
))))))
1450 (defun math-remove-units (expr)
1451 (if (math-check-unit-name expr
)
1453 (if (Math-primp expr
)
1456 (mapcar 'math-remove-units
(cdr expr
))))))
1458 (defun math-extract-units (expr)
1459 (if (memq (car-safe expr
) '(* /))
1461 (mapcar 'math-extract-units
(cdr expr
)))
1462 (if (math-check-unit-name expr
) expr
1)))
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 ".")
1478 (message "Formatting units table...")
1480 (let ((inhibit-read-only t
))
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")
1488 (when (eq (car u
) 'm
)
1490 (setq shadowed
(and std
(assq (car u
) math-additional-units
)))
1493 (eq (aref name
0) ?\
*))
1494 (unless (eq uptr math-units-table
)
1496 (setq name
(substring name
1)))
1498 (and shadowed
(insert "("))
1499 (insert (symbol-name (car u
)))
1500 (and shadowed
(insert ")"))
1504 (insert (symbol-name (nth 3 u
))))
1510 (and shadowed
(insert "("))
1514 (insert (math-format-value (nth 1 u
) 80))
1515 (insert (symbol-name (car u
)))))
1516 (and shadowed
(insert ")"))
1522 (insert " (redefined above)")
1524 (insert " (base unit)")))
1526 (setq uptr
(cdr uptr
)))
1527 (insert "\n\nUnit Prefix Table:\n\n")
1528 (setq uptr math-unit-prefixes
)
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
)))))
1536 (insert "10^" (int-to-string (nth 2 (nth 1 u
))))
1538 (insert " " (nth 2 u
) "\n")
1539 (while (eq (car (car (setq uptr
(cdr uptr
)))) 0)))
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'."))
1547 (message "Formatting units table...done"))
1548 (setq math-units-table-buffer-valid t
)
1549 (let ((oldbuf (current-buffer)))
1551 (goto-char (point-min))
1552 (set-buffer oldbuf
))
1555 (display-buffer buf
)))
1557 (pop-to-buffer (get-buffer "*Units Table*"))
1558 (display-buffer (get-buffer "*Units Table*")))))
1560 ;;; Logarithmic units functions
1562 (defvar math-logunits
'((var dB var-dB
)
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
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
1579 (defun math-extract-logunits (expr)
1580 (if (memq (car-safe 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))))
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
)
1598 (or (math-lessp acoeff bcoeff
)
1599 (math-equal acoeff bcoeff
)))
1600 (calc-record-why "*Improper coefficients" nil
)
1602 (if (equal aunit
'(var dB var-dB
))
1603 (let ((coef (if power
10 20)))
1605 (math-conditional-apply 'calcFunc-log10
1608 (math-conditional-pow 10 (math-div acoeff coef
))
1609 (math-conditional-pow 10 (math-div bcoeff coef
)))
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)))
1615 (math-conditional-apply 'calcFunc-ln
1618 (math-conditional-apply 'calcFunc-exp
(math-mul coef acoeff
))
1619 (math-conditional-apply 'calcFunc-exp
(math-mul coef bcoeff
)))
1621 (math-conditional-apply 'calcFunc-exp
(math-mul coef acoeff
))
1622 (math-conditional-apply 'calcFunc-exp
(math-mul coef bcoeff
)))))
1626 (defun calcFunc-lufadd (a b
)
1627 (math-logunits-add a b nil nil
))
1629 (defun calcFunc-lupadd (a b
)
1630 (math-logunits-add a b nil t
))
1632 (defun calcFunc-lufsub (a b
)
1633 (math-logunits-add a b t nil
))
1635 (defun calcFunc-lupsub (a b
)
1636 (math-logunits-add a b t t
))
1638 (defun calc-lu-plus (arg)
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
)))))
1649 (defun calc-lu-minus (arg)
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
)))))
1660 (defun math-logunits-mul (a b power
)
1661 (let (logunit coef units number
)
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
)
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
)
1677 (t (setq logunit nil
)))
1680 ((equal logunit
'(var dB var-dB
))
1685 (math-mul (if power
10 20)
1686 (math-conditional-apply 'calcFunc-log10 number
)))
1693 (math-div (math-conditional-apply 'calcFunc-ln number
) (if power
2 1)))
1695 (calc-record-why "*Improper units" nil
))))
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
))))
1706 ((equal logunit
'(var dB var-dB
))
1711 (math-mul (if power
10 20)
1712 (math-conditional-apply 'calcFunc-log10 b
)))
1719 (math-div (math-conditional-apply 'calcFunc-ln b
) (if power
2 1)))
1722 (defun calcFunc-lufmul (a b
)
1723 (math-logunits-mul a b nil
))
1725 (defun calcFunc-lupmul (a b
)
1726 (math-logunits-mul a b t
))
1728 (defun calc-lu-times (arg)
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
)))))
1739 (defun calcFunc-lufdiv (a b
)
1740 (math-logunits-divide a b nil
))
1742 (defun calcFunc-lupdiv (a b
)
1743 (math-logunits-divide a b t
))
1745 (defun calc-lu-divide (arg)
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
)))))
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
))))
1764 (if (equal lunit
'(var dB var-dB
))
1767 (math-conditional-pow
1774 (math-conditional-apply 'calcFunc-exp
1780 (defvar calc-lu-field-reference
)
1781 (defvar calc-lu-power-reference
)
1783 (defun calcFunc-lufquant (val &optional ref
)
1785 (setq ref
(math-read-expr calc-lu-field-reference
)))
1786 (math-logunits-quant val ref nil
))
1788 (defun calcFunc-lupquant (val &optional ref
)
1790 (setq ref
(math-read-expr calc-lu-power-reference
)))
1791 (math-logunits-quant val ref t
))
1793 (defun calc-lu-quant (arg)
1796 (if (calc-is-hyperbolic)
1797 (if (calc-is-option)
1798 (calc-binary-op "lupq" 'calcFunc-lufquant arg
)
1799 (calc-unary-op "lupq" 'calcFunc-lufquant arg
))
1800 (if (calc-is-option)
1801 (calc-binary-op "lufq" 'calcFunc-lupquant arg
)
1802 (calc-unary-op "lufq" 'calcFunc-lupquant arg
)))))
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
))))
1812 (math-mul (if power
10 20)
1813 (math-conditional-apply 'calcFunc-log10 ratiou
))
1816 (math-div (math-conditional-apply 'calcFunc-ln ratiou
) (if power
2 1))
1820 (defun calcFunc-dbfield (val &optional ref
)
1822 (setq ref
(math-read-expr calc-lu-field-reference
)))
1823 (math-logunits-level val ref t nil
))
1825 (defun calcFunc-dbpower (val &optional ref
)
1827 (setq ref
(math-read-expr calc-lu-power-reference
)))
1828 (math-logunits-level val ref t t
))
1830 (defun calcFunc-npfield (val &optional ref
)
1832 (setq ref
(math-read-expr calc-lu-field-reference
)))
1833 (math-logunits-level val ref nil nil
))
1835 (defun calcFunc-nppower (val &optional ref
)
1837 (setq ref
(math-read-expr calc-lu-power-reference
)))
1838 (math-logunits-level val ref nil t
))
1840 (defun calc-db (arg)
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
)))))
1851 (defun calc-np (arg)
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
)))))
1865 (defvar calc-note-threshold
)
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
))
1872 (if (< (math-compare diff
1873 (math-div (math-read-expr calc-note-threshold
) 100)) 0)
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)
1884 ((var Dsharp var-Dsharp
) .
3)
1885 ; ((var D♯ var-D♯) . 3)
1888 ((var Fsharp var-Fsharp
) .
6)
1889 ; ((var F♯ var-F♯) . 6)
1890 ((var Gflat var-Gflat
) .
6)
1891 ; ((var G♭ var-G♭) . 6)
1893 ((var Gsharp var-Gsharp
) .
8)
1894 ; ((var G♯ var-G♯) . 8)
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.")
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
)))
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
))
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
)
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
))
1932 (Math-numberp (setq rcents
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
))
1943 (Math-numberp (setq rcents
1945 (math-div note
'(var cents var-cents
)))))))
1946 (list rnote rcents
)))))
1948 (defun math-freq-to-midi (freq)
1949 "Return the midi note number corresponding to FREQ Hz."
1950 (let ((midi (math-add
1957 (math-midi-round midi
)))
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))
1965 (math-mul 12 octave
)
1968 (math-add midi
(math-div cents
100))
1971 (defun math-midi-to-spn (midi)
1972 "Return the scientific pitch notation corresponding to midi number MIDI."
1974 (if (math-integerp midi
)
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)))
1984 (cons (math-neg (car dm
)) 0)
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
))))
1992 (list '+ (list 'calcFunc-subscr note n
)
1993 (list '* cents
'(var cents var-cents
)))
1994 (list 'calcFunc-subscr note n
)))))
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
))))
2001 (defun math-midi-to-freq (midi)
2002 "Return the frequency of the note with midi number MIDI."
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
)))
2019 (defun calcFunc-spn (expr)
2020 "Return EXPR written as scientific pitch notation + cents."
2021 ;; Get the coeffecient of Hz
2024 ((setq note
(math-freqp expr
))
2025 (math-freq-to-spn note
))
2026 ((setq note
(math-midip expr
))
2027 (math-midi-to-spn note
))
2031 (math-reject-arg expr
"*Improper expression")))))
2033 (defun calcFunc-midi (expr)
2034 "Return EXPR written as a MIDI number."
2037 ((setq note
(math-freqp expr
))
2038 (math-freq-to-midi note
))
2039 ((setq note
(math-spnp expr
))
2040 (math-spn-to-midi note
))
2044 (math-reject-arg expr
"*Improper expression")))))
2046 (defun calcFunc-freq (expr)
2047 "Return the frequency corresponding to EXPR."
2050 ((setq note
(math-midip expr
))
2051 (math-midi-to-freq note
))
2052 ((setq note
(math-spnp expr
))
2053 (math-spn-to-freq note
))
2057 (math-reject-arg expr
"*Improper expression")))))
2059 (defun calc-freq (arg)
2060 "Return the frequency corresponding to the expression on the stack."
2063 (calc-unary-op "freq" 'calcFunc-freq arg
)))
2065 (defun calc-midi (arg)
2066 "Return the MIDI number corresponding to the expression on the stack."
2069 (calc-unary-op "midi" 'calcFunc-midi arg
)))
2071 (defun calc-spn (arg)
2072 "Return the scientific pitch notation corresponding to the expression on the stack."
2075 (calc-unary-op "spn" 'calcFunc-spn arg
)))
2078 (provide 'calc-units
)
2084 ;;; calc-units.el ends here