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authorStefan Monnier2003-10-20 21:38:50 +0000
committerStefan Monnier2003-10-20 21:38:50 +0000
commite1e44180c1cfb20f00bc5c9db4d068746e9c7f73 (patch)
treec7aacd4beed21178b179e6c7726a65e12b469ec7
parentb1664339f4c1adac3f5d1e9a99c3850a28346100 (diff)
downloademacs-e1e44180c1cfb20f00bc5c9db4d068746e9c7f73.tar.gz
emacs-e1e44180c1cfb20f00bc5c9db4d068746e9c7f73.zip
Update for extra bit of integer range.
Diffstat
-rw-r--r--lispref/numbers.texi144
1 files changed, 72 insertions, 72 deletions
diff --git a/lispref/numbers.texi b/lispref/numbers.texi
index 177b229e160..3dc686f452a 100644
--- a/lispref/numbers.texi
+++ b/lispref/numbers.texi
@@ -1,6 +1,6 @@
1@c -*-texinfo-*- 1@c -*-texinfo-*-
2@c This is part of the GNU Emacs Lisp Reference Manual. 2@c This is part of the GNU Emacs Lisp Reference Manual.
3@c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999 3@c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999, 2003
4@c Free Software Foundation, Inc. 4@c Free Software Foundation, Inc.
5@c See the file elisp.texi for copying conditions. 5@c See the file elisp.texi for copying conditions.
6@setfilename ../info/numbers 6@setfilename ../info/numbers
@@ -36,22 +36,22 @@ exact; they have a fixed, limited amount of precision.
36@section Integer Basics 36@section Integer Basics
37 37
38 The range of values for an integer depends on the machine. The 38 The range of values for an integer depends on the machine. The
39minimum range is @minus{}134217728 to 134217727 (28 bits; i.e., 39minimum range is @minus{}268435456 to 268435455 (29 bits; i.e.,
40@ifnottex 40@ifnottex
41-2**27 41-2**28
42@end ifnottex 42@end ifnottex
43@tex 43@tex
44@math{-2^{27}} 44@math{-2^{28}}
45@end tex 45@end tex
46to 46to
47@ifnottex 47@ifnottex
482**27 - 1), 482**28 - 1),
49@end ifnottex 49@end ifnottex
50@tex 50@tex
51@math{2^{27}-1}), 51@math{2^{28}-1}),
52@end tex 52@end tex
53but some machines may provide a wider range. Many examples in this 53but some machines may provide a wider range. Many examples in this
54chapter assume an integer has 28 bits. 54chapter assume an integer has 29 bits.
55@cindex overflow 55@cindex overflow
56 56
57 The Lisp reader reads an integer as a sequence of digits with optional 57 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{#}
86bitwise operators (@pxref{Bitwise Operations}), it is often helpful to 86bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
87view the numbers in their binary form. 87view the numbers in their binary form.
88 88
89 In 28-bit binary, the decimal integer 5 looks like this: 89 In 29-bit binary, the decimal integer 5 looks like this:
90 90
91@example 91@example
920000 0000 0000 0000 0000 0000 0101 920 0000 0000 0000 0000 0000 0000 0101
93@end example 93@end example
94 94
95@noindent 95@noindent
@@ -99,12 +99,12 @@ between groups of 8 bits, to make the binary integer easier to read.)
99 The integer @minus{}1 looks like this: 99 The integer @minus{}1 looks like this:
100 100
101@example 101@example
1021111 1111 1111 1111 1111 1111 1111 1021 1111 1111 1111 1111 1111 1111 1111
103@end example 103@end example
104 104
105@noindent 105@noindent
106@cindex two's complement 106@cindex two's complement
107@minus{}1 is represented as 28 ones. (This is called @dfn{two's 107@minus{}1 is represented as 29 ones. (This is called @dfn{two's
108complement} notation.) 108complement} notation.)
109 109
110 The negative integer, @minus{}5, is creating by subtracting 4 from 110 The negative integer, @minus{}5, is creating by subtracting 4 from
@@ -112,24 +112,24 @@ complement} notation.)
112@minus{}5 looks like this: 112@minus{}5 looks like this:
113 113
114@example 114@example
1151111 1111 1111 1111 1111 1111 1011 1151 1111 1111 1111 1111 1111 1111 1011
116@end example 116@end example
117 117
118 In this implementation, the largest 28-bit binary integer value is 118 In this implementation, the largest 29-bit binary integer value is
119134,217,727 in decimal. In binary, it looks like this: 119268,435,455 in decimal. In binary, it looks like this:
120 120
121@example 121@example
1220111 1111 1111 1111 1111 1111 1111 1220 1111 1111 1111 1111 1111 1111 1111
123@end example 123@end example
124 124
125 Since the arithmetic functions do not check whether integers go 125 Since the arithmetic functions do not check whether integers go
126outside their range, when you add 1 to 134,217,727, the value is the 126outside their range, when you add 1 to 268,435,455, the value is the
127negative integer @minus{}134,217,728: 127negative integer @minus{}268,435,456:
128 128
129@example 129@example
130(+ 1 134217727) 130(+ 1 268435455)
131 @result{} -134217728 131 @result{} -268435456
132 @result{} 1000 0000 0000 0000 0000 0000 0000 132 @result{} 1 0000 0000 0000 0000 0000 0000 0000
133@end example 133@end example
134 134
135 Many of the functions described in this chapter accept markers for 135 Many of the functions described in this chapter accept markers for
@@ -468,8 +468,8 @@ commonly used.
468if any argument is floating. 468if any argument is floating.
469 469
470 It is important to note that in Emacs Lisp, arithmetic functions 470 It is important to note that in Emacs Lisp, arithmetic functions
471do not check for overflow. Thus @code{(1+ 134217727)} may evaluate to 471do not check for overflow. Thus @code{(1+ 268435455)} may evaluate to
472@minus{}134217728, depending on your hardware. 472@minus{}268435456, depending on your hardware.
473 473
474@defun 1+ number-or-marker 474@defun 1+ number-or-marker
475This function returns @var{number-or-marker} plus 1. 475This function returns @var{number-or-marker} plus 1.
@@ -788,19 +788,19 @@ value of a positive integer by two, rounding downward.
788The function @code{lsh}, like all Emacs Lisp arithmetic functions, does 788The function @code{lsh}, like all Emacs Lisp arithmetic functions, does
789not check for overflow, so shifting left can discard significant bits 789not check for overflow, so shifting left can discard significant bits
790and change the sign of the number. For example, left shifting 790and change the sign of the number. For example, left shifting
791134,217,727 produces @minus{}2 on a 28-bit machine: 791268,435,455 produces @minus{}2 on a 29-bit machine:
792 792
793@example 793@example
794(lsh 134217727 1) ; @r{left shift} 794(lsh 268435455 1) ; @r{left shift}
795 @result{} -2 795 @result{} -2
796@end example 796@end example
797 797
798In binary, in the 28-bit implementation, the argument looks like this: 798In binary, in the 29-bit implementation, the argument looks like this:
799 799
800@example 800@example
801@group 801@group
802;; @r{Decimal 134,217,727} 802;; @r{Decimal 268,435,455}
8030111 1111 1111 1111 1111 1111 1111 8030 1111 1111 1111 1111 1111 1111 1111
804@end group 804@end group
805@end example 805@end example
806 806
@@ -810,7 +810,7 @@ which becomes the following when left shifted:
810@example 810@example
811@group 811@group
812;; @r{Decimal @minus{}2} 812;; @r{Decimal @minus{}2}
8131111 1111 1111 1111 1111 1111 1110 8131 1111 1111 1111 1111 1111 1111 1110
814@end group 814@end group
815@end example 815@end example
816@end defun 816@end defun
@@ -833,9 +833,9 @@ looks like this:
833@group 833@group
834(ash -6 -1) @result{} -3 834(ash -6 -1) @result{} -3
835;; @r{Decimal @minus{}6 becomes decimal @minus{}3.} 835;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
8361111 1111 1111 1111 1111 1111 1010 8361 1111 1111 1111 1111 1111 1111 1010
837 @result{} 837 @result{}
8381111 1111 1111 1111 1111 1111 1101 8381 1111 1111 1111 1111 1111 1111 1101
839@end group 839@end group
840@end example 840@end example
841 841
@@ -844,11 +844,11 @@ In contrast, shifting the pattern of bits one place to the right with
844 844
845@example 845@example
846@group 846@group
847(lsh -6 -1) @result{} 134217725 847(lsh -6 -1) @result{} 268435453
848;; @r{Decimal @minus{}6 becomes decimal 134,217,725.} 848;; @r{Decimal @minus{}6 becomes decimal 268,435,453.}
8491111 1111 1111 1111 1111 1111 1010 8491 1111 1111 1111 1111 1111 1111 1010
850 @result{} 850 @result{}
8510111 1111 1111 1111 1111 1111 1101 8510 1111 1111 1111 1111 1111 1111 1101
852@end group 852@end group
853@end example 853@end example
854 854
@@ -858,34 +858,34 @@ Here are other examples:
858@c with smallbook but not with regular book! --rjc 16mar92 858@c with smallbook but not with regular book! --rjc 16mar92
859@smallexample 859@smallexample
860@group 860@group
861 ; @r{ 28-bit binary values} 861 ; @r{ 29-bit binary values}
862 862
863(lsh 5 2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 863(lsh 5 2) ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
864 @result{} 20 ; = @r{0000 0000 0000 0000 0000 0001 0100} 864 @result{} 20 ; = @r{0 0000 0000 0000 0000 0000 0001 0100}
865@end group 865@end group
866@group 866@group
867(ash 5 2) 867(ash 5 2)
868 @result{} 20 868 @result{} 20
869(lsh -5 2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011} 869(lsh -5 2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
870 @result{} -20 ; = @r{1111 1111 1111 1111 1111 1110 1100} 870 @result{} -20 ; = @r{1 1111 1111 1111 1111 1111 1110 1100}
871(ash -5 2) 871(ash -5 2)
872 @result{} -20 872 @result{} -20
873@end group 873@end group
874@group 874@group
875(lsh 5 -2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 875(lsh 5 -2) ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
876 @result{} 1 ; = @r{0000 0000 0000 0000 0000 0000 0001} 876 @result{} 1 ; = @r{0 0000 0000 0000 0000 0000 0000 0001}
877@end group 877@end group
878@group 878@group
879(ash 5 -2) 879(ash 5 -2)
880 @result{} 1 880 @result{} 1
881@end group 881@end group
882@group 882@group
883(lsh -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011} 883(lsh -5 -2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
884 @result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1111 1110} 884 @result{} 134217726 ; = @r{0 0111 1111 1111 1111 1111 1111 1110}
885@end group 885@end group
886@group 886@group
887(ash -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011} 887(ash -5 -2) ; -5 = @r{1 1111 1111 1111 1111 1111 1111 1011}
888 @result{} -2 ; = @r{1111 1111 1111 1111 1111 1111 1110} 888 @result{} -2 ; = @r{1 1111 1111 1111 1111 1111 1111 1110}
889@end group 889@end group
890@end smallexample 890@end smallexample
891@end defun 891@end defun
@@ -922,23 +922,23 @@ because its binary representation consists entirely of ones. If
922 922
923@smallexample 923@smallexample
924@group 924@group
925 ; @r{ 28-bit binary values} 925 ; @r{ 29-bit binary values}
926 926
927(logand 14 13) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110} 927(logand 14 13) ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
928 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101} 928 ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
929 @result{} 12 ; 12 = @r{0000 0000 0000 0000 0000 0000 1100} 929 @result{} 12 ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
930@end group 930@end group
931 931
932@group 932@group
933(logand 14 13 4) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110} 933(logand 14 13 4) ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
934 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101} 934 ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
935 ; 4 = @r{0000 0000 0000 0000 0000 0000 0100} 935 ; 4 = @r{0 0000 0000 0000 0000 0000 0000 0100}
936 @result{} 4 ; 4 = @r{0000 0000 0000 0000 0000 0000 0100} 936 @result{} 4 ; 4 = @r{0 0000 0000 0000 0000 0000 0000 0100}
937@end group 937@end group
938 938
939@group 939@group
940(logand) 940(logand)
941 @result{} -1 ; -1 = @r{1111 1111 1111 1111 1111 1111 1111} 941 @result{} -1 ; -1 = @r{1 1111 1111 1111 1111 1111 1111 1111}
942@end group 942@end group
943@end smallexample 943@end smallexample
944@end defun 944@end defun
@@ -954,18 +954,18 @@ passed just one argument, it returns that argument.
954 954
955@smallexample 955@smallexample
956@group 956@group
957 ; @r{ 28-bit binary values} 957 ; @r{ 29-bit binary values}
958 958
959(logior 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100} 959(logior 12 5) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
960 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 960 ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
961 @result{} 13 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101} 961 @result{} 13 ; 13 = @r{0 0000 0000 0000 0000 0000 0000 1101}
962@end group 962@end group
963 963
964@group 964@group
965(logior 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100} 965(logior 12 5 7) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
966 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 966 ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
967 ; 7 = @r{0000 0000 0000 0000 0000 0000 0111} 967 ; 7 = @r{0 0000 0000 0000 0000 0000 0000 0111}
968 @result{} 15 ; 15 = @r{0000 0000 0000 0000 0000 0000 1111} 968 @result{} 15 ; 15 = @r{0 0000 0000 0000 0000 0000 0000 1111}
969@end group 969@end group
970@end smallexample 970@end smallexample
971@end defun 971@end defun
@@ -981,18 +981,18 @@ result is 0, which is an identity element for this operation. If
981 981
982@smallexample 982@smallexample
983@group 983@group
984 ; @r{ 28-bit binary values} 984 ; @r{ 29-bit binary values}
985 985
986(logxor 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100} 986(logxor 12 5) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
987 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 987 ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
988 @result{} 9 ; 9 = @r{0000 0000 0000 0000 0000 0000 1001} 988 @result{} 9 ; 9 = @r{0 0000 0000 0000 0000 0000 0000 1001}
989@end group 989@end group
990 990
991@group 991@group
992(logxor 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100} 992(logxor 12 5 7) ; 12 = @r{0 0000 0000 0000 0000 0000 0000 1100}
993 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 993 ; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
994 ; 7 = @r{0000 0000 0000 0000 0000 0000 0111} 994 ; 7 = @r{0 0000 0000 0000 0000 0000 0000 0111}
995 @result{} 14 ; 14 = @r{0000 0000 0000 0000 0000 0000 1110} 995 @result{} 14 ; 14 = @r{0 0000 0000 0000 0000 0000 0000 1110}
996@end group 996@end group
997@end smallexample 997@end smallexample
998@end defun 998@end defun
@@ -1007,9 +1007,9 @@ bit is one in the result if, and only if, the @var{n}th bit is zero in
1007@example 1007@example
1008(lognot 5) 1008(lognot 5)
1009 @result{} -6 1009 @result{} -6
1010;; 5 = @r{0000 0000 0000 0000 0000 0000 0101} 1010;; 5 = @r{0 0000 0000 0000 0000 0000 0000 0101}
1011;; @r{becomes} 1011;; @r{becomes}
1012;; -6 = @r{1111 1111 1111 1111 1111 1111 1010} 1012;; -6 = @r{1 1111 1111 1111 1111 1111 1111 1010}
1013@end example 1013@end example
1014@end defun 1014@end defun
1015 1015
generated by cgit v1.2.1 (git 2.18.0) at 2026-04-14 07:12:26 +0000