@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
-@c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999, 2001,
-@c 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011
+@c Copyright (C) 1990-1995, 1998-1999, 2001-2012
@c Free Software Foundation, Inc.
@c See the file elisp.texi for copying conditions.
@setfilename ../../info/numbers
@tex
@math{2^{29}-1}),
@end tex
-but some machines may provide a wider range. Many examples in this
-chapter assume an integer has 30 bits.
+but some machines provide a wider range. Many examples in this
+chapter assume that an integer has 30 bits and that floating point
+numbers are IEEE double precision.
@cindex overflow
The Lisp reader reads an integer as a sequence of digits with optional
-initial sign and optional final period.
+initial sign and optional final period. An integer that is out of the
+Emacs range is treated as a floating-point number.
@example
1 ; @r{The integer 1.}
1. ; @r{The integer 1.}
+1 ; @r{Also the integer 1.}
-1 ; @r{The integer @minus{}1.}
- 1073741825 ; @r{Also the integer 1, due to overflow.}
+ 1073741825 ; @r{The floating point number 1073741825.0.}
0 ; @r{The integer 0.}
-0 ; @r{The integer 0.}
@end example
In 30-bit binary, the decimal integer 5 looks like this:
@example
-00 0000 0000 0000 0000 0000 0000 0101
+0000...000101 (30 bits total)
@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 @samp{...} stands for enough bits to fill out a 30-bit word; in
+this case, @samp{...} stands for twenty 0 bits. Later examples also
+use the @samp{...} notation to make binary integers easier to read.)
The integer @minus{}1 looks like this:
@example
-11 1111 1111 1111 1111 1111 1111 1111
+1111...111111 (30 bits total)
@end example
@noindent
@minus{}5 looks like this:
@example
-11 1111 1111 1111 1111 1111 1111 1011
+1111...111011 (30 bits total)
@end example
In this implementation, the largest 30-bit binary integer value is
536,870,911 in decimal. In binary, it looks like this:
@example
-01 1111 1111 1111 1111 1111 1111 1111
+0111...111111 (30 bits total)
@end example
Since the arithmetic functions do not check whether integers go
@example
(+ 1 536870911)
@result{} -536870912
- @result{} 10 0000 0000 0000 0000 0000 0000 0000
+ @result{} 1000...000000 (30 bits total)
@end example
Many of the functions described in this chapter accept markers for
give these arguments the name @var{number-or-marker}. When the argument
value is a marker, its position value is used and its buffer is ignored.
+@cindex largest Lisp integer number
+@cindex maximum Lisp integer number
@defvar most-positive-fixnum
The value of this variable is the largest integer that Emacs Lisp
can handle.
@end defvar
+@cindex smallest Lisp integer number
+@cindex minimum Lisp integer number
@defvar most-negative-fixnum
The value of this variable is the smallest integer that Emacs Lisp can
handle. It is negative.
@samp{1.0e+INF}
@item negative infinity
@samp{-1.0e+INF}
-@item Not-a-number
+@item Not-a-number
@samp{0.0e+NaN} or @samp{-0.0e+NaN}.
@end table
if any argument is floating.
It is important to note that in Emacs Lisp, arithmetic functions
-do not check for overflow. Thus @code{(1+ 268435455)} may evaluate to
-@minus{}268435456, depending on your hardware.
+do not check for overflow. Thus @code{(1+ 536870911)} may evaluate to
+@minus{}536870912, depending on your hardware.
@defun 1+ number-or-marker
This function returns @var{number-or-marker} plus 1.
The function @code{lsh}, like all Emacs Lisp arithmetic functions, does
not check for overflow, so shifting left can discard significant bits
and change the sign of the number. For example, left shifting
-536,870,911 produces @minus{}2 on a 30-bit machine:
+536,870,911 produces @minus{}2 in the 30-bit implementation:
@example
(lsh 536870911 1) ; @r{left shift}
@result{} -2
@end example
-In binary, in the 30-bit implementation, the argument looks like this:
+In binary, the argument looks like this:
@example
@group
;; @r{Decimal 536,870,911}
-01 1111 1111 1111 1111 1111 1111 1111
+0111...111111 (30 bits total)
@end group
@end example
@example
@group
;; @r{Decimal @minus{}2}
-11 1111 1111 1111 1111 1111 1111 1110
+1111...111110 (30 bits total)
@end group
@end example
@end defun
@group
(ash -6 -1) @result{} -3
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
-11 1111 1111 1111 1111 1111 1111 1010
+1111...111010 (30 bits total)
@result{}
-11 1111 1111 1111 1111 1111 1111 1101
+1111...111101 (30 bits total)
@end group
@end example
@group
(lsh -6 -1) @result{} 536870909
;; @r{Decimal @minus{}6 becomes decimal 536,870,909.}
-11 1111 1111 1111 1111 1111 1111 1010
+1111...111010 (30 bits total)
@result{}
-01 1111 1111 1111 1111 1111 1111 1101
+0111...111101 (30 bits total)
@end group
@end example
@c with smallbook but not with regular book! --rjc 16mar92
@smallexample
@group
- ; @r{ 30-bit binary values}
+ ; @r{ 30-bit binary values}
-(lsh 5 2) ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- @result{} 20 ; = @r{00 0000 0000 0000 0000 0000 0001 0100}
+(lsh 5 2) ; 5 = @r{0000...000101}
+ @result{} 20 ; = @r{0000...010100}
@end group
@group
(ash 5 2)
@result{} 20
-(lsh -5 2) ; -5 = @r{11 1111 1111 1111 1111 1111 1111 1011}
- @result{} -20 ; = @r{11 1111 1111 1111 1111 1111 1110 1100}
+(lsh -5 2) ; -5 = @r{1111...111011}
+ @result{} -20 ; = @r{1111...101100}
(ash -5 2)
@result{} -20
@end group
@group
-(lsh 5 -2) ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- @result{} 1 ; = @r{00 0000 0000 0000 0000 0000 0000 0001}
+(lsh 5 -2) ; 5 = @r{0000...000101}
+ @result{} 1 ; = @r{0000...000001}
@end group
@group
(ash 5 -2)
@result{} 1
@end group
@group
-(lsh -5 -2) ; -5 = @r{11 1111 1111 1111 1111 1111 1111 1011}
- @result{} 268435454 ; = @r{00 0111 1111 1111 1111 1111 1111 1110}
+(lsh -5 -2) ; -5 = @r{1111...111011}
+ @result{} 268435454
+ ; = @r{0011...111110}
@end group
@group
-(ash -5 -2) ; -5 = @r{11 1111 1111 1111 1111 1111 1111 1011}
- @result{} -2 ; = @r{11 1111 1111 1111 1111 1111 1111 1110}
+(ash -5 -2) ; -5 = @r{1111...111011}
+ @result{} -2 ; = @r{1111...111110}
@end group
@end smallexample
@end defun
@smallexample
@group
- ; @r{ 30-bit binary values}
+ ; @r{ 30-bit binary values}
-(logand 14 13) ; 14 = @r{00 0000 0000 0000 0000 0000 0000 1110}
- ; 13 = @r{00 0000 0000 0000 0000 0000 0000 1101}
- @result{} 12 ; 12 = @r{00 0000 0000 0000 0000 0000 0000 1100}
+(logand 14 13) ; 14 = @r{0000...001110}
+ ; 13 = @r{0000...001101}
+ @result{} 12 ; 12 = @r{0000...001100}
@end group
@group
-(logand 14 13 4) ; 14 = @r{00 0000 0000 0000 0000 0000 0000 1110}
- ; 13 = @r{00 0000 0000 0000 0000 0000 0000 1101}
- ; 4 = @r{00 0000 0000 0000 0000 0000 0000 0100}
- @result{} 4 ; 4 = @r{00 0000 0000 0000 0000 0000 0000 0100}
+(logand 14 13 4) ; 14 = @r{0000...001110}
+ ; 13 = @r{0000...001101}
+ ; 4 = @r{0000...000100}
+ @result{} 4 ; 4 = @r{0000...000100}
@end group
@group
(logand)
- @result{} -1 ; -1 = @r{11 1111 1111 1111 1111 1111 1111 1111}
+ @result{} -1 ; -1 = @r{1111...111111}
@end group
@end smallexample
@end defun
@smallexample
@group
- ; @r{ 30-bit binary values}
+ ; @r{ 30-bit binary values}
-(logior 12 5) ; 12 = @r{00 0000 0000 0000 0000 0000 0000 1100}
- ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- @result{} 13 ; 13 = @r{00 0000 0000 0000 0000 0000 0000 1101}
+(logior 12 5) ; 12 = @r{0000...001100}
+ ; 5 = @r{0000...000101}
+ @result{} 13 ; 13 = @r{0000...001101}
@end group
@group
-(logior 12 5 7) ; 12 = @r{00 0000 0000 0000 0000 0000 0000 1100}
- ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- ; 7 = @r{00 0000 0000 0000 0000 0000 0000 0111}
- @result{} 15 ; 15 = @r{00 0000 0000 0000 0000 0000 0000 1111}
+(logior 12 5 7) ; 12 = @r{0000...001100}
+ ; 5 = @r{0000...000101}
+ ; 7 = @r{0000...000111}
+ @result{} 15 ; 15 = @r{0000...001111}
@end group
@end smallexample
@end defun
@smallexample
@group
- ; @r{ 30-bit binary values}
+ ; @r{ 30-bit binary values}
-(logxor 12 5) ; 12 = @r{00 0000 0000 0000 0000 0000 0000 1100}
- ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- @result{} 9 ; 9 = @r{00 0000 0000 0000 0000 0000 0000 1001}
+(logxor 12 5) ; 12 = @r{0000...001100}
+ ; 5 = @r{0000...000101}
+ @result{} 9 ; 9 = @r{0000...001001}
@end group
@group
-(logxor 12 5 7) ; 12 = @r{00 0000 0000 0000 0000 0000 0000 1100}
- ; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
- ; 7 = @r{00 0000 0000 0000 0000 0000 0000 0111}
- @result{} 14 ; 14 = @r{00 0000 0000 0000 0000 0000 0000 1110}
+(logxor 12 5 7) ; 12 = @r{0000...001100}
+ ; 5 = @r{0000...000101}
+ ; 7 = @r{0000...000111}
+ @result{} 14 ; 14 = @r{0000...001110}
@end group
@end smallexample
@end defun
@example
(lognot 5)
@result{} -6
-;; 5 = @r{00 0000 0000 0000 0000 0000 0000 0101}
+;; 5 = @r{0000...000101} (30 bits total)
;; @r{becomes}
-;; -6 = @r{11 1111 1111 1111 1111 1111 1111 1010}
+;; -6 = @r{1111...111010} (30 bits total)
@end example
@end defun
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
-
-@ignore
- arch-tag: 574e8dd2-d513-4616-9844-c9a27869782e
-@end ignore