@setchapternewpage odd
@comment %**end of header (This is for running Texinfo on a region.)
+@include emacsver.texi
+
@c The following macros are used for conditional output for single lines.
@c @texline foo
@c `foo' will appear only in TeX output
This file documents Calc, the GNU Emacs calculator.
@end ifinfo
@ifnotinfo
-This file documents Calc, the GNU Emacs calculator, included with GNU Emacs 23.1.
+This file documents Calc, the GNU Emacs calculator, included with
+GNU Emacs @value{EMACSVER}.
@end ifnotinfo
-Copyright @copyright{} 1990, 1991, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+Copyright @copyright{} 1990-1991, 2001-2011 Free Software Foundation, Inc.
@quotation
Permission is granted to copy, distribute and/or modify this document
@end quotation
@end copying
-@dircategory Emacs
+@dircategory Emacs misc features
@direntry
* Calc: (calc). Advanced desk calculator and mathematical tool.
@end direntry
@texline @math{\sin(2 + x)}.
@infoline @expr{sin(2 + x)}.
+The @TeX{} specific unit names (@pxref{Predefined Units}) will not use
+the @samp{tex} prefix; the unit name for a @TeX{} point will be
+@samp{pt} instead of @samp{texpt}, for example.
+
Function and variable names not treated specially by @TeX{} and La@TeX{}
are simply written out as-is, which will cause them to come out in
italic letters in the printed document. If you invoke @kbd{d T} or
* The Units Table::
* Predefined Units::
* User-Defined Units::
+* Logarithmic Units::
@end menu
@node Basic Operations on Units, The Units Table, Units, Units
@code{texcc} (a Cicero) and @code{texsp} (a scaled @TeX{} point,
all dimensions representable in @TeX{} are multiples of this value).
+When Calc is using the @TeX{} or La@TeX{} language mode (@pxref{TeX
+and LaTeX Language Modes}), the @TeX{} specific unit names will not
+use the @samp{tex} prefix; the unit name for a @TeX{} point will be
+@samp{pt} instead of @samp{texpt}, for example. To avoid conflicts,
+the unit names for pint and parsec will simply be @samp{pint} and
+@samp{parsec} instead of @samp{pt} and @samp{pc}.
+
+
The unit @code{e} stands for the elementary (electron) unit of charge;
because algebra command could mistake this for the special constant
@expr{e}, Calc provides the alternate unit name @code{ech} which is
@c Describe angular units, luminosity vs. steradians problem.
-@node User-Defined Units, , Predefined Units, Units
+@node User-Defined Units, Logarithmic Units, Predefined Units, Units
@section User-Defined Units
@noindent
is replaced by the new set. (@xref{General Mode Commands}, for a way to
tell Calc to use a different file for the Calc init file.)
+@node Logarithmic Units, , User-Defined Units, Units
+@section Logarithmic Units
+
+The units @code{dB} (decibels) and @code{Np} (nepers) are logarithmic
+units which are typically manipulated differently than standard units.
+Calc provides commands to work with these logarithmic units.
+
+Decibels and nepers are used to measure power quantities as well as
+field quantities (quantities whose squares are proportional to power).
+The decibel and neper values of a quantity are relative to
+a reference quantity; for example, the decibel value of a sound
+pressure level of
+@infoline @math{60 uPa}
+@texline @math{60 \mu{\rm Pa}}
+relative to
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+(the threshhold of human hearing) is
+@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB},
+@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}},
+which is about
+@infoline @math{9.54 dB}.
+@texline @math{9.54 {\rm dB}}.
+Note that in taking the ratio, the original units cancel and so these
+logarithmic units are dimensionless.
+
+@vindex calc-logunits-power-reference
+@vindex calc-logunits-field-reference
+The Calc commands for the logarithmic units assume that power quantities
+are being used unless the @kbd{H} prefix is used, in which case they assume that
+field quantities are being used. For power quantities, Calc uses
+@infoline @math{1 mW}
+@texline @math{1 {\rm mW}}
+as the default reference quantity; this default can be changed by changing
+the value of the customizable variable
+@code{calc-logunits-power-reference} (@pxref{Customizing Calc}).
+For field quantities, Calc uses
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+as the default reference quantity; this is the value used in acoustics
+which is where decibels are commonly encountered. This default can be
+changed by changing the value of the customizable variable
+@code{calc-logunits-field-reference} (@pxref{Customizing Calc}). A
+non-default reference quantity will be read from the stack if the
+capital @kbd{O} prefix is used.
+
+The decibel level of a power
+@infoline @math{P1},
+@texline @math{P_1},
+relative to a reference power
+@infoline @math{P0},
+@texline @math{P_0},
+is defined to be
+@infoline @math{10 log10(P1/P0) dB}.
+@texline @math{10 \log_{10}(P_{1}/P_{0}) {\rm dB}}.
+(The factor of 10 is because a decibel, as its name implies, is
+one-tenth of a bel. The bel, named after Alexander Graham Bell, was
+considered to be too large of a unit and was effectively replaced by
+the decibel.) If @math{F} is a field quantity with power
+@math{P=k F^2}, then a reference quantity of
+@infoline @math{F0}
+@texline @math{F_0}
+would correspond to a power of
+@infoline @math{P0=k F0^2}.
+@texline @math{P_{0}=kF_{0}^2}.
+If
+@infoline @math{P1=k F1^2},
+@texline @math{P_{1}=kF_{1}^2},
+then
+
+@ifnottex
+@example
+10 log10(P1/P0) = 10 log10(F1^2/F0^2) = 20 log10(F1/F0).
+@end example
+@end ifnottex
+@tex
+$$ 10 \log_{10}(P_1/P_0) = 10 \log_{10}(F_1^2/F_0^2) = 20
+\log_{10}(F_1/F_0)$$
+@end tex
+
+@noindent
+In order to get the same decibel level regardless of whether a field
+quantity or the corresponding power quantity is used, the decibel
+level of a field quantity
+@infoline @math{F1},
+@texline @math{F_1},
+relative to a reference
+@infoline @math{F0},
+@texline @math{F_0},
+is defined as
+@infoline @math{20 log10(F1/F0) dB}.
+@texline @math{20 \log_{10}(F_{1}/F_{0}) {\rm dB}}.
+
+Nepers (named after John Napier, who is credited with inventing the
+logarithm) are similar to bels except they use natural logarithms instead
+of common logarithms. The neper level of a power
+@infoline @math{P1},
+@texline @math{P_1},
+relative to a reference power
+@infoline @math{P0},
+@texline @math{P_0},
+is
+@infoline @math{(1/2) ln(P1/P0) Np}.
+@texline @math{(1/2) \ln(P_1/P_0) {\rm Np}}.
+The neper level of a field
+@infoline @math{F1},
+@texline @math{F_1},
+relative to a reference field
+@infoline @math{F0},
+@texline @math{F_0},
+is
+@infoline @math{ln(F1/F0) Np}.
+@texline @math{\ln(F_1/F_0) {\rm Np}}.
+
+@kindex l q
+@pindex calc-logunits-quantity
+@tindex powerquant
+@tindex fieldquant
+The @kbd{l q} (@code{calc-logunits-quantity}) [@code{powerquant}]
+command computes the power quantity corresponding to a given number of
+logarithmic units. With the capital @kbd{O} prefix, @kbd{O l q}, the
+reference level will be read from the top of the stack. (In an
+algebraic formula, @code{powerquant} can be given an optional second
+argument which will be used for the reference level.) For example,
+@code{20 dB @key{RET} l q} will return @code{100 mW};
+@code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}.
+The @kbd{H l q} [@code{fieldquant}] command behaves like @kbd{l q} but
+computes field quantities instead of power quantities.
+
+@kindex l d
+@pindex calc-dblevel
+@tindex dbpowerlevel
+@tindex dbfieldlevel
+@kindex l n
+@pindex calc-nplevel
+@tindex nppowerlevel
+@tindex npfieldlevel
+The @kbd{l d} (@code{calc-dblevel}) [@code{dbpowerlevel}]
+command will compute the decibel level of a power quantity using the
+default reference level; @kbd{H l d} [@code{dbfieldlevel}] will
+compute the decibel level of a field quantity. The commands @kbd{l n}
+(@code{calc-nplevel}) [@code{nppowerlevel}] and @kbd{H l n}
+[@code{npfieldlevel}] will similarly compute neper levels. With the
+capital @kbd{O} prefix these commands will read a reference level
+from the stack; in an algebraic formula the reference level can be
+given as an optional second argument.
+
+@kindex l +
+@pindex calc-logunits-add
+@tindex lupoweradd
+@tindex lufieldadd
+@kindex l -
+@pindex calc-logunits-sub
+@tindex lupowersub
+@tindex lufieldsub
+@kindex l *
+@pindex calc-logunits-mul
+@tindex lupowermul
+@tindex lufieldmul
+@kindex l /
+@pindex calc-logunits-div
+@tindex lupowerdiv
+@tindex lufielddiv
+The sum of two power or field quantities doesn't correspond to the sum
+of the corresponding decibel or neper levels. If the powers
+corresponding to decibel levels
+@infoline @math{D1}
+@texline @math{D_1}
+and
+@infoline @math{D2}
+@texline @math{D_2}
+are added, the corresponding decibel level ``sum'' will be
+
+@ifnottex
+@example
+ 10 log10(10^(D1/10) + 10^(D2/10)) dB.
+@end example
+@end ifnottex
+@tex
+$$ 10 \log_{10}(10^{D_1/10} + 10^{D_2/10}) {\rm dB}.$$
+@end tex
+
+@noindent
+When field quantities are combined, it often means the
+corresponding powers are added and so the above formula might be used.
+In acoustics, for example, the decibel sound pressure level is defined
+using the field formula but the sound pressure levels are combined
+as the sound power levels, and so the above formula should be used. If
+two field quantities themselves are added, the new decibel level will be
+
+
+@ifnottex
+@example
+ 20 log10(10^(D1/20) + 10^(D2/20)) dB.
+@end example
+@end ifnottex
+@tex
+$$ 20 \log_{10}(10^{D_1/20} + 10^{D_2/20}) {\rm dB}.$$
+@end tex
+
+@noindent
+If the power corresponding to @math{D} dB is multiplied by a number @math{N},
+then the corresponding decibel level will be
+
+@ifnottex
+@example
+ D + 10 log10(N) dB,
+@end example
+@end ifnottex
+@tex
+$$ D + 10 \log_{10}(N) {\rm dB},$$
+@end tex
+
+@noindent
+if a field quantity is multiplied by @math{N} the corresponding decibel level
+will be
+
+@ifnottex
+@example
+ D + 20 log10(N) dB.
+@end example
+@end ifnottex
+@tex
+$$ D + 20 \log_{10}(N) {\rm dB}.$$
+@end tex
+
+@noindent
+There are similar formulas for combining nepers.
+The @kbd{l +} (@code{calc-logunits-add}) [@code{lupoweradd}] command
+will ``add'' two logarithmic unit power levels this way; with the
+@kbd{H} prefix, @kbd{H l +} [@code{lufieldadd}] will add logarithmic
+unit field levels. Similarly, logarithmic units can be
+``subtracted'' with @kbd{l -} (@code{calc-logunits-sub})
+[@code{lupowersub}] or @kbd{H l -} [@code{lufieldsub}].
+The @kbd{l *} (@code{calc-logunits-mul}) [@code{lupowermul}]
+and @kbd{H l *} [@code{lufieldmul}] commands will ``multiply''
+a logarithmic unit by a number; the @kbd{l /}
+(@code{calc-logunits-divide}) [@code{lupowerdiv}] and
+@kbd{H l /} [@code{lufielddiv}] commands will ``divide'' a
+logarithmic unit by a number. Note that the reference quantities don't
+play a role in this arithmetic.
+
@node Store and Recall, Graphics, Units, Top
@chapter Storing and Recalling
and @code{calc-embedded-open-close-plain-alist}.
@end defvar
+@defvar calc-logunits-power-reference
+@defvarx calc-logunits-field-reference
+See @ref{Logarithmic Units}.@*
+The variables @code{calc-logunits-power-reference} and
+@code{calc-logunits-field-reference} are unit expressions (written as
+strings) which Calc will use as reference quantities for logarithmic
+units.
+
+The default value of @code{calc-logunits-power-reference} is @code{"mW"}
+and the default value of @code{calc-logunits-field-reference} is
+@code{"20 uPa"}.
+@end defvar
+
@defvar calc-highlight-selections-with-faces
@defvarx calc-selected-face
@defvarx calc-nonselected-face
@r{ v x@: k T @: @: @:utpt@:(x,v)}
@r{ v x@: I k T @: @: @:ltpt@:(x,v)}
+@c
+@r{ a b@: l + @: @: 2 @:lupoweradd@:(a,b)}
+@r{ a b@: H l + @: @: 2 @:lufieldadd@:(a,b)}
+@r{ a b@: l - @: @: 2 @:lupowersub@:(a,b)}
+@r{ a b@: H l - @: @: 2 @:lufieldsub@:(a,b)}
+@r{ a b@: l * @: @: 2 @:lupowermul@:(a,b)}
+@r{ a b@: H l * @: @: 2 @:lufieldmul@:(a,b)}
+@r{ a b@: l / @: @: 2 @:lupowerdiv@:(a,b)}
+@r{ a b@: H l / @: @: 2 @:lufielddiv@:(a,b)}
+@r{ a@: l d @: @: 1 @:dbpowerlevel@:(a)}
+@r{ a b@: O l d @: @: 2 @:dbpowerlevel@:(a,b)}
+@r{ a@: H l d @: @: 1 @:dbfieldlevel@:(a)}
+@r{ a b@: O H l d @: @: 2 @:dbfieldlevel@:(a,b)}
+@r{ a@: l n @: @: 1 @:nppowerlevel@:(a)}
+@r{ a b@: O l n @: @: 2 @:nppowerlevel@:(a,b)}
+@r{ a@: H l n @: @: 1 @:npfieldlevel@:(a)}
+@r{ a b@: O H l n @: @: 2 @:npfieldlevel@:(a,b)}
+@r{ a@: l q @: @: 1 @:powerquant@:(a)}
+@r{ a b@: O l q @: @: 2 @:powerquant@:(a,b)}
+@r{ a@: H l q @: @: 1 @:fieldquant@:(a)}
+@r{ a b@: O H l q @: @: 2 @:fieldquant@:(a,b)}
+
@c
@r{ @: m a @: @: 12,13 @:calc-algebraic-mode@:}
@r{ @: m d @: @: @:calc-degrees-mode@:}
@printindex fn
@bye
-
-
-@ignore
- arch-tag: 77a71809-fa4d-40be-b2cc-da3e8fb137c0
-@end ignore
HCoop / bpt / emacs.git / blobdiff