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+@c -*-texinfo-*-
+@c This is part of the GNU Emacs Lisp Reference Manual.
+@c Copyright (C) 1990, 1991, 1992, 1993, 1994 Free Software Foundation, Inc. 
+@c See the file elisp.texi for copying conditions.
+@setfilename ../info/numbers
+@node Numbers, Strings and Characters, Types of Lisp Object, Top
+@chapter Numbers
+@cindex integers
+@cindex numbers
+
+  GNU Emacs supports two numeric data types: @dfn{integers} and
+@dfn{floating point numbers}.  Integers are whole numbers such as
+@minus{}3, 0, 7, 13, and 511.  Their values are exact.  Floating point
+numbers are numbers with fractional parts, such as @minus{}4.5, 0.0, or
+2.71828.  They can also be expressed in an exponential notation as well:
+thus, 1.5e2 equals 150; in this example, @samp{e2} stands for ten to the
+second power, and is multiplied by 1.5.  Floating point values are not
+exact; they have a fixed, limited amount of precision.
+
+  Support for floating point numbers is a new feature in Emacs 19, and it
+is controlled by a separate compilation option, so you may encounter a site
+where Emacs does not support them.
+
+@menu
+* Integer Basics::            Representation and range of integers.
+* Float Basics::              Representation and range of floating point.
+* Predicates on Numbers::     Testing for numbers.
+* Comparison of Numbers::     Equality and inequality predicates.
+* Numeric Conversions::       Converting float to integer and vice versa.
+* Arithmetic Operations::     How to add, subtract, multiply and divide.
+* Rounding Operations::       Explicitly rounding floating point numbers.
+* Bitwise Operations::        Logical and, or, not, shifting.
+* Transcendental Functions::  Trig, exponential and logarithmic functions.
+* Random Numbers::            Obtaining random integers, predictable or not.
+@end menu
+
+@node Integer Basics
+@comment  node-name,  next,  previous,  up
+@section Integer Basics
+
+  The range of values for an integer depends on the machine.  The
+range is @minus{}8388608 to 8388607 (24 bits; i.e.,
+@ifinfo 
+-2**23
+@end ifinfo
+@tex 
+$-2^{23}$ 
+@end tex
+to 
+@ifinfo 
+2**23 - 1)
+@end ifinfo
+@tex 
+$2^{23}-1$)
+@end tex
+on most machines, but on others it is @minus{}16777216 to 16777215 (25
+bits), or @minus{}33554432 to 33554431 (26 bits).  Many examples in this
+chapter assume an integer has 24 bits.
+@cindex overflow
+
+  The Lisp reader reads an integer as a sequence of digits with optional
+initial sign and optional final period.
+
+@example
+ 1               ; @r{The integer 1.}
+ 1.              ; @r{The integer 1.}
++1               ; @r{Also the integer 1.}
+-1               ; @r{The integer @minus{}1.}
+ 16777217        ; @r{Also the integer 1, due to overflow.}
+ 0               ; @r{The integer 0.}
+-0               ; @r{The integer 0.}
+@end example
+
+  To understand how various functions work on integers, especially the
+bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
+view the numbers in their binary form.
+
+  In 24 bit binary, the decimal integer 5 looks like this:
+
+@example
+0000 0000  0000 0000  0000 0101
+@end example
+
+@noindent
+(We have inserted spaces between groups of 4 bits, and two spaces
+between groups of 8 bits, to make the binary integer easier to read.)
+
+  The integer @minus{}1 looks like this:
+
+@example
+1111 1111  1111 1111  1111 1111
+@end example
+
+@noindent
+@cindex two's complement
+@minus{}1 is represented as 24 ones.  (This is called @dfn{two's
+complement} notation.)
+
+  The negative integer, @minus{}5, is creating by subtracting 4 from
+@minus{}1.  In binary, the decimal integer 4 is 100.  Consequently,
+@minus{}5 looks like this:
+
+@example
+1111 1111  1111 1111  1111 1011
+@end example
+
+  In this implementation, the largest 24 bit binary integer is the
+decimal integer 8,388,607.  In binary, it looks like this:
+
+@example
+0111 1111  1111 1111  1111 1111
+@end example
+
+  Since the arithmetic functions do not check whether integers go
+outside their range, when you add 1 to 8,388,607, the value is negative
+integer @minus{}8,388,608:
+
+@example
+(+ 1 8388607)
+     @result{} -8388608
+     @result{} 1000 0000  0000 0000  0000 0000
+@end example
+
+  Many of the following functions accept markers for arguments as well
+as integers.  (@xref{Markers}.)  More precisely, the actual arguments to
+such functions may be either integers or markers, which is why we often
+give these arguments the name @var{int-or-marker}.  When the argument
+value is a marker, its position value is used and its buffer is ignored.
+
+@ignore
+  In version 19, except where @emph{integer} is specified as an
+argument, all of the functions for markers and integers also work for
+floating point numbers.
+@end ignore
+
+@node Float Basics
+@section Floating Point Basics
+
+@cindex @code{LISP_FLOAT_TYPE} configuration macro
+  Emacs version 19 supports floating point numbers, if compiled with the
+macro @code{LISP_FLOAT_TYPE} defined.  The precise range of floating
+point numbers is machine-specific; it is the same as the range of the C
+data type @code{double} on the machine in question.
+
+  The printed representation for floating point numbers requires either
+a decimal point (with at least one digit following), an exponent, or
+both.  For example, @samp{1500.0}, @samp{15e2}, @samp{15.0e2},
+@samp{1.5e3}, and @samp{.15e4} are five ways of writing a floating point
+number whose value is 1500.  They are all equivalent.  You can also use
+a minus sign to write negative floating point numbers, as in
+@samp{-1.0}.
+
+@cindex IEEE floating point
+@cindex positive infinity
+@cindex negative infinity
+@cindex infinity
+@cindex NaN
+   Most modern computers support the IEEE floating point standard, which
+provides for positive infinity and negative infinity as floating point
+values.  It also provides for a value called NaN or ``not-a-number''
+which is the result you get from numerical functions in cases where
+there is no correct answer.  For example, @code{(sqrt -1.0)} returns
+NaN.  There is no read syntax for NaN or infinities; perhaps we should
+create a syntax in the future.
+
+  You can use @code{logb} to extract the binary exponent of a floating
+point number (or estimate the logarithm of an integer):
+
+@defun logb number
+This function returns the binary exponent of @var{number}.  More
+precisely, the value is the logarithm of @var{number} base 2, rounded
+down to an integer.
+@end defun
+
+@node Predicates on Numbers
+@section Type Predicates for Numbers
+
+  The functions in this section test whether the argument is a number or
+whether it is a certain sort of number.  The functions @code{integerp}
+and @code{floatp} can take any type of Lisp object as argument (the
+predicates would not be of much use otherwise); but the @code{zerop}
+predicate requires a number as its argument.  See also
+@code{integer-or-marker-p} and @code{number-or-marker-p}, in
+@ref{Predicates on Markers}.
+
+@defun floatp object
+This predicate tests whether its argument is a floating point
+number and returns @code{t} if so, @code{nil} otherwise.
+
+@code{floatp} does not exist in Emacs versions 18 and earlier.
+@end defun
+
+@defun integerp object
+This predicate tests whether its argument is an integer, and returns
+@code{t} if so, @code{nil} otherwise.
+@end defun
+
+@defun numberp object
+This predicate tests whether its argument is a number (either integer or
+floating point), and returns @code{t} if so, @code{nil} otherwise.
+@end defun
+
+@defun natnump object
+@cindex natural numbers
+The @code{natnump} predicate (whose name comes from the phrase
+``natural-number-p'') tests to see whether its argument is a nonnegative
+integer, and returns @code{t} if so, @code{nil} otherwise.  0 is
+considered non-negative.
+
+Markers are not converted to integers, hence @code{natnump} of a marker
+is always @code{nil}.
+
+People have pointed out that this function is misnamed, because the term
+``natural number'' is usually understood as excluding zero.  We are open
+to suggestions for a better name to use in a future version.
+@end defun
+
+@defun zerop number
+This predicate tests whether its argument is zero, and returns @code{t}
+if so, @code{nil} otherwise.  The argument must be a number.
+
+These two forms are equivalent: @code{(zerop x)} @equiv{} @code{(= x 0)}.
+@end defun
+
+@node Comparison of Numbers
+@section Comparison of Numbers
+@cindex number equality
+
+  Floating point numbers in Emacs Lisp actually take up storage, and
+there can be many distinct floating point number objects with the same
+numeric value.  If you use @code{eq} to compare them, then you test
+whether two values are the same @emph{object}.  If you want to test for
+numerical equality, use @code{=}.
+
+  If you use @code{eq} to compare two integers, it always returns
+@code{t} if they have the same value.  This is sometimes useful, because
+@code{eq} accepts arguments of any type and never causes an error, 
+whereas @code{=} signals an error if the arguments are not numbers or
+markers.  However, it is a good idea to use @code{=} if you can, even
+for comparing integers, just in case we change the representation of
+integers in a future Emacs version.
+
+  There is another wrinkle: because floating point arithmetic is not
+exact, it is often a bad idea to check for equality of two floating
+point values.  Usually it is better to test for approximate equality.
+Here's a function to do this:
+
+@example
+(defvar fuzz-factor 1.0e-6)
+(defun approx-equal (x y)
+  (< (/ (abs (- x y))
+        (max (abs x) (abs y)))
+     fuzz-factor))
+@end example
+
+@cindex CL note---integers vrs @code{eq}
+@quotation
+@b{Common Lisp note:} comparing numbers in Common Lisp always requires
+@code{=} because Common Lisp implements multi-word integers, and two
+distinct integer objects can have the same numeric value.  Emacs Lisp
+can have just one integer object for any given value because it has a
+limited range of integer values.
+@end quotation
+
+@defun = number-or-marker1 number-or-marker2
+This function tests whether its arguments are numerically equal, and
+returns @code{t} if so, @code{nil} otherwise.
+@end defun
+
+@defun /= number-or-marker1 number-or-marker2
+This function tests whether its arguments are numerically equal, and
+returns @code{t} if they are not, and @code{nil} if they are.
+@end defun
+
+@defun <  number-or-marker1 number-or-marker2
+This function tests whether its first argument is strictly less than
+its second argument.  It returns @code{t} if so, @code{nil} otherwise.
+@end defun
+
+@defun <=  number-or-marker1 number-or-marker2
+This function tests whether its first argument is less than or equal
+to its second argument.  It returns @code{t} if so, @code{nil}
+otherwise.
+@end defun
+
+@defun >  number-or-marker1 number-or-marker2
+This function tests whether its first argument is strictly greater
+than its second argument.  It returns @code{t} if so, @code{nil}
+otherwise.
+@end defun
+
+@defun >=  number-or-marker1 number-or-marker2
+This function tests whether its first argument is greater than or
+equal to its second argument.  It returns @code{t} if so, @code{nil}
+otherwise.
+@end defun
+
+@defun max number-or-marker &rest numbers-or-markers
+This function returns the largest of its arguments.
+
+@example
+(max 20)
+     @result{} 20
+(max 1 2.5)
+     @result{} 2.5
+(max 1 3 2.5)
+     @result{} 3
+@end example
+@end defun
+
+@defun min number-or-marker &rest numbers-or-markers
+This function returns the smallest of its arguments.
+
+@example
+(min -4 1)
+     @result{} -4
+@end example
+@end defun
+
+@node Numeric Conversions
+@section Numeric Conversions
+@cindex rounding in conversions
+
+To convert an integer to floating point, use the function @code{float}.
+
+@defun float number
+This returns @var{number} converted to floating point.
+If @var{number} is already a floating point number, @code{float} returns
+it unchanged.
+@end defun
+
+There are four functions to convert floating point numbers to integers;
+they differ in how they round.  These functions accept integer arguments
+also, and return such arguments unchanged.
+
+@defun truncate number
+This returns @var{number}, converted to an integer by rounding towards
+zero.
+@end defun
+
+@defun floor number &optional divisor
+This returns @var{number}, converted to an integer by rounding downward
+(towards negative infinity).
+
+If @var{divisor} is specified, @var{number} is divided by @var{divisor}
+before the floor is taken; this is the division operation that
+corresponds to @code{mod}.  An @code{arith-error} results if
+@var{divisor} is 0.
+@end defun
+
+@defun ceiling number
+This returns @var{number}, converted to an integer by rounding upward
+(towards positive infinity).
+@end defun
+
+@defun round number
+This returns @var{number}, converted to an integer by rounding towards the
+nearest integer.
+@end defun
+
+@node Arithmetic Operations
+@section Arithmetic Operations
+
+  Emacs Lisp provides the traditional four arithmetic operations:
+addition, subtraction, multiplication, and division.  Remainder and modulus
+functions supplement the division functions.  The functions to
+add or subtract 1 are provided because they are traditional in Lisp and
+commonly used.
+
+  All of these functions except @code{%} return a floating point value
+if any argument is floating.
+
+  It is important to note that in GNU Emacs Lisp, arithmetic functions
+do not check for overflow.  Thus @code{(1+ 8388607)} may evaluate to
+@minus{}8388608, depending on your hardware.
+
+@defun 1+ number-or-marker
+This function returns @var{number-or-marker} plus 1.
+For example,
+
+@example
+(setq foo 4)
+     @result{} 4
+(1+ foo)
+     @result{} 5
+@end example
+
+This function is not analogous to the C operator @code{++}---it does
+not increment a variable.  It just computes a sum.  Thus,
+
+@example
+foo
+     @result{} 4
+@end example
+
+If you want to increment the variable, you must use @code{setq},
+like this:
+
+@example
+(setq foo (1+ foo))
+     @result{} 5
+@end example
+@end defun
+
+@defun 1- number-or-marker
+This function returns @var{number-or-marker} minus 1.
+@end defun
+
+@defun abs number
+This returns the absolute value of @var{number}.
+@end defun
+
+@defun + &rest numbers-or-markers
+This function adds its arguments together.  When given no arguments,
+@code{+} returns 0.  It does not check for overflow.
+
+@example
+(+)
+     @result{} 0
+(+ 1)
+     @result{} 1
+(+ 1 2 3 4)
+     @result{} 10
+@end example
+@end defun
+
+@defun - &optional number-or-marker &rest other-numbers-or-markers
+The @code{-} function serves two purposes: negation and subtraction.
+When @code{-} has a single argument, the value is the negative of the
+argument.  When there are multiple arguments, @code{-} subtracts each of
+the @var{other-numbers-or-markers} from @var{number-or-marker},
+cumulatively.  If there are no arguments, the result is 0.  This
+function does not check for overflow.
+
+@example
+(- 10 1 2 3 4)
+     @result{} 0
+(- 10)
+     @result{} -10
+(-)
+     @result{} 0
+@end example
+@end defun
+
+@defun * &rest numbers-or-markers
+This function multiplies its arguments together, and returns the
+product.  When given no arguments, @code{*} returns 1.  It does
+not check for overflow.
+
+@example
+(*)
+     @result{} 1
+(* 1)
+     @result{} 1
+(* 1 2 3 4)
+     @result{} 24
+@end example
+@end defun
+
+@defun / dividend divisor &rest divisors
+This function divides @var{dividend} by @var{divisors} and returns the
+quotient.  If there are additional arguments @var{divisors}, then it
+divides @var{dividend} by each divisor in turn.  Each argument may be a
+number or a marker.
+
+If all the arguments are integers, then the result is an integer too.
+This means the result has to be rounded.  On most machines, the result
+is rounded towards zero after each division, but some machines may round
+differently with negative arguments.  This is because the Lisp function
+@code{/} is implemented using the C division operator, which also
+permits machine-dependent rounding.  As a practical matter, all known
+machines round in the standard fashion.
+
+@cindex @code{arith-error} in division
+If you divide by 0, an @code{arith-error} error is signaled.
+(@xref{Errors}.)
+
+@example
+(/ 6 2)
+     @result{} 3
+(/ 5 2)
+     @result{} 2
+(/ 25 3 2)
+     @result{} 4
+(/ -17 6)
+     @result{} -2
+@end example
+
+The result of @code{(/ -17 6)} could in principle be -3 on some
+machines.
+@end defun
+
+@defun % dividend divisor
+@cindex remainder
+This function returns the integer remainder after division of @var{dividend}
+by @var{divisor}.  The arguments must be integers or markers.
+
+For negative arguments, the remainder is in principle machine-dependent
+since the quotient is; but in practice, all known machines behave alike.
+
+An @code{arith-error} results if @var{divisor} is 0.
+
+@example
+(% 9 4)
+     @result{} 1
+(% -9 4)
+     @result{} -1
+(% 9 -4)
+     @result{} 1
+(% -9 -4)
+     @result{} -1
+@end example
+
+For any two integers @var{dividend} and @var{divisor},
+
+@example
+@group
+(+ (% @var{dividend} @var{divisor})
+   (* (/ @var{dividend} @var{divisor}) @var{divisor}))
+@end group
+@end example
+
+@noindent
+always equals @var{dividend}.
+@end defun
+
+@defun mod dividend divisor
+@cindex modulus
+This function returns the value of @var{dividend} modulo @var{divisor};
+in other words, the remainder after division of @var{dividend}
+by @var{divisor}, but with the same sign as @var{divisor}.
+The arguments must be numbers or markers.
+
+Unlike @code{%}, @code{mod} returns a well-defined result for negative
+arguments.  It also permits floating point arguments; it rounds the
+quotient downward (towards minus infinity) to an integer, and uses that
+quotient to compute the remainder.
+
+An @code{arith-error} results if @var{divisor} is 0.
+
+@example
+(mod 9 4)
+     @result{} 1
+(mod -9 4)
+     @result{} 3
+(mod 9 -4)
+     @result{} -3
+(mod -9 -4)
+     @result{} -1
+(mod 5.5 2.5)
+     @result{} .5
+@end example
+
+For any two numbers @var{dividend} and @var{divisor},
+
+@example
+@group
+(+ (mod @var{dividend} @var{divisor})
+   (* (floor @var{dividend} @var{divisor}) @var{divisor}))
+@end group
+@end example
+
+@noindent
+always equals @var{dividend}, subject to rounding error if
+either argument is floating point.
+@end defun
+
+@node Rounding Operations
+@section Rounding Operations
+@cindex rounding without conversion
+
+The functions @code{ffloor}, @code{fceil}, @code{fround} and
+@code{ftruncate} take a floating point argument and return a floating
+point result whose value is a nearby integer.  @code{ffloor} returns the
+nearest integer below; @code{fceil}, the nearest integer above;
+@code{ftrucate}, the nearest integer in the direction towards zero;
+@code{fround}, the nearest integer.
+
+@defun ffloor float
+This function rounds @var{float} to the next lower integral value, and
+returns that value as a floating point number.
+@end defun
+
+@defun fceil float
+This function rounds @var{float} to the next higher integral value, and
+returns that value as a floating point number.
+@end defun
+
+@defun ftrunc float
+This function rounds @var{float} towards zero to an integral value, and
+returns that value as a floating point number.
+@end defun
+
+@defun fround float
+This function rounds @var{float} to the nearest integral value,
+and returns that value as a floating point number.
+@end defun
+
+@node Bitwise Operations
+@section Bitwise Operations on Integers
+
+  In a computer, an integer is represented as a binary number, a
+sequence of @dfn{bits} (digits which are either zero or one).  A bitwise
+operation acts on the individual bits of such a sequence.  For example,
+@dfn{shifting} moves the whole sequence left or right one or more places,
+reproducing the same pattern ``moved over''.
+
+  The bitwise operations in Emacs Lisp apply only to integers.
+
+@defun lsh integer1 count
+@cindex logical shift
+@code{lsh}, which is an abbreviation for @dfn{logical shift}, shifts the
+bits in @var{integer1} to the left @var{count} places, or to the
+right if @var{count} is negative.  If @var{count} is negative,
+@code{lsh} shifts zeros into the most-significant bit, producing a
+positive result even if @var{integer1} is negative.  Contrast this with
+@code{ash}, below.
+
+Thus, the decimal number 5 is the binary number 00000101.  Shifted once
+to the left, with a zero put in the one's place, the number becomes
+00001010, decimal 10.
+
+Here are two examples of shifting the pattern of bits one place to the
+left.  Since the contents of the rightmost place has been moved one
+place to the left, a value has to be inserted into the rightmost place.
+With @code{lsh}, a zero is placed into the rightmost place.  (These
+examples show only the low-order eight bits of the binary pattern; the
+rest are all zero.)
+
+@example
+@group
+(lsh 5 1)
+     @result{} 10
+;; @r{Decimal 5 becomes decimal 10.}
+00000101 @result{} 00001010
+
+(lsh 7 1)
+     @result{} 14
+;; @r{Decimal 7 becomes decimal 14.}
+00000111 @result{} 00001110
+@end group
+@end example
+
+@noindent
+As the examples illustrate, shifting the pattern of bits one place to
+the left produces a number that is twice the value of the previous
+number.
+
+Note, however that functions do not check for overflow, and a returned
+value may be negative (and in any case, no more than a 24 bit value)
+when an integer is sufficiently left shifted.  
+
+For example, left shifting 8,388,607 produces @minus{}2:
+
+@example
+(lsh 8388607 1)          ; @r{left shift}
+     @result{} -2
+@end example
+
+In binary, in the 24 bit implementation, the numbers looks like this:
+
+@example
+@group
+;; @r{Decimal 8,388,607}
+0111 1111  1111 1111  1111 1111         
+@end group
+@end example
+
+@noindent
+which becomes the following when left shifted:
+
+@example
+@group
+;; @r{Decimal @minus{}2}
+1111 1111  1111 1111  1111 1110         
+@end group
+@end example
+
+Shifting the pattern of bits two places to the left produces results
+like this (with 8-bit binary numbers):
+
+@example
+@group
+(lsh 3 2)
+     @result{} 12
+;; @r{Decimal 3 becomes decimal 12.}
+00000011 @result{} 00001100       
+@end group
+@end example
+
+On the other hand, shifting the pattern of bits one place to the right
+looks like this:
+
+@example
+@group
+(lsh 6 -1)
+     @result{} 3
+;; @r{Decimal 6 becomes decimal 3.}
+00000110 @result{} 00000011       
+@end group
+
+@group
+(lsh 5 -1)
+     @result{} 2
+;; @r{Decimal 5 becomes decimal 2.}
+00000101 @result{} 00000010       
+@end group
+@end example
+
+@noindent
+As the example illustrates, shifting the pattern of bits one place to
+the right divides the value of the binary number by two, rounding downward.
+@end defun
+
+@defun ash integer1 count
+@cindex arithmetic shift
+@code{ash} (@dfn{arithmetic shift}) shifts the bits in @var{integer1}
+to the left @var{count} places, or to the right if @var{count}
+is negative.
+
+@code{ash} gives the same results as @code{lsh} except when
+@var{integer1} and @var{count} are both negative.  In that case,
+@code{ash} puts a one in the leftmost position, while @code{lsh} puts
+a zero in the leftmost position.
+
+Thus, with @code{ash}, shifting the pattern of bits one place to the right
+looks like this:
+
+@example
+@group
+(ash -6 -1) @result{} -3            
+;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
+1111 1111  1111 1111  1111 1010
+     @result{} 
+1111 1111  1111 1111  1111 1101
+@end group
+@end example
+
+In contrast, shifting the pattern of bits one place to the right with
+@code{lsh} looks like this:
+
+@example
+@group
+(lsh -6 -1) @result{} 8388605       
+;; @r{Decimal @minus{}6 becomes decimal 8,388,605.}
+1111 1111  1111 1111  1111 1010
+     @result{} 
+0111 1111  1111 1111  1111 1101
+@end group
+@end example
+
+@noindent
+In this case, the 1 in the leftmost position is shifted one place to the
+right, and a zero is shifted into the leftmost position.
+
+Here are other examples:
+
+@c !!! Check if lined up in smallbook format!  XDVI shows problem
+@c     with smallbook but not with regular book! --rjc 16mar92
+@smallexample
+@group
+                   ;  @r{             24-bit binary values}
+
+(lsh 5 2)          ;   5  =  @r{0000 0000  0000 0000  0000 0101}
+     @result{} 20         ;  20  =  @r{0000 0000  0000 0000  0001 0100}
+@end group
+@group
+(ash 5 2)
+     @result{} 20
+(lsh -5 2)         ;  -5  =  @r{1111 1111  1111 1111  1111 1011}
+     @result{} -20        ; -20  =  @r{1111 1111  1111 1111  1110 1100}
+(ash -5 2)
+     @result{} -20
+@end group
+@group
+(lsh 5 -2)         ;   5  =  @r{0000 0000  0000 0000  0000 0101}
+     @result{} 1          ;   1  =  @r{0000 0000  0000 0000  0000 0001}
+@end group
+@group
+(ash 5 -2)
+     @result{} 1
+@end group
+@group
+(lsh -5 -2)        ;  -5  =  @r{1111 1111  1111 1111  1111 1011}
+     @result{} 4194302    ;         @r{0011 1111  1111 1111  1111 1110}
+@end group
+@group
+(ash -5 -2)        ;  -5  =  @r{1111 1111  1111 1111  1111 1011}
+     @result{} -2         ;  -2  =  @r{1111 1111  1111 1111  1111 1110}
+@end group
+@end smallexample
+@end defun
+
+@defun logand &rest ints-or-markers
+@cindex logical and
+@cindex bitwise and
+This function returns the ``logical and'' of the arguments: the
+@var{n}th bit is set in the result if, and only if, the @var{n}th bit is
+set in all the arguments.  (``Set'' means that the value of the bit is 1
+rather than 0.)
+
+For example, using 4-bit binary numbers, the ``logical and'' of 13 and
+12 is 12: 1101 combined with 1100 produces 1100.
+
+In both the binary numbers, the leftmost two bits are set (i.e., they
+are 1's), so the leftmost two bits of the returned value are set.
+However, for the rightmost two bits, each is zero in at least one of
+the arguments, so the rightmost two bits of the returned value are 0's.
+
+@noindent
+Therefore,
+
+@example
+@group
+(logand 13 12)
+     @result{} 12
+@end group
+@end example
+
+If @code{logand} is not passed any argument, it returns a value of
+@minus{}1.  This number is an identity element for @code{logand}
+because its binary representation consists entirely of ones.  If
+@code{logand} is passed just one argument, it returns that argument.
+
+@smallexample
+@group
+                   ; @r{               24-bit binary values}
+
+(logand 14 13)     ; 14  =  @r{0000 0000  0000 0000  0000 1110}
+                   ; 13  =  @r{0000 0000  0000 0000  0000 1101}
+     @result{} 12         ; 12  =  @r{0000 0000  0000 0000  0000 1100}
+@end group
+
+@group
+(logand 14 13 4)   ; 14  =  @r{0000 0000  0000 0000  0000 1110}
+                   ; 13  =  @r{0000 0000  0000 0000  0000 1101}
+                   ;  4  =  @r{0000 0000  0000 0000  0000 0100}
+     @result{} 4          ;  4  =  @r{0000 0000  0000 0000  0000 0100}
+@end group
+
+@group
+(logand)
+     @result{} -1         ; -1  =  @r{1111 1111  1111 1111  1111 1111}
+@end group
+@end smallexample
+@end defun
+
+@defun logior &rest ints-or-markers
+@cindex logical inclusive or
+@cindex bitwise or
+This function returns the ``inclusive or'' of its arguments: the @var{n}th bit
+is set in the result if, and only if, the @var{n}th bit is set in at least
+one of the arguments.  If there are no arguments, the result is zero,
+which is an identity element for this operation.  If @code{logior} is
+passed just one argument, it returns that argument.
+
+@smallexample
+@group
+                   ; @r{              24-bit binary values}
+
+(logior 12 5)      ; 12  =  @r{0000 0000  0000 0000  0000 1100}
+                   ;  5  =  @r{0000 0000  0000 0000  0000 0101}
+     @result{} 13         ; 13  =  @r{0000 0000  0000 0000  0000 1101}
+@end group
+
+@group
+(logior 12 5 7)    ; 12  =  @r{0000 0000  0000 0000  0000 1100}
+                   ;  5  =  @r{0000 0000  0000 0000  0000 0101}
+                   ;  7  =  @r{0000 0000  0000 0000  0000 0111}
+     @result{} 15         ; 15  =  @r{0000 0000  0000 0000  0000 1111}
+@end group
+@end smallexample
+@end defun
+
+@defun logxor &rest ints-or-markers
+@cindex bitwise exclusive or
+@cindex logical exclusive or
+This function returns the ``exclusive or'' of its arguments: the
+@var{n}th bit is set in the result if, and only if, the @var{n}th bit
+is set in an odd number of the arguments.  If there are no arguments,
+the result is 0.  If @code{logxor} is passed just one argument, it returns
+that argument.
+
+@smallexample
+@group
+                   ; @r{              24-bit binary values}
+
+(logxor 12 5)      ; 12  =  @r{0000 0000  0000 0000  0000 1100}
+                   ;  5  =  @r{0000 0000  0000 0000  0000 0101}
+     @result{} 9          ;  9  =  @r{0000 0000  0000 0000  0000 1001}
+@end group
+
+@group
+(logxor 12 5 7)    ; 12  =  @r{0000 0000  0000 0000  0000 1100}
+                   ;  5  =  @r{0000 0000  0000 0000  0000 0101}
+                   ;  7  =  @r{0000 0000  0000 0000  0000 0111}
+     @result{} 14         ; 14  =  @r{0000 0000  0000 0000  0000 1110}
+@end group
+@end smallexample
+@end defun
+
+@defun lognot integer
+@cindex logical not
+@cindex bitwise not
+This function returns the logical complement of its argument: the @var{n}th
+bit is one in the result if, and only if, the @var{n}th bit is zero in
+@var{integer}, and vice-versa.
+
+@example
+(lognot 5)             
+     @result{} -6
+;;  5  =  @r{0000 0000  0000 0000  0000 0101}
+;; @r{becomes}
+;; -6  =  @r{1111 1111  1111 1111  1111 1010}
+@end example
+@end defun
+
+@node Transcendental Functions
+@section Transcendental Functions
+@cindex transcendental functions
+@cindex mathematical functions
+
+These mathematical functions are available if floating point is
+supported.  They allow integers as well as floating point numbers
+as arguments.
+
+@defun sin arg
+@defunx cos arg
+@defunx tan arg
+These are the ordinary trigonometric functions, with argument measured
+in radians.
+@end defun
+
+@defun asin arg
+The value of @code{(asin @var{arg})} is a number between @minus{} pi / 2
+and pi / 2 (inclusive) whose sine is @var{arg}; if, however, @var{arg}
+is out of range (outside [-1, 1]), then the result is a NaN.
+@end defun
+
+@defun acos arg
+The value of @code{(acos @var{arg})} is a number between 0 and pi
+(inclusive) whose cosine is @var{arg}; if, however, @var{arg}
+is out of range (outside [-1, 1]), then the result is a NaN.
+@end defun
+
+@defun atan arg
+The value of @code{(atan @var{arg})} is a number between @minus{} pi / 2
+and pi / 2 (exclusive) whose tangent is @var{arg}.
+@end defun
+
+@defun exp arg
+This is the exponential function; it returns @i{e} to the power
+@var{arg}.  @i{e} is a fundamental mathematical constant also called the
+base of natural logarithms.
+@end defun
+
+@defun log arg &optional base
+This function returns the logarithm of @var{arg}, with base @var{base}.
+If you don't specify @var{base}, the base @var{e} is used.  If @var{arg}
+is negative, the result is a NaN.
+@end defun
+
+@ignore
+@defun expm1 arg
+This function returns @code{(1- (exp @var{arg}))}, but it is more
+accurate than that when @var{arg} is negative and @code{(exp @var{arg})}
+is close to 1.
+@end defun
+
+@defun log1p arg
+This function returns @code{(log (1+ @var{arg}))}, but it is more
+accurate than that when @var{arg} is so small that adding 1 to it would
+lose accuracy.
+@end defun
+@end ignore
+
+@defun log10 arg
+This function returns the logarithm of @var{arg}, with base 10.  If
+@var{arg} is negative, the result is a NaN.
+@end defun
+
+@defun expt x y
+This function returns @var{x} raised to power @var{y}.
+@end defun
+
+@defun sqrt arg
+This returns the square root of @var{arg}.  If @var{arg} is negative,
+the value is a NaN.
+@end defun
+
+@node Random Numbers
+@section Random Numbers
+@cindex random numbers
+
+A deterministic computer program cannot generate true random numbers.
+For most purposes, @dfn{pseudo-random numbers} suffice.  A series of
+pseudo-random numbers is generated in a deterministic fashion.  The
+numbers are not truly random, but they have certain properties that
+mimic a random series.  For example, all possible values occur equally
+often in a pseudo-random series.
+
+In Emacs, pseudo-random numbers are generated from a ``seed'' number.
+Starting from any given seed, the @code{random} function always
+generates the same sequence of numbers.  Emacs always starts with the
+same seed value, so the sequence of values of @code{random} is actually
+the same in each Emacs run!  For example, in one operating system, the
+first call to @code{(random)} after you start Emacs always returns
+-1457731, and the second one always returns -7692030.  This
+repeatability is helpful for debugging.
+
+If you want truly unpredictable random numbers, execute @code{(random
+t)}.  This chooses a new seed based on the current time of day and on
+Emacs's process @sc{id} number.
+
+@defun random &optional limit
+This function returns a pseudo-random integer.  Repeated calls return a
+series of pseudo-random integers.
+
+If @var{limit} is @code{nil}, then the value may in principle be any
+integer.  If @var{limit} is a positive integer, the value is chosen to
+be nonnegative and less than @var{limit} (only in Emacs 19).
+
+If @var{limit} is @code{t}, it means to choose a new seed based on the
+current time of day and on Emacs's process @sc{id} number.
+@c "Emacs'" is incorrect usage!
+
+On some machines, any integer representable in Lisp may be the result
+of @code{random}.  On other machines, the result can never be larger
+than a certain maximum or less than a certain (negative) minimum.
+@end defun
diff --git a/lispref/variables.texi b/lispref/variables.texi
new file mode 100644
index 00000000000..2b12607d488
--- /dev/null
+++ b/lispref/variables.texi
@@ -0,0 +1,1262 @@
+@c -*-texinfo-*-
+@c This is part of the GNU Emacs Lisp Reference Manual.
+@c Copyright (C) 1990, 1991, 1992, 1993, 1994 Free Software Foundation, Inc. 
+@c See the file elisp.texi for copying conditions.
+@setfilename ../info/variables
+@node Variables, Functions, Control Structures, Top
+@chapter Variables
+@cindex variable
+
+  A @dfn{variable} is a name used in a program to stand for a value.
+Nearly all programming languages have variables of some sort.  In the
+text of a Lisp program, variables are written using the syntax for
+symbols.
+
+  In Lisp, unlike most programming languages, programs are represented
+primarily as Lisp objects and only secondarily as text.  The Lisp
+objects used for variables are symbols: the symbol name is the variable
+name, and the variable's value is stored in the value cell of the
+symbol.  The use of a symbol as a variable is independent of its use as
+a function name.  @xref{Symbol Components}.
+
+  The Lisp objects that constitute a Lisp program determine the textual
+form of the program--it is simply the read syntax for those Lisp
+objects.  This is why, for example, a variable in a textual Lisp program
+is written using the read syntax for the symbol that represents the
+variable.
+
+@menu
+* Global Variables::      Variable values that exist permanently, everywhere.
+* Constant Variables::    Certain "variables" have values that never change.
+* Local Variables::       Variable values that exist only temporarily.
+* Void Variables::        Symbols that lack values.
+* Defining Variables::    A definition says a symbol is used as a variable.
+* Accessing Variables::   Examining values of variables whose names
+                            are known only at run time.
+* Setting Variables::     Storing new values in variables.
+* Variable Scoping::      How Lisp chooses among local and global values.
+* Buffer-Local Variables::  Variable values in effect only in one buffer.
+@end menu
+
+@node Global Variables
+@section Global Variables
+@cindex global variable
+
+  The simplest way to use a variable is @dfn{globally}.  This means that
+the variable has just one value at a time, and this value is in effect
+(at least for the moment) throughout the Lisp system.  The value remains
+in effect until you specify a new one.  When a new value replaces the
+old one, no trace of the old value remains in the variable.
+
+  You specify a value for a symbol with @code{setq}.  For example,
+
+@example
+(setq x '(a b))
+@end example
+
+@noindent
+gives the variable @code{x} the value @code{(a b)}.  Note that
+@code{setq} does not evaluate its first argument, the name of the
+variable, but it does evaluate the second argument, the new value.
+
+  Once the variable has a value, you can refer to it by using the symbol
+by itself as an expression.  Thus,
+
+@example
+@group
+x @result{} (a b)
+@end group
+@end example
+
+@noindent
+assuming the @code{setq} form shown above has already been executed.
+
+  If you do another @code{setq}, the new value replaces the old one:
+
+@example
+@group
+x
+     @result{} (a b)
+@end group
+@group
+(setq x 4)
+     @result{} 4
+@end group
+@group
+x
+     @result{} 4
+@end group
+@end example
+
+@node Constant Variables
+@section Variables That Never Change
+@vindex nil
+@vindex t
+@kindex setting-constant
+
+  Emacs Lisp has two special symbols, @code{nil} and @code{t}, that
+always evaluate to themselves.  These symbols cannot be rebound, nor can
+their value cells be changed.  An attempt to change the value of
+@code{nil} or @code{t} signals a @code{setting-constant} error.
+
+@example
+@group
+nil @equiv{} 'nil
+     @result{} nil
+@end group
+@group
+(setq nil 500)
+@error{} Attempt to set constant symbol: nil
+@end group
+@end example
+
+@node Local Variables
+@section Local Variables
+@cindex binding local variables
+@cindex local variables
+@cindex local binding
+@cindex global binding
+
+  Global variables have values that last until explicitly superseded
+with new values.  Sometimes it is useful to create variable values that
+exist temporarily---only while within a certain part of the program.
+These values are called @dfn{local}, and the variables so used are
+called @dfn{local variables}.
+
+  For example, when a function is called, its argument variables receive
+new local values that last until the function exits.  The @code{let}
+special form explicitly establishes new local values for specified
+variables; these last until exit from the @code{let} form.
+
+@cindex shadowing of variables
+  Establishing a local value saves away the previous value (or lack of
+one) of the variable.  When the life span of the local value is over,
+the previous value is restored.  In the mean time, we say that the
+previous value is @dfn{shadowed} and @dfn{not visible}.  Both global and
+local values may be shadowed (@pxref{Scope}).
+
+  If you set a variable (such as with @code{setq}) while it is local,
+this replaces the local value; it does not alter the global value, or
+previous local values that are shadowed.  To model this behavior, we
+speak of a @dfn{local binding} of the variable as well as a local value.
+
+  The local binding is a conceptual place that holds a local value.
+Entry to a function, or a special form such as @code{let}, creates the
+local binding; exit from the function or from the @code{let} removes the
+local binding.  As long as the local binding lasts, the variable's value
+is stored within it.  Use of @code{setq} or @code{set} while there is a
+local binding stores a different value into the local binding; it does
+not create a new binding.
+
+  We also speak of the @dfn{global binding}, which is where
+(conceptually) the global value is kept.
+
+@cindex current binding
+  A variable can have more than one local binding at a time (for
+example, if there are nested @code{let} forms that bind it).  In such a
+case, the most recently created local binding that still exists is the
+@dfn{current binding} of the variable.  (This is called @dfn{dynamic
+scoping}; see @ref{Variable Scoping}.)  If there are no local bindings,
+the variable's global binding is its current binding.  We also call the
+current binding the @dfn{most-local existing binding}, for emphasis.
+Ordinary evaluation of a symbol always returns the value of its current
+binding.
+
+  The special forms @code{let} and @code{let*} exist to create
+local bindings.
+
+@defspec let (bindings@dots{}) forms@dots{}
+This function binds variables according to @var{bindings} and then
+evaluates all of the @var{forms} in textual order.  The @code{let}-form
+returns the value of the last form in @var{forms}.
+
+Each of the @var{bindings} is either @w{(i) a} symbol, in which case
+that symbol is bound to @code{nil}; or @w{(ii) a} list of the form
+@code{(@var{symbol} @var{value-form})}, in which case @var{symbol} is
+bound to the result of evaluating @var{value-form}.  If @var{value-form}
+is omitted, @code{nil} is used.
+
+All of the @var{value-form}s in @var{bindings} are evaluated in the
+order they appear and @emph{before} any of the symbols are bound.  Here
+is an example of this: @code{Z} is bound to the old value of @code{Y},
+which is 2, not the new value, 1.
+
+@example
+@group
+(setq Y 2)
+     @result{} 2
+@end group
+@group
+(let ((Y 1) 
+      (Z Y))
+  (list Y Z))
+     @result{} (1 2)
+@end group
+@end example
+@end defspec
+
+@defspec let* (bindings@dots{}) forms@dots{}
+This special form is like @code{let}, but it binds each variable right
+after computing its local value, before computing the local value for
+the next variable.  Therefore, an expression in @var{bindings} can
+reasonably refer to the preceding symbols bound in this @code{let*}
+form.  Compare the following example with the example above for
+@code{let}.
+
+@example
+@group
+(setq Y 2)
+     @result{} 2
+@end group
+@group
+(let* ((Y 1)
+       (Z Y))    ; @r{Use the just-established value of @code{Y}.}
+  (list Y Z))
+     @result{} (1 1)
+@end group
+@end example
+@end defspec
+
+  Here is a complete list of the other facilities which create local
+bindings:
+
+@itemize @bullet
+@item
+Function calls (@pxref{Functions}).
+
+@item
+Macro calls (@pxref{Macros}).
+
+@item
+@code{condition-case} (@pxref{Errors}).
+@end itemize
+
+@defvar max-specpdl-size
+@cindex variable limit error
+@cindex evaluation error
+@cindex infinite recursion
+  This variable defines the limit on the total number of local variable
+bindings and @code{unwind-protect} cleanups (@pxref{Nonlocal Exits})
+that are allowed before signaling an error (with data @code{"Variable
+binding depth exceeds max-specpdl-size"}).
+
+  This limit, with the associated error when it is exceeded, is one way
+that Lisp avoids infinite recursion on an ill-defined function.
+
+  The default value is 600.
+
+  @code{max-lisp-eval-depth} provides another limit on depth of nesting.
+@xref{Eval}.
+@end defvar
+
+@node Void Variables
+@section When a Variable is ``Void''
+@kindex void-variable
+@cindex void variable
+
+  If you have never given a symbol any value as a global variable, we
+say that that symbol's global value is @dfn{void}.  In other words, the
+symbol's value cell does not have any Lisp object in it.  If you try to
+evaluate the symbol, you get a @code{void-variable} error rather than
+a value.
+
+  Note that a value of @code{nil} is not the same as void.  The symbol
+@code{nil} is a Lisp object and can be the value of a variable just as any
+other object can be; but it is @emph{a value}.  A void variable does not
+have any value.
+
+  After you have given a variable a value, you can make it void once more
+using @code{makunbound}.
+
+@defun makunbound symbol
+This function makes the current binding of @var{symbol} void.
+Subsequent attempts to use this symbol's value as a variable will signal
+the error @code{void-variable}, unless or until you set it again.
+
+@code{makunbound} returns @var{symbol}.
+
+@example
+@group
+(makunbound 'x)      ; @r{Make the global value}
+                     ;   @r{of @code{x} void.}
+     @result{} x
+@end group
+@group
+x
+@error{} Symbol's value as variable is void: x
+@end group
+@end example
+
+If @var{symbol} is locally bound, @code{makunbound} affects the most
+local existing binding.  This is the only way a symbol can have a void
+local binding, since all the constructs that create local bindings
+create them with values.  In this case, the voidness lasts at most as
+long as the binding does; when the binding is removed due to exit from
+the construct that made it, the previous or global binding is reexposed
+as usual, and the variable is no longer void unless the newly reexposed
+binding was void all along.
+
+@smallexample
+@group
+(setq x 1)               ; @r{Put a value in the global binding.}
+     @result{} 1
+(let ((x 2))             ; @r{Locally bind it.}
+  (makunbound 'x)        ; @r{Void the local binding.}
+  x)
+@error{} Symbol's value as variable is void: x
+@end group
+@group
+x                        ; @r{The global binding is unchanged.}
+     @result{} 1
+
+(let ((x 2))             ; @r{Locally bind it.}
+  (let ((x 3))           ; @r{And again.}
+    (makunbound 'x)      ; @r{Void the innermost-local binding.}
+    x))                  ; @r{And refer: it's void.}
+@error{} Symbol's value as variable is void: x
+@end group
+
+@group
+(let ((x 2))
+  (let ((x 3))
+    (makunbound 'x))     ; @r{Void inner binding, then remove it.}
+  x)                     ; @r{Now outer @code{let} binding is visible.}
+     @result{} 2
+@end group
+@end smallexample
+@end defun
+
+  A variable that has been made void with @code{makunbound} is
+indistinguishable from one that has never received a value and has
+always been void.
+
+  You can use the function @code{boundp} to test whether a variable is
+currently void.
+
+@defun boundp variable
+@code{boundp} returns @code{t} if @var{variable} (a symbol) is not void;
+more precisely, if its current binding is not void.  It returns
+@code{nil} otherwise.
+
+@smallexample
+@group
+(boundp 'abracadabra)          ; @r{Starts out void.}
+     @result{} nil
+@end group
+@group
+(let ((abracadabra 5))         ; @r{Locally bind it.}
+  (boundp 'abracadabra))
+     @result{} t
+@end group
+@group
+(boundp 'abracadabra)          ; @r{Still globally void.}
+     @result{} nil
+@end group
+@group
+(setq abracadabra 5)           ; @r{Make it globally nonvoid.}
+     @result{} 5
+@end group
+@group
+(boundp 'abracadabra)
+     @result{} t
+@end group
+@end smallexample
+@end defun
+
+@node Defining Variables
+@section Defining Global Variables
+
+  You may announce your intention to use a symbol as a global variable
+with a definition, using @code{defconst} or @code{defvar}.
+
+  In Emacs Lisp, definitions serve three purposes.  First, they inform
+people who read the code that certain symbols are @emph{intended} to be
+used a certain way (as variables).  Second, they inform the Lisp system
+of these things, supplying a value and documentation.  Third, they
+provide information to utilities such as @code{etags} and
+@code{make-docfile}, which create data bases of the functions and
+variables in a program.
+
+  The difference between @code{defconst} and @code{defvar} is primarily
+a matter of intent, serving to inform human readers of whether programs
+will change the variable.  Emacs Lisp does not restrict the ways in
+which a variable can be used based on @code{defconst} or @code{defvar}
+declarations.  However, it also makes a difference for initialization:
+@code{defconst} unconditionally initializes the variable, while
+@code{defvar} initializes it only if it is void.
+
+  One would expect user option variables to be defined with
+@code{defconst}, since programs do not change them.  Unfortunately, this
+has bad results if the definition is in a library that is not preloaded:
+@code{defconst} would override any prior value when the library is
+loaded.  Users would like to be able to set user options in their init
+files, and override the default values given in the definitions.  For
+this reason, user options must be defined with @code{defvar}.
+
+@defspec defvar symbol [value [doc-string]]
+This special form defines @var{symbol} as a value and initializes it.
+The definition informs a person reading your code that @var{symbol} is
+used as a variable that programs are likely to set or change.  It is
+also used for all user option variables except in the preloaded parts of
+Emacs.  Note that @var{symbol} is not evaluated; the symbol to be
+defined must appear explicitly in the @code{defvar}.
+
+If @var{symbol} already has a value (i.e., it is not void), @var{value}
+is not even evaluated, and @var{symbol}'s value remains unchanged.  If
+@var{symbol} is void and @var{value} is specified, @code{defvar}
+evaluates it and sets @var{symbol} to the result.  (If @var{value} is
+omitted, the value of @var{symbol} is not changed in any case.)
+
+If @var{symbol} has a buffer-local binding in the current buffer,
+@code{defvar} sets the default value, not the local value.
+@xref{Buffer-Local Variables}.
+
+If the @var{doc-string} argument appears, it specifies the documentation
+for the variable.  (This opportunity to specify documentation is one of
+the main benefits of defining the variable.)  The documentation is
+stored in the symbol's @code{variable-documentation} property.  The
+Emacs help functions (@pxref{Documentation}) look for this property.
+
+If the first character of @var{doc-string} is @samp{*}, it means that
+this variable is considered a user option.  This lets users set the
+variable conventiently using the commands @code{set-variable} and
+@code{edit-options}.
+
+For example, this form defines @code{foo} but does not set its value:
+
+@example
+@group
+(defvar foo)
+     @result{} foo
+@end group
+@end example
+
+The following example sets the value of @code{bar} to @code{23}, and
+gives it a documentation string:
+
+@example
+@group
+(defvar bar 23
+  "The normal weight of a bar.")
+     @result{} bar
+@end group
+@end example
+
+The following form changes the documentation string for @code{bar},
+making it a user option, but does not change the value, since @code{bar}
+already has a value.  (The addition @code{(1+ 23)} is not even
+performed.)
+
+@example
+@group
+(defvar bar (1+ 23)
+  "*The normal weight of a bar.")
+     @result{} bar
+@end group
+@group
+bar
+     @result{} 23
+@end group
+@end example
+
+Here is an equivalent expression for the @code{defvar} special form:
+
+@example
+@group
+(defvar @var{symbol} @var{value} @var{doc-string})
+@equiv{}
+(progn
+  (if (not (boundp '@var{symbol}))
+      (setq @var{symbol} @var{value}))
+  (put '@var{symbol} 'variable-documentation '@var{doc-string})
+  '@var{symbol})
+@end group
+@end example
+
+The @code{defvar} form returns @var{symbol}, but it is normally used
+at top level in a file where its value does not matter.
+@end defspec
+
+@defspec defconst symbol [value [doc-string]]
+This special form defines @var{symbol} as a value and initializes it.
+It informs a person reading your code that @var{symbol} has a global
+value, established here, that will not normally be changed or locally
+bound by the execution of the program.  The user, however, may be
+welcome to change it.  Note that @var{symbol} is not evaluated; the
+symbol to be defined must appear explicitly in the @code{defconst}.
+
+@code{defconst} always evaluates @var{value} and sets the global value
+of @var{symbol} to the result, provided @var{value} is given.  If
+@var{symbol} has a buffer-local binding in the current buffer,
+@code{defconst} sets the default value, not the local value.
+
+@strong{Please note:} don't use @code{defconst} for user option
+variables in libraries that are not standardly preloaded.  The user
+should be able to specify a value for such a variable in the
+@file{.emacs} file, so that it will be in effect if and when the library
+is loaded later.
+
+Here, @code{pi} is a constant that presumably ought not to be changed
+by anyone (attempts by the Indiana State Legislature notwithstanding).
+As the second form illustrates, however, this is only advisory.
+
+@example
+@group
+(defconst pi 3.1415 "Pi to five places.")
+     @result{} pi
+@end group
+@group
+(setq pi 3)
+     @result{} pi
+@end group
+@group
+pi
+     @result{} 3
+@end group
+@end example
+@end defspec
+
+@defun user-variable-p variable
+@cindex user option
+This function returns @code{t} if @var{variable} is a user option--- a
+variable intended to be set by the user for customization---and
+@code{nil} otherwise.  (Variables other than user options exist for the
+internal purposes of Lisp programs, and users need not know about them.)
+
+User option variables are distinguished from other variables by the
+first character of the @code{variable-documentation} property.  If the
+property exists and is a string, and its first character is @samp{*},
+then the variable is a user option.
+@end defun
+
+  If a user option variable has a @code{variable-interactive} property,
+@code{set-variable} uses that value to control reading the new value for
+the variable.  The property's value is used as if it were the argument
+to @code{interactive}.
+
+  @strong{Warning:} if the @code{defconst} and @code{defvar} special
+forms are used while the variable has a local binding, they set the
+local binding's value; the global binding is not changed.  This is not
+what we really want.  To prevent it, use these special forms at top
+level in a file, where normally no local binding is in effect, and make
+sure to load the file before making a local binding for the variable.
+
+@node Accessing Variables
+@section Accessing Variable Values
+
+  The usual way to reference a variable is to write the symbol which
+names it (@pxref{Symbol Forms}).  This requires you to specify the
+variable name when you write the program.  Usually that is exactly what
+you want to do.  Occasionally you need to choose at run time which
+variable to reference; then you can use @code{symbol-value}.
+
+@defun symbol-value symbol
+This function returns the value of @var{symbol}.  This is the value in
+the innermost local binding of the symbol, or its global value if it
+has no local bindings.
+
+@example
+@group
+(setq abracadabra 5)
+     @result{} 5
+@end group
+@group
+(setq foo 9)
+     @result{} 9
+@end group
+
+@group
+;; @r{Here the symbol @code{abracadabra}}
+;;   @r{is the symbol whose value is examined.}
+(let ((abracadabra 'foo))
+  (symbol-value 'abracadabra))
+     @result{} foo
+@end group
+
+@group
+;; @r{Here the value of @code{abracadabra},}
+;;   @r{which is @code{foo},}
+;;   @r{is the symbol whose value is examined.}
+(let ((abracadabra 'foo))
+  (symbol-value abracadabra))
+     @result{} 9
+@end group
+
+@group
+(symbol-value 'abracadabra)
+     @result{} 5
+@end group
+@end example
+
+A @code{void-variable} error is signaled if @var{symbol} has neither a
+local binding nor a global value.
+@end defun
+
+@node Setting Variables
+@section How to Alter a Variable Value
+
+  The usual way to change the value of a variable is with the special
+form @code{setq}.  When you need to compute the choice of variable at
+run time, use the function @code{set}.
+
+@defspec setq [symbol form]@dots{}
+This special form is the most common method of changing a variable's
+value.  Each @var{symbol} is given a new value, which is the result of
+evaluating the corresponding @var{form}.  The most-local existing
+binding of the symbol is changed.
+
+@code{setq} does not evaluate @var{symbol}; it sets the symbol that you
+write.  We say that this argument is @dfn{automatically quoted}.  The
+@samp{q} in @code{setq} stands for ``quoted.''
+
+The value of the @code{setq} form is the value of the last @var{form}.
+
+@example
+@group
+(setq x (1+ 2))
+     @result{} 3
+@end group
+x                   ; @r{@code{x} now has a global value.}
+     @result{} 3
+@group
+(let ((x 5)) 
+  (setq x 6)        ; @r{The local binding of @code{x} is set.}
+  x)
+     @result{} 6
+@end group
+x                   ; @r{The global value is unchanged.}
+     @result{} 3
+@end example
+
+Note that the first @var{form} is evaluated, then the first
+@var{symbol} is set, then the second @var{form} is evaluated, then the
+second @var{symbol} is set, and so on:
+
+@example
+@group
+(setq x 10          ; @r{Notice that @code{x} is set before}
+      y (1+ x))     ;   @r{the value of @code{y} is computed.}
+     @result{} 11             
+@end group
+@end example
+@end defspec
+
+@defun set symbol value
+This function sets @var{symbol}'s value to @var{value}, then returns
+@var{value}.  Since @code{set} is a function, the expression written for
+@var{symbol} is evaluated to obtain the symbol to set.
+
+The most-local existing binding of the variable is the binding that is
+set; shadowed bindings are not affected.  If @var{symbol} is not
+actually a symbol, a @code{wrong-type-argument} error is signaled.
+
+@example
+@group
+(set one 1)
+@error{} Symbol's value as variable is void: one
+@end group
+@group
+(set 'one 1)
+     @result{} 1
+@end group
+@group
+(set 'two 'one)
+     @result{} one
+@end group
+@group
+(set two 2)         ; @r{@code{two} evaluates to symbol @code{one}.}
+     @result{} 2
+@end group
+@group
+one                 ; @r{So it is @code{one} that was set.}
+     @result{} 2
+(let ((one 1))      ; @r{This binding of @code{one} is set,}
+  (set 'one 3)      ;   @r{not the global value.}
+  one)
+     @result{} 3
+@end group
+@group
+one
+     @result{} 2
+@end group
+@end example
+
+Logically speaking, @code{set} is a more fundamental primitive than
+@code{setq}.  Any use of @code{setq} can be trivially rewritten to use
+@code{set}; @code{setq} could even be defined as a macro, given the
+availability of @code{set}.  However, @code{set} itself is rarely used;
+beginners hardly need to know about it.  It is needed for choosing which
+variable to set is made at run time.  For example, the command
+@code{set-variable}, which reads a variable name from the user and then
+sets the variable, needs to use @code{set}.
+
+@cindex CL note---@code{set} local
+@quotation
+@b{Common Lisp note:} in Common Lisp, @code{set} always changes the
+symbol's special value, ignoring any lexical bindings.  In Emacs Lisp,
+all variables and all bindings are (in effect) special, so @code{set}
+always affects the most local existing binding.
+@end quotation
+@end defun
+
+@node Variable Scoping
+@section Scoping Rules for Variable Bindings
+
+  A given symbol @code{foo} may have several local variable bindings,
+established at different places in the Lisp program, as well as a global
+binding.  The most recently established binding takes precedence over
+the others.
+
+@cindex scope
+@cindex extent
+@cindex dynamic scoping
+  Local bindings in Emacs Lisp have @dfn{indefinite scope} and
+@dfn{dynamic extent}.  @dfn{Scope} refers to @emph{where} textually in
+the source code the binding can be accessed.  Indefinite scope means
+that any part of the program can potentially access the variable
+binding.  @dfn{Extent} refers to @emph{when}, as the program is
+executing, the binding exists.  Dynamic extent means that the binding
+lasts as long as the activation of the construct that established it.
+
+  The combination of dynamic extent and indefinite scope is called
+@dfn{dynamic scoping}.  By contrast, most programming languages use
+@dfn{lexical scoping}, in which references to a local variable must be
+located textually within the function or block that binds the variable.
+
+@cindex CL note---special variables
+@quotation
+@b{Common Lisp note:} variables declared ``special'' in Common Lisp
+are dynamically scoped like variables in Emacs Lisp.
+@end quotation
+
+@menu
+* Scope::          Scope means where in the program a value is visible.
+                     Comparison with other languages.
+* Extent::         Extent means how long in time a value exists.
+* Impl of Scope::  Two ways to implement dynamic scoping.
+* Using Scoping::  How to use dynamic scoping carefully and avoid problems.
+@end menu
+
+@node Scope
+@subsection Scope
+
+  Emacs Lisp uses @dfn{indefinite scope} for local variable bindings.
+This means that any function anywhere in the program text might access a
+given binding of a variable.  Consider the following function
+definitions:
+
+@example
+@group
+(defun binder (x)   ; @r{@code{x} is bound in @code{binder}.}
+   (foo 5))         ; @r{@code{foo} is some other function.}
+@end group
+
+@group
+(defun user ()      ; @r{@code{x} is used in @code{user}.}
+  (list x))
+@end group
+@end example
+
+  In a lexically scoped language, the binding of @code{x} in
+@code{binder} would never be accessible in @code{user}, because
+@code{user} is not textually contained within the function
+@code{binder}.  However, in dynamically scoped Emacs Lisp, @code{user}
+may or may not refer to the binding of @code{x} established in
+@code{binder}, depending on circumstances:
+
+@itemize @bullet
+@item
+If we call @code{user} directly without calling @code{binder} at all,
+then whatever binding of @code{x} is found, it cannot come from
+@code{binder}.
+
+@item
+If we define @code{foo} as follows and call @code{binder}, then the
+binding made in @code{binder} will be seen in @code{user}:
+
+@example
+@group
+(defun foo (lose)
+  (user))
+@end group
+@end example
+
+@item
+If we define @code{foo} as follows and call @code{binder}, then the
+binding made in @code{binder} @emph{will not} be seen in @code{user}:
+
+@example
+(defun foo (x)
+  (user))
+@end example
+
+@noindent
+Here, when @code{foo} is called by @code{binder}, it binds @code{x}.
+(The binding in @code{foo} is said to @dfn{shadow} the one made in
+@code{binder}.)  Therefore, @code{user} will access the @code{x} bound
+by @code{foo} instead of the one bound by @code{binder}.
+@end itemize
+
+@node Extent
+@subsection Extent
+
+  @dfn{Extent} refers to the time during program execution that a
+variable name is valid.  In Emacs Lisp, a variable is valid only while
+the form that bound it is executing.  This is called @dfn{dynamic
+extent}.  ``Local'' or ``automatic'' variables in most languages,
+including C and Pascal, have dynamic extent.
+
+  One alternative to dynamic extent is @dfn{indefinite extent}.  This
+means that a variable binding can live on past the exit from the form
+that made the binding.  Common Lisp and Scheme, for example, support
+this, but Emacs Lisp does not.
+
+  To illustrate this, the function below, @code{make-add}, returns a
+function that purports to add @var{n} to its own argument @var{m}.
+This would work in Common Lisp, but it does not work as intended in
+Emacs Lisp, because after the call to @code{make-add} exits, the
+variable @code{n} is no longer bound to the actual argument 2.
+
+@example
+(defun make-add (n)
+    (function (lambda (m) (+ n m))))  ; @r{Return a function.}
+     @result{} make-add
+(fset 'add2 (make-add 2))  ; @r{Define function @code{add2}}
+                           ;   @r{with @code{(make-add 2)}.}
+     @result{} (lambda (m) (+ n m))
+(add2 4)                   ; @r{Try to add 2 to 4.}
+@error{} Symbol's value as variable is void: n
+@end example
+
+@cindex closures not available
+  Some Lisp dialects have ``closures'', objects that are like functions
+but record additional variable bindings.  Emacs Lisp does not have
+closures.
+
+@node Impl of Scope
+@subsection Implementation of Dynamic Scoping
+@cindex deep binding
+
+  A simple sample implementation (which is not how Emacs Lisp actually
+works) may help you understand dynamic binding.  This technique is
+called @dfn{deep binding} and was used in early Lisp systems.
+
+  Suppose there is a stack of bindings: variable-value pairs.  At entry
+to a function or to a @code{let} form, we can push bindings on the stack
+for the arguments or local variables created there.  We can pop those
+bindings from the stack at exit from the binding construct.
+
+  We can find the value of a variable by searching the stack from top to
+bottom for a binding for that variable; the value from that binding is
+the value of the variable.  To set the variable, we search for the
+current binding, then store the new value into that binding.
+
+  As you can see, a function's bindings remain in effect as long as it
+continues execution, even during its calls to other functions.  That is
+why we say the extent of the binding is dynamic.  And any other function
+can refer to the bindings, if it uses the same variables while the
+bindings are in effect.  That is why we say the scope is indefinite.
+
+@cindex shallow binding
+  The actual implementation of variable scoping in GNU Emacs Lisp uses a
+technique called @dfn{shallow binding}.  Each variable has a standard
+place in which its current value is always found---the value cell of the
+symbol.
+
+  In shallow binding, setting the variable works by storing a value in
+the value cell.  Creating a new binding works by pushing the old value
+(belonging to a previous binding) on a stack, and storing the local value
+in the value cell.  Eliminating a binding works by popping the old value
+off the stack, into the value cell.
+
+  We use shallow binding because it has the same results as deep
+binding, but runs faster, since there is never a need to search for a
+binding.
+
+@node Using Scoping
+@subsection Proper Use of Dynamic Scoping
+
+  Binding a variable in one function and using it in another is a
+powerful technique, but if used without restraint, it can make programs
+hard to understand.  There are two clean ways to use this technique:
+
+@itemize @bullet
+@item
+Use or bind the variable only in a few related functions, written close
+together in one file.  Such a variable is used for communication within
+one program.
+
+You should write comments to inform other programmers that they can see
+all uses of the variable before them, and to advise them not to add uses
+elsewhere.
+
+@item
+Give the variable a well-defined, documented meaning, and make all
+appropriate functions refer to it (but not bind it or set it) wherever
+that meaning is relevant.  For example, the variable
+@code{case-fold-search} is defined as ``non-@code{nil} means ignore case
+when searching''; various search and replace functions refer to it
+directly or through their subroutines, but do not bind or set it.
+
+Then you can bind the variable in other programs, knowing reliably what
+the effect will be.
+@end itemize
+
+@node Buffer-Local Variables
+@section Buffer-Local Variables
+@cindex variables, buffer-local
+@cindex buffer-local variables
+
+  Global and local variable bindings are found in most programming
+languages in one form or another.  Emacs also supports another, unusual
+kind of variable binding: @dfn{buffer-local} bindings, which apply only
+to one buffer.  Emacs Lisp is meant for programming editing commands,
+and having different values for a variable in different buffers is an
+important customization method.
+
+@menu
+* Intro to Buffer-Local::      Introduction and concepts.
+* Creating Buffer-Local::      Creating and destroying buffer-local bindings.
+* Default Value::              The default value is seen in buffers
+                                 that don't have their own local values.
+@end menu
+
+@node Intro to Buffer-Local
+@subsection Introduction to Buffer-Local Variables
+
+  A buffer-local variable has a buffer-local binding associated with a
+particular buffer.  The binding is in effect when that buffer is
+current; otherwise, it is not in effect.  If you set the variable while
+a buffer-local binding is in effect, the new value goes in that binding,
+so the global binding is unchanged; this means that the change is
+visible in that buffer alone.
+
+  A variable may have buffer-local bindings in some buffers but not in
+others.  The global binding is shared by all the buffers that don't have
+their own bindings.  Thus, if you set the variable in a buffer that does
+not have a buffer-local binding for it, the new value is visible in all
+buffers except those with buffer-local bindings.  (Here we are assuming
+that there are no @code{let}-style local bindings to complicate the issue.)
+
+  The most common use of buffer-local bindings is for major modes to change
+variables that control the behavior of commands.  For example, C mode and
+Lisp mode both set the variable @code{paragraph-start} to specify that only
+blank lines separate paragraphs.  They do this by making the variable
+buffer-local in the buffer that is being put into C mode or Lisp mode, and
+then setting it to the new value for that mode.
+
+  The usual way to make a buffer-local binding is with
+@code{make-local-variable}, which is what major mode commands use.  This
+affects just the current buffer; all other buffers (including those yet to
+be created) continue to share the global value.
+
+@cindex automatically buffer-local
+  A more powerful operation is to mark the variable as
+@dfn{automatically buffer-local} by calling
+@code{make-variable-buffer-local}.  You can think of this as making the
+variable local in all buffers, even those yet to be created.  More
+precisely, the effect is that setting the variable automatically makes
+the variable local to the current buffer if it is not already so.  All
+buffers start out by sharing the global value of the variable as usual,
+but any @code{setq} creates a buffer-local binding for the current
+buffer.  The new value is stored in the buffer-local binding, leaving
+the (default) global binding untouched.  The global value can no longer
+be changed with @code{setq}; you need to use @code{setq-default} to do
+that.
+
+  @strong{Warning:} when a variable has local values in one or more
+buffers, you can get Emacs very confused by binding the variable with
+@code{let}, changing to a different current buffer in which a different
+binding is in effect, and then exiting the @code{let}.  This can
+scramble the values of the global and local bindings.
+
+  To preserve your sanity, avoid that series of actions.  If you use
+@code{save-excursion} around each piece of code that changes to a
+different current buffer, you will not have this problem.  Here is an
+example of what to avoid:
+
+@example
+@group
+(setq foo 'b)
+(set-buffer "a")
+(make-local-variable 'foo)
+@end group
+(setq foo 'a)
+(let ((foo 'temp))
+  (set-buffer "b")
+  @dots{})
+@group
+foo @result{} 'a      ; @r{The old buffer-local value from buffer @samp{a}}
+               ;   @r{is now the default value.}
+@end group
+@group
+(set-buffer "a")
+foo @result{} 'temp   ; @r{The local value that should be gone}
+               ;   @r{is now the buffer-local value in buffer @samp{a}.}
+@end group
+@end example
+
+@noindent
+But @code{save-excursion} as shown here avoids the problem:
+
+@example
+@group
+(let ((foo 'temp))
+  (save-excursion
+    (set-buffer "b")
+    @var{body}@dots{}))
+@end group
+@end example
+
+  Note that references to @code{foo} in @var{body} access the
+buffer-local binding of buffer @samp{b}.
+
+  When a file specifies local variable values, these become buffer-local
+value when you visit the file.  @xref{Auto Major Mode}.
+
+@node Creating Buffer-Local
+@subsection Creating and Deleting Buffer-Local Bindings
+
+@deffn Command make-local-variable variable
+This function creates a buffer-local binding in the current buffer for
+@var{variable} (a symbol).  Other buffers are not affected.  The value
+returned is @var{variable}.
+
+@c Emacs 19 feature
+The buffer-local value of @var{variable} starts out as the same value
+@var{variable} previously had.  If @var{variable} was void, it remains
+void.
+
+@example
+@group
+;; @r{In buffer @samp{b1}:}
+(setq foo 5)                ; @r{Affects all buffers.}
+     @result{} 5
+@end group
+@group
+(make-local-variable 'foo)  ; @r{Now it is local in @samp{b1}.}
+     @result{} foo
+@end group
+@group
+foo                         ; @r{That did not change}
+     @result{} 5                   ;   @r{the value.}
+@end group
+@group
+(setq foo 6)                ; @r{Change the value}
+     @result{} 6                   ;   @r{in @samp{b1}.}
+@end group
+@group
+foo
+     @result{} 6
+@end group
+
+@group
+;; @r{In buffer @samp{b2}, the value hasn't changed.}
+(save-excursion
+  (set-buffer "b2")
+  foo)
+     @result{} 5
+@end group
+@end example
+@end deffn
+
+@deffn Command make-variable-buffer-local variable
+This function marks @var{variable} (a symbol) automatically
+buffer-local, so that any subsequent attempt to set it will make it
+local to the current buffer at the time.
+
+The value returned is @var{variable}.
+@end deffn
+
+@defun buffer-local-variables &optional buffer
+This function returns a list describing the buffer-local variables in
+buffer @var{buffer}.  It returns an association list (@pxref{Association
+Lists}) in which each association contains one buffer-local variable and
+its value.  When a buffer-local variable is void in @var{buffer}, then
+it appears directly in the resulting list.  If @var{buffer} is omitted,
+the current buffer is used.
+
+@example
+@group
+(make-local-variable 'foobar)
+(makunbound 'foobar)
+(make-local-variable 'bind-me)
+(setq bind-me 69)
+@end group
+(setq lcl (buffer-local-variables))
+    ;; @r{First, built-in variables local in all buffers:}
+@result{} ((mark-active . nil)
+    (buffer-undo-list nil)
+    (mode-name . "Fundamental")
+    @dots{}
+@group
+    ;; @r{Next, non-built-in local variables.} 
+    ;; @r{This one is local and void:}
+    foobar
+    ;; @r{This one is local and nonvoid:}
+    (bind-me . 69))
+@end group
+@end example
+
+Note that storing new values into the @sc{cdr}s of cons cells in this
+list does @emph{not} change the local values of the variables.
+@end defun
+
+@deffn Command kill-local-variable variable
+This function deletes the buffer-local binding (if any) for
+@var{variable} (a symbol) in the current buffer.  As a result, the
+global (default) binding of @var{variable} becomes visible in this
+buffer.  Usually this results in a change in the value of
+@var{variable}, since the global value is usually different from the
+buffer-local value just eliminated.
+
+If you kill the local binding of a variable that automatically becomes
+local when set, this makes the global value visible in the current
+buffer.  However, if you set the variable again, that will once again
+create a local binding for it.
+
+@code{kill-local-variable} returns @var{variable}.
+@end deffn
+
+@defun kill-all-local-variables
+This function eliminates all the buffer-local variable bindings of the
+current buffer except for variables marked as ``permanent''.  As a
+result, the buffer will see the default values of most variables.
+
+This function also resets certain other information pertaining to the
+buffer: it sets the local keymap to @code{nil}, the syntax table to the
+value of @code{standard-syntax-table}, and the abbrev table to the value
+of @code{fundamental-mode-abbrev-table}.
+
+Every major mode command begins by calling this function, which has the
+effect of switching to Fundamental mode and erasing most of the effects
+of the previous major mode.  To ensure that this does its job, the
+variables that major modes set should not be marked permanent.
+
+@code{kill-all-local-variables} returns @code{nil}.
+@end defun
+
+@c Emacs 19 feature
+@cindex permanent local variable
+A local variable is @dfn{permanent} if the variable name (a symbol) has a
+@code{permanent-local} property that is non-@code{nil}.  Permanent
+locals are appropriate for data pertaining to where the file came from
+or how to save it, rather than with how to edit the contents.
+
+@node Default Value
+@subsection The Default Value of a Buffer-Local Variable
+@cindex default value
+
+  The global value of a variable with buffer-local bindings is also
+called the @dfn{default} value, because it is the value that is in
+effect except when specifically overridden.
+
+  The functions @code{default-value} and @code{setq-default} access and
+change a variable's default value regardless of whether the current
+buffer has a buffer-local binding.  For example, you could use
+@code{setq-default} to change the default setting of
+@code{paragraph-start} for most buffers; and this would work even when
+you are in a C or Lisp mode buffer which has a buffer-local value for
+this variable.
+
+@c Emacs 19 feature
+  The special forms @code{defvar} and @code{defconst} also set the
+default value (if they set the variable at all), rather than any local
+value.
+
+@defun default-value symbol
+This function returns @var{symbol}'s default value.  This is the value
+that is seen in buffers that do not have their own values for this
+variable.  If @var{symbol} is not buffer-local, this is equivalent to
+@code{symbol-value} (@pxref{Accessing Variables}).
+@end defun
+
+@c Emacs 19 feature
+@defun default-boundp variable
+The function @code{default-boundp} tells you whether @var{variable}'s
+default value is nonvoid.  If @code{(default-boundp 'foo)} returns
+@code{nil}, then @code{(default-value 'foo)} would get an error.
+
+@code{default-boundp} is to @code{default-value} as @code{boundp} is to
+@code{symbol-value}.
+@end defun
+
+@defspec setq-default symbol value
+This sets the default value of @var{symbol} to @var{value}.  It does not
+evaluate @var{symbol}, but does evaluate @var{value}.  The value of the
+@code{setq-default} form is @var{value}.
+
+If a @var{symbol} is not buffer-local for the current buffer, and is not
+marked automatically buffer-local, @code{setq-default} has the same
+effect as @code{setq}.  If @var{symbol} is buffer-local for the current
+buffer, then this changes the value that other buffers will see (as long
+as they don't have a buffer-local value), but not the value that the
+current buffer sees.
+
+@example
+@group
+;; @r{In buffer @samp{foo}:}
+(make-local-variable 'local)
+     @result{} local
+@end group
+@group
+(setq local 'value-in-foo)
+     @result{} value-in-foo
+@end group
+@group
+(setq-default local 'new-default)
+     @result{} new-default
+@end group
+@group
+local
+     @result{} value-in-foo
+@end group
+@group
+(default-value 'local)
+     @result{} new-default
+@end group
+
+@group
+;; @r{In (the new) buffer @samp{bar}:}
+local
+     @result{} new-default
+@end group
+@group
+(default-value 'local)
+     @result{} new-default
+@end group
+@group
+(setq local 'another-default)
+     @result{} another-default
+@end group
+@group
+(default-value 'local)
+     @result{} another-default
+@end group
+
+@group
+;; @r{Back in buffer @samp{foo}:}
+local
+     @result{} value-in-foo
+(default-value 'local)
+     @result{} another-default
+@end group
+@end example
+@end defspec
+
+@defun set-default symbol value
+This function is like @code{setq-default}, except that @var{symbol} is
+evaluated.
+
+@example
+@group
+(set-default (car '(a b c)) 23)
+     @result{} 23
+@end group
+@group
+(default-value 'a)
+     @result{} 23
+@end group
+@end example
+@end defun
+