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[Emacs-diffs] Changes to emacs/lispref/numbers.texi
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From: |
Stefan Monnier |
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Subject: |
[Emacs-diffs] Changes to emacs/lispref/numbers.texi |
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Date: |
Mon, 20 Oct 2003 17:38:50 -0400 |
Index: emacs/lispref/numbers.texi
diff -c emacs/lispref/numbers.texi:1.26 emacs/lispref/numbers.texi:1.27
*** emacs/lispref/numbers.texi:1.26 Thu Oct 16 12:35:14 2003
--- emacs/lispref/numbers.texi Mon Oct 20 17:38:50 2003
***************
*** 1,6 ****
@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
! @c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999
@c Free Software Foundation, Inc.
@c See the file elisp.texi for copying conditions.
@setfilename ../info/numbers
--- 1,6 ----
@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
! @c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999, 2003
@c Free Software Foundation, Inc.
@c See the file elisp.texi for copying conditions.
@setfilename ../info/numbers
***************
*** 36,57 ****
@section Integer Basics
The range of values for an integer depends on the machine. The
! minimum range is @minus{}134217728 to 134217727 (28 bits; i.e.,
@ifnottex
! -2**27
@end ifnottex
@tex
! @math{-2^{27}}
@end tex
to
@ifnottex
! 2**27 - 1),
@end ifnottex
@tex
! @math{2^{27}-1}),
@end tex
but some machines may provide a wider range. Many examples in this
! chapter assume an integer has 28 bits.
@cindex overflow
The Lisp reader reads an integer as a sequence of digits with optional
--- 36,57 ----
@section Integer Basics
The range of values for an integer depends on the machine. The
! minimum range is @minus{}268435456 to 268435455 (29 bits; i.e.,
@ifnottex
! -2**28
@end ifnottex
@tex
! @math{-2^{28}}
@end tex
to
@ifnottex
! 2**28 - 1),
@end ifnottex
@tex
! @math{2^{28}-1}),
@end tex
but some machines may provide a wider range. Many examples in this
! chapter assume an integer has 29 bits.
@cindex overflow
The Lisp reader reads an integer as a sequence of digits with optional
***************
*** 86,95 ****
bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
view the numbers in their binary form.
! In 28-bit binary, the decimal integer 5 looks like this:
@example
! 0000 0000 0000 0000 0000 0000 0101
@end example
@noindent
--- 86,95 ----
bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
view the numbers in their binary form.
! In 29-bit binary, the decimal integer 5 looks like this:
@example
! 0 0000 0000 0000 0000 0000 0000 0101
@end example
@noindent
***************
*** 99,110 ****
The integer @minus{}1 looks like this:
@example
! 1111 1111 1111 1111 1111 1111 1111
@end example
@noindent
@cindex two's complement
! @minus{}1 is represented as 28 ones. (This is called @dfn{two's
complement} notation.)
The negative integer, @minus{}5, is creating by subtracting 4 from
--- 99,110 ----
The integer @minus{}1 looks like this:
@example
! 1 1111 1111 1111 1111 1111 1111 1111
@end example
@noindent
@cindex two's complement
! @minus{}1 is represented as 29 ones. (This is called @dfn{two's
complement} notation.)
The negative integer, @minus{}5, is creating by subtracting 4 from
***************
*** 112,135 ****
@minus{}5 looks like this:
@example
! 1111 1111 1111 1111 1111 1111 1011
@end example
! In this implementation, the largest 28-bit binary integer value is
! 134,217,727 in decimal. In binary, it looks like this:
@example
! 0111 1111 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 134,217,727, the value is the
! negative integer @minus{}134,217,728:
@example
! (+ 1 134217727)
! @result{} -134217728
! @result{} 1000 0000 0000 0000 0000 0000 0000
@end example
Many of the functions described in this chapter accept markers for
--- 112,135 ----
@minus{}5 looks like this:
@example
! 1 1111 1111 1111 1111 1111 1111 1011
@end example
! In this implementation, the largest 29-bit binary integer value is
! 268,435,455 in decimal. In binary, it looks like this:
@example
! 0 1111 1111 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 268,435,455, the value is the
! negative integer @minus{}268,435,456:
@example
! (+ 1 268435455)
! @result{} -268435456
! @result{} 1 0000 0000 0000 0000 0000 0000 0000
@end example
Many of the functions described in this chapter accept markers for
***************
*** 468,475 ****
if any argument is floating.
It is important to note that in Emacs Lisp, arithmetic functions
! do not check for overflow. Thus @code{(1+ 134217727)} may evaluate to
! @minus{}134217728, depending on your hardware.
@defun 1+ number-or-marker
This function returns @var{number-or-marker} plus 1.
--- 468,475 ----
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.
@defun 1+ number-or-marker
This function returns @var{number-or-marker} plus 1.
***************
*** 788,806 ****
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
! 134,217,727 produces @minus{}2 on a 28-bit machine:
@example
! (lsh 134217727 1) ; @r{left shift}
@result{} -2
@end example
! In binary, in the 28-bit implementation, the argument looks like this:
@example
@group
! ;; @r{Decimal 134,217,727}
! 0111 1111 1111 1111 1111 1111 1111
@end group
@end example
--- 788,806 ----
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
! 268,435,455 produces @minus{}2 on a 29-bit machine:
@example
! (lsh 268435455 1) ; @r{left shift}
@result{} -2
@end example
! In binary, in the 29-bit implementation, the argument looks like this:
@example
@group
! ;; @r{Decimal 268,435,455}
! 0 1111 1111 1111 1111 1111 1111 1111
@end group
@end example
***************
*** 810,816 ****
@example
@group
;; @r{Decimal @minus{}2}
! 1111 1111 1111 1111 1111 1111 1110
@end group
@end example
@end defun
--- 810,816 ----
@example
@group
;; @r{Decimal @minus{}2}
! 1 1111 1111 1111 1111 1111 1111 1110
@end group
@end example
@end defun
***************
*** 833,841 ****
@group
(ash -6 -1) @result{} -3
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
! 1111 1111 1111 1111 1111 1111 1010
@result{}
! 1111 1111 1111 1111 1111 1111 1101
@end group
@end example
--- 833,841 ----
@group
(ash -6 -1) @result{} -3
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
! 1 1111 1111 1111 1111 1111 1111 1010
@result{}
! 1 1111 1111 1111 1111 1111 1111 1101
@end group
@end example
***************
*** 844,854 ****
@example
@group
! (lsh -6 -1) @result{} 134217725
! ;; @r{Decimal @minus{}6 becomes decimal 134,217,725.}
! 1111 1111 1111 1111 1111 1111 1010
@result{}
! 0111 1111 1111 1111 1111 1111 1101
@end group
@end example
--- 844,854 ----
@example
@group
! (lsh -6 -1) @result{} 268435453
! ;; @r{Decimal @minus{}6 becomes decimal 268,435,453.}
! 1 1111 1111 1111 1111 1111 1111 1010
@result{}
! 0 1111 1111 1111 1111 1111 1111 1101
@end group
@end example
***************
*** 858,891 ****
@c with smallbook but not with regular book! --rjc 16mar92
@smallexample
@group
! ; @r{ 28-bit binary values}
! (lsh 5 2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! @result{} 20 ; = @r{0000 0000 0000 0000 0000 0001 0100}
@end group
@group
(ash 5 2)
@result{} 20
! (lsh -5 2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011}
! @result{} -20 ; = @r{1111 1111 1111 1111 1111 1110 1100}
(ash -5 2)
@result{} -20
@end group
@group
! (lsh 5 -2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! @result{} 1 ; = @r{0000 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 1111 1011}
! @result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1111 1110}
@end group
@group
! (ash -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011}
! @result{} -2 ; = @r{1111 1111 1111 1111 1111 1111 1110}
@end group
@end smallexample
@end defun
--- 858,891 ----
@c with smallbook but not with regular book! --rjc 16mar92
@smallexample
@group
! ; @r{ 29-bit binary values}
! (lsh 5 2) ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! @result{} 20 ; = @r{0 0000 0000 0000 0000 0000 0001
0100}
@end group
@group
(ash 5 2)
@result{} 20
! (lsh -5 2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
! @result{} -20 ; = @r{1 1111 1111 1111 1111 1111 1110
1100}
(ash -5 2)
@result{} -20
@end group
@group
! (lsh 5 -2) ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! @result{} 1 ; = @r{0 0000 0000 0000 0000 0000 0000
0001}
@end group
@group
(ash 5 -2)
@result{} 1
@end group
@group
! (lsh -5 -2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
! @result{} 134217726 ; = @r{0 0111 1111 1111 1111 1111 1111
1110}
@end group
@group
! (ash -5 -2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
! @result{} -2 ; = @r{1 1111 1111 1111 1111 1111 1111
1110}
@end group
@end smallexample
@end defun
***************
*** 922,944 ****
@smallexample
@group
! ; @r{ 28-bit binary values}
! (logand 14 13) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
! ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
! @result{} 12 ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
@end group
@group
! (logand 14 13 4) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
! ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
! ; 4 = @r{0000 0000 0000 0000 0000 0000 0100}
! @result{} 4 ; 4 = @r{0000 0000 0000 0000 0000 0000 0100}
@end group
@group
(logand)
! @result{} -1 ; -1 = @r{1111 1111 1111 1111 1111 1111 1111}
@end group
@end smallexample
@end defun
--- 922,944 ----
@smallexample
@group
! ; @r{ 29-bit binary values}
! (logand 14 13) ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
! ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
! @result{} 12 ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
@end group
@group
! (logand 14 13 4) ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
! ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
! ; 4 = @r{0 0000 0000 0000 0000 0000 0000 0100}
! @result{} 4 ; 4 = @r{0 0000 0000 0000 0000 0000 0000 0100}
@end group
@group
(logand)
! @result{} -1 ; -1 = @r{1 1111 1111 1111 1111 1111 1111 1111}
@end group
@end smallexample
@end defun
***************
*** 954,971 ****
@smallexample
@group
! ; @r{ 28-bit binary values}
! (logior 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! @result{} 13 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
@end group
@group
! (logior 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! ; 7 = @r{0000 0000 0000 0000 0000 0000 0111}
! @result{} 15 ; 15 = @r{0000 0000 0000 0000 0000 0000 1111}
@end group
@end smallexample
@end defun
--- 954,971 ----
@smallexample
@group
! ; @r{ 29-bit binary values}
! (logior 12 5) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! @result{} 13 ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
@end group
@group
! (logior 12 5 7) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! ; 7 = @r{0 0000 0000 0000 0000 0000 0000 0111}
! @result{} 15 ; 15 = @r{0 0000 0000 0000 0000 0000 0000 1111}
@end group
@end smallexample
@end defun
***************
*** 981,998 ****
@smallexample
@group
! ; @r{ 28-bit binary values}
! (logxor 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! @result{} 9 ; 9 = @r{0000 0000 0000 0000 0000 0000 1001}
@end group
@group
! (logxor 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
! ; 7 = @r{0000 0000 0000 0000 0000 0000 0111}
! @result{} 14 ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
@end group
@end smallexample
@end defun
--- 981,998 ----
@smallexample
@group
! ; @r{ 29-bit binary values}
! (logxor 12 5) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! @result{} 9 ; 9 = @r{0 0000 0000 0000 0000 0000 0000 1001}
@end group
@group
! (logxor 12 5 7) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
! ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
! ; 7 = @r{0 0000 0000 0000 0000 0000 0000 0111}
! @result{} 14 ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
@end group
@end smallexample
@end defun
***************
*** 1007,1015 ****
@example
(lognot 5)
@result{} -6
! ;; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
;; @r{becomes}
! ;; -6 = @r{1111 1111 1111 1111 1111 1111 1010}
@end example
@end defun
--- 1007,1015 ----
@example
(lognot 5)
@result{} -6
! ;; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
;; @r{becomes}
! ;; -6 = @r{1 1111 1111 1111 1111 1111 1111 1010}
@end example
@end defun