Update for extra bit of integer range.
This commit is contained in:
Stefan Monnier
parent
b1664339f4
commit
e1e44180c1
1 changed files with 72 additions and 72 deletions
|
|
@ -1,6 +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 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
|
||||
|
|
@ -36,22 +36,22 @@ exact; they have a fixed, limited amount of precision.
|
|||
@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.,
|
||||
minimum range is @minus{}268435456 to 268435455 (29 bits; i.e.,
|
||||
@ifnottex
|
||||
-2**27
|
||||
-2**28
|
||||
@end ifnottex
|
||||
@tex
|
||||
@math{-2^{27}}
|
||||
@math{-2^{28}}
|
||||
@end tex
|
||||
to
|
||||
@ifnottex
|
||||
2**27 - 1),
|
||||
2**28 - 1),
|
||||
@end ifnottex
|
||||
@tex
|
||||
@math{2^{27}-1}),
|
||||
@math{2^{28}-1}),
|
||||
@end tex
|
||||
but some machines may provide a wider range. Many examples in this
|
||||
chapter assume an integer has 28 bits.
|
||||
chapter assume an integer has 29 bits.
|
||||
@cindex overflow
|
||||
|
||||
The Lisp reader reads an integer as a sequence of digits with optional
|
||||
|
|
@ -86,10 +86,10 @@ inclusively). Case is not significant for the letter after @samp{#}
|
|||
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:
|
||||
In 29-bit binary, the decimal integer 5 looks like this:
|
||||
|
||||
@example
|
||||
0000 0000 0000 0000 0000 0000 0101
|
||||
0 0000 0000 0000 0000 0000 0000 0101
|
||||
@end example
|
||||
|
||||
@noindent
|
||||
|
|
@ -99,12 +99,12 @@ 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 1111
|
||||
1 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
|
||||
@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
|
||||
|
|
@ -112,24 +112,24 @@ complement} notation.)
|
|||
@minus{}5 looks like this:
|
||||
|
||||
@example
|
||||
1111 1111 1111 1111 1111 1111 1011
|
||||
1 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:
|
||||
In this implementation, the largest 29-bit binary integer value is
|
||||
268,435,455 in decimal. In binary, it looks like this:
|
||||
|
||||
@example
|
||||
0111 1111 1111 1111 1111 1111 1111
|
||||
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 134,217,727, the value is the
|
||||
negative integer @minus{}134,217,728:
|
||||
outside their range, when you add 1 to 268,435,455, the value is the
|
||||
negative integer @minus{}268,435,456:
|
||||
|
||||
@example
|
||||
(+ 1 134217727)
|
||||
@result{} -134217728
|
||||
@result{} 1000 0000 0000 0000 0000 0000 0000
|
||||
(+ 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
|
||||
|
|
@ -468,8 +468,8 @@ commonly used.
|
|||
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.
|
||||
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.
|
||||
|
|
@ -788,19 +788,19 @@ value of a positive integer by two, rounding downward.
|
|||
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:
|
||||
268,435,455 produces @minus{}2 on a 29-bit machine:
|
||||
|
||||
@example
|
||||
(lsh 134217727 1) ; @r{left shift}
|
||||
(lsh 268435455 1) ; @r{left shift}
|
||||
@result{} -2
|
||||
@end example
|
||||
|
||||
In binary, in the 28-bit implementation, the argument looks like this:
|
||||
In binary, in the 29-bit implementation, the argument looks like this:
|
||||
|
||||
@example
|
||||
@group
|
||||
;; @r{Decimal 134,217,727}
|
||||
0111 1111 1111 1111 1111 1111 1111
|
||||
;; @r{Decimal 268,435,455}
|
||||
0 1111 1111 1111 1111 1111 1111 1111
|
||||
@end group
|
||||
@end example
|
||||
|
||||
|
|
@ -810,7 +810,7 @@ which becomes the following when left shifted:
|
|||
@example
|
||||
@group
|
||||
;; @r{Decimal @minus{}2}
|
||||
1111 1111 1111 1111 1111 1111 1110
|
||||
1 1111 1111 1111 1111 1111 1111 1110
|
||||
@end group
|
||||
@end example
|
||||
@end defun
|
||||
|
|
@ -833,9 +833,9 @@ looks like this:
|
|||
@group
|
||||
(ash -6 -1) @result{} -3
|
||||
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
|
||||
1111 1111 1111 1111 1111 1111 1010
|
||||
1 1111 1111 1111 1111 1111 1111 1010
|
||||
@result{}
|
||||
1111 1111 1111 1111 1111 1111 1101
|
||||
1 1111 1111 1111 1111 1111 1111 1101
|
||||
@end group
|
||||
@end example
|
||||
|
||||
|
|
@ -844,11 +844,11 @@ In contrast, shifting the pattern of bits one place to the right with
|
|||
|
||||
@example
|
||||
@group
|
||||
(lsh -6 -1) @result{} 134217725
|
||||
;; @r{Decimal @minus{}6 becomes decimal 134,217,725.}
|
||||
1111 1111 1111 1111 1111 1111 1010
|
||||
(lsh -6 -1) @result{} 268435453
|
||||
;; @r{Decimal @minus{}6 becomes decimal 268,435,453.}
|
||||
1 1111 1111 1111 1111 1111 1111 1010
|
||||
@result{}
|
||||
0111 1111 1111 1111 1111 1111 1101
|
||||
0 1111 1111 1111 1111 1111 1111 1101
|
||||
@end group
|
||||
@end example
|
||||
|
||||
|
|
@ -858,34 +858,34 @@ Here are other examples:
|
|||
@c with smallbook but not with regular book! --rjc 16mar92
|
||||
@smallexample
|
||||
@group
|
||||
; @r{ 28-bit binary values}
|
||||
; @r{ 29-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}
|
||||
(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{1111 1111 1111 1111 1111 1111 1011}
|
||||
@result{} -20 ; = @r{1111 1111 1111 1111 1111 1110 1100}
|
||||
(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{0000 0000 0000 0000 0000 0000 0101}
|
||||
@result{} 1 ; = @r{0000 0000 0000 0000 0000 0000 0001}
|
||||
(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{1111 1111 1111 1111 1111 1111 1011}
|
||||
@result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1111 1110}
|
||||
(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{1111 1111 1111 1111 1111 1111 1011}
|
||||
@result{} -2 ; = @r{1111 1111 1111 1111 1111 1111 1110}
|
||||
(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
|
||||
|
|
@ -922,23 +922,23 @@ because its binary representation consists entirely of ones. If
|
|||
|
||||
@smallexample
|
||||
@group
|
||||
; @r{ 28-bit binary values}
|
||||
; @r{ 29-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}
|
||||
(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{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}
|
||||
(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{1111 1111 1111 1111 1111 1111 1111}
|
||||
@result{} -1 ; -1 = @r{1 1111 1111 1111 1111 1111 1111 1111}
|
||||
@end group
|
||||
@end smallexample
|
||||
@end defun
|
||||
|
|
@ -954,18 +954,18 @@ passed just one argument, it returns that argument.
|
|||
|
||||
@smallexample
|
||||
@group
|
||||
; @r{ 28-bit binary values}
|
||||
; @r{ 29-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}
|
||||
(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{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}
|
||||
(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
|
||||
|
|
@ -981,18 +981,18 @@ result is 0, which is an identity element for this operation. If
|
|||
|
||||
@smallexample
|
||||
@group
|
||||
; @r{ 28-bit binary values}
|
||||
; @r{ 29-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}
|
||||
(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{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}
|
||||
(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
|
||||
|
|
@ -1007,9 +1007,9 @@ bit is one in the result if, and only if, the @var{n}th bit is zero in
|
|||
@example
|
||||
(lognot 5)
|
||||
@result{} -6
|
||||
;; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
|
||||
;; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
|
||||
;; @r{becomes}
|
||||
;; -6 = @r{1111 1111 1111 1111 1111 1111 1010}
|
||||
;; -6 = @r{1 1111 1111 1111 1111 1111 1111 1010}
|
||||
@end example
|
||||
@end defun
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue