;;; calc-units.el --- unit conversion functions for Calc
-;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, 2005,
-;; 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+;; Copyright (C) 1990-1993, 2001-2011 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
"149597870691 m (*)")
;; (approx) NASA JPL (http://neo.jpl.nasa.gov/glossary/au.html)
( lyr "c yr" "Light Year" )
- ( pc "3.0856775854*10^16 m" "Parsec" nil
+ ( pc "3.0856775854*10^16 m" "Parsec (**)" nil
"3.0856775854 10^16 m (*)") ;; (approx) ESUWM
( nmi "1852 m" "Nautical Mile" )
( fath "6 ft" "Fathom" )
( fur "660 ft" "Furlong")
( mu "1 um" "Micron" )
( mil "(1/1000) in" "Mil" )
- ( point "(1/72) in" "Point (1/72 inch)" )
+ ( point "(1/72) in" "Point (PostScript convention)" )
( Ang "10^(-10) m" "Angstrom" )
( mfi "mi+ft+in" "Miles + feet + inches" )
;; TeX lengths
- ( texpt "(100/7227) in" "Point (TeX conventions)" )
- ( texpc "12 texpt" "Pica" )
- ( texbp "point" "Big point (TeX conventions)" )
- ( texdd "(1238/1157) texpt" "Didot point" )
- ( texcc "12 texdd" "Cicero" )
- ( texsp "(1/65536) texpt" "Scaled TeX point" )
+ ( texpt "(100/7227) in" "Point (TeX convention) (**)" )
+ ( texpc "12 texpt" "Pica (TeX convention) (**)" )
+ ( texbp "point" "Big point (TeX convention) (**)" )
+ ( texdd "(1238/1157) texpt" "Didot point (TeX convention) (**)" )
+ ( texcc "12 texdd" "Cicero (TeX convention) (**)" )
+ ( texsp "(1/65536) texpt" "Scaled TeX point (TeX convention) (**)" )
;; Area
( hect "10000 m^2" "*Hectare" )
( l "L" "Liter" )
( gal "4 qt" "US Gallon" )
( qt "2 pt" "Quart" )
- ( pt "2 cup" "Pint" )
+ ( pt "2 cup" "Pint (**)" )
( cup "8 ozfl" "Cup" )
( ozfl "2 tbsp" "Fluid Ounce" )
( floz "2 tbsp" "Fluid Ounce" )
( R0 "8.314472 J/(mol K)" "Molar gas constant" nil
"8.314472 J/(mol K) (*)")
( V0 "22.710981*10^(-3) m^3/mol" "Standard volume of ideal gas" nil
- "22.710981 10^-3 m^3/mol (*)")))
+ "22.710981 10^-3 m^3/mol (*)")
+ ;; Logarithmic units
+ ( Np nil "*Neper")
+ ( dB "(ln(10)/20) Np" "decibel")))
(defvar math-additional-units nil
(or (eq (nth 1 expr) 'pi)
(error "Unknown name %s in defining expression for unit %s"
(nth 1 expr) (car math-fbu-entry))))
+ ((equal expr '(calcFunc-ln 10)))
(t (error "Malformed defining expression for unit %s" (car math-fbu-entry))))))
(if (eq base 'pi)
(math-pi)
expr)))
- (if (Math-primp expr)
+ (if (or
+ (Math-primp expr)
+ (and (eq (car-safe expr) 'calcFunc-subscr)
+ (eq (car-safe (nth 1 expr)) 'var)))
expr
(cons (car expr)
(mapcar 'math-to-standard-rec (cdr expr))))))
(indent-to 15)
(insert " " (nth 2 u) "\n")
(while (eq (car (car (setq uptr (cdr uptr)))) 0)))
- (insert "\n"))
+ (insert "\n\n")
+ (insert "(**) When in TeX or LaTeX display mode, the TeX specific unit\n"
+ "names will not use the `tex' prefix; the unit name for a\n"
+ "TeX point will be `pt' instead of `texpt', for example.\n"
+ "To avoid conflicts, the unit names for pint and parsec will\n"
+ "be `pint' and `parsec' instead of `pt' and `pc'."))
(view-mode)
(message "Formatting units table...done"))
(setq math-units-table-buffer-valid t)
(pop-to-buffer (get-buffer "*Units Table*"))
(display-buffer (get-buffer "*Units Table*")))))
+;;; Logarithmic units functions
+
+(defvar math-logunits '((var dB var-dB)
+ (var Np var-Np)))
+
+(defun math-conditional-apply (fn &rest args)
+ "Evaluate f(args) unless in symbolic mode.
+In symbolic mode, return the list (fn args)."
+ (if calc-symbolic-mode
+ (cons fn args)
+ (apply fn args)))
+
+(defun math-conditional-pow (a b)
+ "Evaluate a^b unless in symbolic mode.
+In symbolic mode, return the list (^ a b)."
+ (if calc-symbolic-mode
+ (list '^ a b)
+ (math-pow a b)))
+
+(defun math-extract-logunits (expr)
+ (if (memq (car-safe expr) '(* /))
+ (cons (car expr)
+ (mapcar 'math-extract-logunits (cdr expr)))
+ (if (memq (car-safe expr) '(^))
+ (list '^ (math-extract-logunits (nth 1 expr)) (nth 2 expr))
+ (if (member expr math-logunits) expr 1))))
+
+(defun math-logunits-add (a b neg power)
+ (let ((aunit (math-simplify (math-extract-logunits a))))
+ (if (not (eq (car-safe aunit) 'var))
+ (calc-record-why "*Improper logarithmic unit" aunit)
+ (let* ((units (math-extract-units a))
+ (acoeff (math-simplify (math-remove-units a)))
+ (bcoeff (math-simplify (math-to-standard-units
+ (list '/ b units) nil))))
+ (if (math-units-in-expr-p bcoeff nil)
+ (calc-record-why "*Inconsistent units" nil)
+ (if (and neg
+ (or (math-lessp acoeff bcoeff)
+ (math-equal acoeff bcoeff)))
+ (calc-record-why "*Improper coefficients" nil)
+ (math-mul
+ (if (equal aunit '(var dB var-dB))
+ (let ((coef (if power 10 20)))
+ (math-mul coef
+ (math-conditional-apply 'calcFunc-log10
+ (if neg
+ (math-sub
+ (math-conditional-pow 10 (math-div acoeff coef))
+ (math-conditional-pow 10 (math-div bcoeff coef)))
+ (math-add
+ (math-conditional-pow 10 (math-div acoeff coef))
+ (math-conditional-pow 10 (math-div bcoeff coef)))))))
+ (let ((coef (if power 2 1)))
+ (math-div
+ (math-conditional-apply 'calcFunc-ln
+ (if neg
+ (math-sub
+ (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
+ (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))
+ (math-add
+ (math-conditional-apply 'calcFunc-exp (math-mul coef acoeff))
+ (math-conditional-apply 'calcFunc-exp (math-mul coef bcoeff)))))
+ coef)))
+ units)))))))
+
+(defun calcFunc-lufadd (a b)
+ (math-logunits-add a b nil nil))
+
+(defun calcFunc-lupadd (a b)
+ (math-logunits-add a b nil t))
+
+(defun calcFunc-lufsub (a b)
+ (math-logunits-add a b t nil))
+
+(defun calcFunc-lupsub (a b)
+ (math-logunits-add a b t t))
+
+(defun calc-lu-plus (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu-" 'calcFunc-lufsub arg)
+ (calc-binary-op "lu-" 'calcFunc-lupsub arg))
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu+" 'calcFunc-lufadd arg)
+ (calc-binary-op "lu+" 'calcFunc-lupadd arg)))))
+
+(defun calc-lu-minus (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu+" 'calcFunc-lufadd arg)
+ (calc-binary-op "lu+" 'calcFunc-lupadd arg))
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu-" 'calcFunc-lufsub arg)
+ (calc-binary-op "lu-" 'calcFunc-lupsub arg)))))
+
+(defun math-logunits-mul (a b power)
+ (let (logunit coef units number)
+ (cond
+ ((and
+ (setq logunit (math-simplify (math-extract-logunits a)))
+ (eq (car-safe logunit) 'var)
+ (eq (math-simplify (math-extract-units b)) 1))
+ (setq coef (math-simplify (math-remove-units a))
+ units (math-extract-units a)
+ number b))
+ ((and
+ (setq logunit (math-simplify (math-extract-logunits b)))
+ (eq (car-safe logunit) 'var)
+ (eq (math-simplify (math-extract-units a)) 1))
+ (setq coef (math-simplify (math-remove-units b))
+ units (math-extract-units b)
+ number a))
+ (t (setq logunit nil)))
+ (if logunit
+ (cond
+ ((equal logunit '(var dB var-dB))
+ (math-simplify
+ (math-mul
+ (math-add
+ coef
+ (math-mul (if power 10 20)
+ (math-conditional-apply 'calcFunc-log10 number)))
+ units)))
+ (t
+ (math-simplify
+ (math-mul
+ (math-add
+ coef
+ (math-div (math-conditional-apply 'calcFunc-ln number) (if power 2 1)))
+ units))))
+ (calc-record-why "*Improper units" nil))))
+
+(defun math-logunits-divide (a b power)
+ (let ((logunit (math-simplify (math-extract-logunits a))))
+ (if (not (eq (car-safe logunit) 'var))
+ (calc-record-why "*Improper logarithmic unit" logunit)
+ (if (math-units-in-expr-p b nil)
+ (calc-record-why "*Improper units quantity" b)
+ (let* ((units (math-extract-units a))
+ (coef (math-simplify (math-remove-units a))))
+ (cond
+ ((equal logunit '(var dB var-dB))
+ (math-simplify
+ (math-mul
+ (math-sub
+ coef
+ (math-mul (if power 10 20)
+ (math-conditional-apply 'calcFunc-log10 b)))
+ units)))
+ (t
+ (math-simplify
+ (math-mul
+ (math-sub
+ coef
+ (math-div (math-conditional-apply 'calcFunc-ln b) (if power 2 1)))
+ units)))))))))
+
+(defun calcFunc-lufmul (a b)
+ (math-logunits-mul a b nil))
+
+(defun calcFunc-lupmul (a b)
+ (math-logunits-mul a b t))
+
+(defun calc-lu-times (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
+ (calc-binary-op "lu/" 'calcFunc-lupdiv arg))
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu*" 'calcFunc-lufmul arg)
+ (calc-binary-op "lu*" 'calcFunc-lupmul arg)))))
+
+(defun calcFunc-lufdiv (a b)
+ (math-logunits-divide a b nil))
+
+(defun calcFunc-lupdiv (a b)
+ (math-logunits-divide a b t))
+
+(defun calc-lu-divide (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu*" 'calcFunc-lufmul arg)
+ (calc-binary-op "lu*" 'calcFunc-lupmul arg))
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "lu/" 'calcFunc-lufdiv arg)
+ (calc-binary-op "lu/" 'calcFunc-lupdiv arg)))))
+
+(defun math-logunits-quant (val ref power)
+ (let* ((units (math-simplify (math-extract-units val)))
+ (lunit (math-simplify (math-extract-logunits units))))
+ (if (not (eq (car-safe lunit) 'var))
+ (calc-record-why "*Improper logarithmic unit" lunit)
+ (let ((runits (math-simplify (math-div units lunit)))
+ (coeff (math-simplify (math-div val units))))
+ (math-mul
+ (if (equal lunit '(var dB var-dB))
+ (math-mul
+ ref
+ (math-conditional-pow
+ 10
+ (math-div
+ coeff
+ (if power 10 20))))
+ (math-mul
+ ref
+ (math-conditional-apply 'calcFunc-exp
+ (if power
+ (math-mul 2 coeff)
+ coeff))))
+ runits)))))
+
+(defvar calc-lu-field-reference)
+(defvar calc-lu-power-reference)
+
+(defun calcFunc-lufquant (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-field-reference)))
+ (math-logunits-quant val ref nil))
+
+(defun calcFunc-lupquant (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-power-reference)))
+ (math-logunits-quant val ref t))
+
+(defun calc-lu-quant (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-hyperbolic)
+ (if (calc-is-option)
+ (calc-binary-op "lupq" 'calcFunc-lufquant arg)
+ (calc-unary-op "lupq" 'calcFunc-lufquant arg))
+ (if (calc-is-option)
+ (calc-binary-op "lufq" 'calcFunc-lupquant arg)
+ (calc-unary-op "lufq" 'calcFunc-lupquant arg)))))
+
+(defun math-logunits-level (val ref db power)
+ "Compute the value of VAL in decibels or nepers."
+ (let* ((ratio (math-simplify-units (math-div val ref)))
+ (ratiou (math-simplify-units (math-remove-units ratio)))
+ (units (math-simplify (math-extract-units ratio))))
+ (math-mul
+ (if db
+ (math-mul
+ (math-mul (if power 10 20)
+ (math-conditional-apply 'calcFunc-log10 ratiou))
+ '(var dB var-dB))
+ (math-mul
+ (math-div (math-conditional-apply 'calcFunc-ln ratiou) (if power 2 1))
+ '(var Np var-Np)))
+ units)))
+
+(defun calcFunc-dbfield (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-field-reference)))
+ (math-logunits-level val ref t nil))
+
+(defun calcFunc-dbpower (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-power-reference)))
+ (math-logunits-level val ref t t))
+
+(defun calcFunc-npfield (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-field-reference)))
+ (math-logunits-level val ref nil nil))
+
+(defun calcFunc-nppower (val &optional ref)
+ (unless ref
+ (setq ref (math-read-expr calc-lu-power-reference)))
+ (math-logunits-level val ref nil t))
+
+(defun calc-db (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-hyperbolic)
+ (if (calc-is-option)
+ (calc-binary-op "ludb" 'calcFunc-dbfield arg)
+ (calc-unary-op "ludb" 'calcFunc-dbfield arg))
+ (if (calc-is-option)
+ (calc-binary-op "ludb" 'calcFunc-dbpower arg)
+ (calc-unary-op "ludb" 'calcFunc-dbpower arg)))))
+
+(defun calc-np (arg)
+ (interactive "P")
+ (calc-slow-wrapper
+ (if (calc-is-hyperbolic)
+ (if (calc-is-option)
+ (calc-binary-op "lunp" 'calcFunc-npfield arg)
+ (calc-unary-op "lunp" 'calcFunc-npfield arg))
+ (if (calc-is-option)
+ (calc-binary-op "lunp" 'calcFunc-nppower arg)
+ (calc-unary-op "lunp" 'calcFunc-nppower arg)))))
+
+;;; Musical notes
+
+
+(defvar calc-note-threshold)
+
+(defun math-midi-round (num)
+ "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
+ (let* ((n (math-round num))
+ (diff (math-abs
+ (math-sub num n))))
+ (if (< (math-compare diff
+ (math-div (math-read-expr calc-note-threshold) 100)) 0)
+ n
+ num)))
+
+(defconst math-notes
+ '(((var C var-C) . 0)
+ ((var Csharp var-Csharp) . 1)
+; ((var C♯ var-C♯) . 1)
+ ((var Dflat var-Dflat) . 1)
+; ((var D♭ var-D♭) . 1)
+ ((var D var-D) . 2)
+ ((var Dsharp var-Dsharp) . 3)
+; ((var D♯ var-D♯) . 3)
+ ((var E var-E) . 4)
+ ((var F var-F) . 5)
+ ((var Fsharp var-Fsharp) . 6)
+; ((var F♯ var-F♯) . 6)
+ ((var Gflat var-Gflat) . 6)
+; ((var G♭ var-G♭) . 6)
+ ((var G var-G) . 7)
+ ((var Gsharp var-Gsharp) . 8)
+; ((var G♯ var-G♯) . 8)
+ ((var A var-A) . 9)
+ ((var Asharp var-Asharp) . 10)
+; ((var A♯ var-A♯) . 10)
+ ((var Bflat var-Bflat) . 10)
+; ((var B♭ var-B♭) . 10)
+ ((var B var-B) . 11))
+ "An alist of notes with their number of semitones above C.")
+
+(defun math-freqp (freq)
+ "Non-nil if FREQ is a positive number times the unit Hz.
+If non-nil, return the coefficient of Hz."
+ (let ((freqcoef (math-simplify-units
+ (math-div freq '(var Hz var-Hz)))))
+ (if (Math-posp freqcoef) freqcoef)))
+
+(defun math-midip (num)
+ "Non-nil if NUM is a possible MIDI note number.
+If non-nil, return NUM."
+ (if (Math-numberp num) num))
+
+(defun math-spnp (spn)
+ "Non-nil if NUM is a scientific pitch note (note + cents).
+If non-nil, return a list consisting of the note and the cents coefficient."
+ (let (note cents rnote rcents)
+ (if (eq (car-safe spn) '+)
+ (setq note (nth 1 spn)
+ cents (nth 2 spn))
+ (setq note spn
+ cents nil))
+ (cond
+ ((and ;; NOTE is a note, CENTS is nil or cents.
+ (eq (car-safe note) 'calcFunc-subscr)
+ (assoc (nth 1 note) math-notes)
+ (integerp (nth 2 note))
+ (setq rnote note)
+ (or
+ (not cents)
+ (Math-numberp (setq rcents
+ (math-simplify
+ (math-div cents '(var cents var-cents)))))))
+ (list rnote rcents))
+ ((and ;; CENTS is a note, NOTE is cents.
+ (eq (car-safe cents) 'calcFunc-subscr)
+ (assoc (nth 1 cents) math-notes)
+ (integerp (nth 2 cents))
+ (setq rnote cents)
+ (or
+ (not note)
+ (Math-numberp (setq rcents
+ (math-simplify
+ (math-div note '(var cents var-cents)))))))
+ (list rnote rcents)))))
+
+(defun math-freq-to-midi (freq)
+ "Return the midi note number corresponding to FREQ Hz."
+ (let ((midi (math-add
+ 69
+ (math-mul
+ 12
+ (calcFunc-log
+ (math-div freq 440)
+ 2)))))
+ (math-midi-round midi)))
+
+(defun math-spn-to-midi (spn)
+ "Return the MIDI number corresponding to SPN."
+ (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
+ (octave (math-add (nth 2 (car spn)) 1))
+ (cents (nth 1 spn))
+ (midi (math-add
+ (math-mul 12 octave)
+ note)))
+ (if cents
+ (math-add midi (math-div cents 100))
+ midi)))
+
+(defun math-midi-to-spn (midi)
+ "Return the scientific pitch notation corresponding to midi number MIDI."
+ (let (midin cents)
+ (if (math-integerp midi)
+ (setq midin midi
+ cents nil)
+ (setq midin (math-floor midi)
+ cents (math-mul 100 (math-sub midi midin))))
+ (let* ((nr ;; This should be (math-idivmod midin 12), but with
+ ;; better behavior for negative midin.
+ (if (Math-negp midin)
+ (let ((dm (math-idivmod (math-neg midin) 12)))
+ (if (= (cdr dm) 0)
+ (cons (math-neg (car dm)) 0)
+ (cons
+ (math-sub (math-neg (car dm)) 1)
+ (math-sub 12 (cdr dm)))))
+ (math-idivmod midin 12)))
+ (n (math-sub (car nr) 1))
+ (note (car (rassoc (cdr nr) math-notes))))
+ (if cents
+ (list '+ (list 'calcFunc-subscr note n)
+ (list '* cents '(var cents var-cents)))
+ (list 'calcFunc-subscr note n)))))
+
+(defun math-freq-to-spn (freq)
+ "Return the scientific pitch notation corresponding to FREQ Hz."
+ (math-with-extra-prec 3
+ (math-midi-to-spn (math-freq-to-midi freq))))
+
+(defun math-midi-to-freq (midi)
+ "Return the frequency of the note with midi number MIDI."
+ (list '*
+ (math-mul
+ 440
+ (math-pow
+ 2
+ (math-div
+ (math-sub
+ midi
+ 69)
+ 12)))
+ '(var Hz var-Hz)))
+
+(defun math-spn-to-freq (spn)
+ "Return the frequency of the note with scientific pitch notation SPN."
+ (math-midi-to-freq (math-spn-to-midi spn)))
+
+(defun calcFunc-spn (expr)
+ "Return EXPR written as scientific pitch notation + cents."
+ ;; Get the coeffecient of Hz
+ (let (note)
+ (cond
+ ((setq note (math-freqp expr))
+ (math-freq-to-spn note))
+ ((setq note (math-midip expr))
+ (math-midi-to-spn note))
+ ((math-spnp expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calcFunc-midi (expr)
+ "Return EXPR written as a MIDI number."
+ (let (note)
+ (cond
+ ((setq note (math-freqp expr))
+ (math-freq-to-midi note))
+ ((setq note (math-spnp expr))
+ (math-spn-to-midi note))
+ ((math-midip expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calcFunc-freq (expr)
+ "Return the frequency corresponding to EXPR."
+ (let (note)
+ (cond
+ ((setq note (math-midip expr))
+ (math-midi-to-freq note))
+ ((setq note (math-spnp expr))
+ (math-spn-to-freq note))
+ ((math-freqp expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calc-freq (arg)
+ "Return the frequency corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "freq" 'calcFunc-freq arg)))
+
+(defun calc-midi (arg)
+ "Return the MIDI number corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "midi" 'calcFunc-midi arg)))
+
+(defun calc-spn (arg)
+ "Return the scientific pitch notation corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "spn" 'calcFunc-spn arg)))
+
+
(provide 'calc-units)
;; Local variables:
;; coding: utf-8
;; End:
-;; arch-tag: e993314f-3adc-4191-be61-4ef8874881c4
;;; calc-units.el ends here