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authorRichard M. Stallman1995-01-02 06:51:21 +0000
committerRichard M. Stallman1995-01-02 06:51:21 +0000
commit8be5e0fcc3559112ef6c047fcb68132961b1081c (patch)
treedccba81822e4e988c8652a4e57692414bc3d1f02
parent32ce36ad51e3c0eb7a7c2eabe8ee88cf489dd02d (diff)
downloademacs-8be5e0fcc3559112ef6c047fcb68132961b1081c.tar.gz
emacs-8be5e0fcc3559112ef6c047fcb68132961b1081c.zip
Integers now at least 28 bits.
Diffstat
-rw-r--r--lispref/numbers.texi142
1 files changed, 72 insertions, 70 deletions
diff --git a/lispref/numbers.texi b/lispref/numbers.texi
index b083d73c4aa..dec1af1c93f 100644
--- a/lispref/numbers.texi
+++ b/lispref/numbers.texi
@@ -39,23 +39,22 @@ where Emacs does not support them.
39@section Integer Basics 39@section Integer Basics
40 40
41 The range of values for an integer depends on the machine. The 41 The range of values for an integer depends on the machine. The
42range is @minus{}8388608 to 8388607 (24 bits; i.e., 42range is @minus{}8388608 to 8388607 (28 bits; i.e.,
43@ifinfo 43@ifinfo
44-2**23 44-2**27
45@end ifinfo 45@end ifinfo
46@tex 46@tex
47$-2^{23}$ 47$-2^{27}$
48@end tex 48@end tex
49to 49to
50@ifinfo 50@ifinfo
512**23 - 1) 512**27 - 1)
52@end ifinfo 52@end ifinfo
53@tex 53@tex
54$2^{23}-1$) 54$2^{27}-1$)
55@end tex 55@end tex
56on most machines, but on others it is @minus{}16777216 to 16777215 (25 56on most machines, but some machines may have a wider range. Many
57bits), or @minus{}33554432 to 33554431 (26 bits). Many examples in this 57examples in this chapter assume an integer has 28 bits.
58chapter assume an integer has 24 bits.
59@cindex overflow 58@cindex overflow
60 59
61 The Lisp reader reads an integer as a sequence of digits with optional 60 The Lisp reader reads an integer as a sequence of digits with optional
@@ -66,7 +65,7 @@ initial sign and optional final period.
66 1. ; @r{The integer 1.} 65 1. ; @r{The integer 1.}
67+1 ; @r{Also the integer 1.} 66+1 ; @r{Also the integer 1.}
68-1 ; @r{The integer @minus{}1.} 67-1 ; @r{The integer @minus{}1.}
69 16777217 ; @r{Also the integer 1, due to overflow.} 68 268435457 ; @r{Also the integer 1, due to overflow.}
70 0 ; @r{The integer 0.} 69 0 ; @r{The integer 0.}
71-0 ; @r{The integer 0.} 70-0 ; @r{The integer 0.}
72@end example 71@end example
@@ -75,10 +74,10 @@ initial sign and optional final period.
75bitwise operators (@pxref{Bitwise Operations}), it is often helpful to 74bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
76view the numbers in their binary form. 75view the numbers in their binary form.
77 76
78 In 24-bit binary, the decimal integer 5 looks like this: 77 In 28-bit binary, the decimal integer 5 looks like this:
79 78
80@example 79@example
810000 0000 0000 0000 0000 0101 800000 0000 0000 0000 0000 0000 0101
82@end example 81@end example
83 82
84@noindent 83@noindent
@@ -88,12 +87,12 @@ between groups of 8 bits, to make the binary integer easier to read.)
88 The integer @minus{}1 looks like this: 87 The integer @minus{}1 looks like this:
89 88
90@example 89@example
911111 1111 1111 1111 1111 1111 901111 1111 1111 1111 1111 1111 1111
92@end example 91@end example
93 92
94@noindent 93@noindent
95@cindex two's complement 94@cindex two's complement
96@minus{}1 is represented as 24 ones. (This is called @dfn{two's 95@minus{}1 is represented as 28 ones. (This is called @dfn{two's
97complement} notation.) 96complement} notation.)
98 97
99 The negative integer, @minus{}5, is creating by subtracting 4 from 98 The negative integer, @minus{}5, is creating by subtracting 4 from
@@ -101,24 +100,24 @@ complement} notation.)
101@minus{}5 looks like this: 100@minus{}5 looks like this:
102 101
103@example 102@example
1041111 1111 1111 1111 1111 1011 1031111 1111 1111 1111 1111 1111 1011
105@end example 104@end example
106 105
107 In this implementation, the largest 24-bit binary integer is the 106 In this implementation, the largest 24-bit binary integer is the
108decimal integer 8,388,607. In binary, it looks like this: 107decimal integer 134,217,727. In binary, it looks like this:
109 108
110@example 109@example
1110111 1111 1111 1111 1111 1111 1100111 1111 1111 1111 1111 1111 1111
112@end example 111@end example
113 112
114 Since the arithmetic functions do not check whether integers go 113 Since the arithmetic functions do not check whether integers go
115outside their range, when you add 1 to 8,388,607, the value is the 114outside their range, when you add 1 to 134,217,727, the value is the
116negative integer @minus{}8,388,608: 115negative integer @minus{}134,217,728:
117 116
118@example 117@example
119(+ 1 8388607) 118(+ 1 134217727)
120 @result{} -8388608 119 @result{} -134217728
121 @result{} 1000 0000 0000 0000 0000 0000 120 @result{} 1000 0000 0000 0000 0000 0000 0000
122@end example 121@end example
123 122
124 Many of the following functions accept markers for arguments as well 123 Many of the following functions accept markers for arguments as well
@@ -651,12 +650,12 @@ produces @minus{}2 on a 24-bit machine:
651 @result{} -2 650 @result{} -2
652@end example 651@end example
653 652
654In binary, in the 24-bit implementation, the argument looks like this: 653In binary, in the 28-bit implementation, the argument looks like this:
655 654
656@example 655@example
657@group 656@group
658;; @r{Decimal 8,388,607} 657;; @r{Decimal 134.217,727}
6590111 1111 1111 1111 1111 1111 6580111 1111 1111 1111 1111 1111 1111
660@end group 659@end group
661@end example 660@end example
662 661
@@ -666,7 +665,7 @@ which becomes the following when left shifted:
666@example 665@example
667@group 666@group
668;; @r{Decimal @minus{}2} 667;; @r{Decimal @minus{}2}
6691111 1111 1111 1111 1111 1110 6681111 1111 1111 1111 1111 1111 1110
670@end group 669@end group
671@end example 670@end example
672 671
@@ -724,9 +723,9 @@ looks like this:
724@group 723@group
725(ash -6 -1) @result{} -3 724(ash -6 -1) @result{} -3
726;; @r{Decimal @minus{}6 becomes decimal @minus{}3.} 725;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
7271111 1111 1111 1111 1111 1010 7261111 1111 1111 1111 1111 1111 1010
728 @result{} 727 @result{}
7291111 1111 1111 1111 1111 1101 7281111 1111 1111 1111 1111 1111 1101
730@end group 729@end group
731@end example 730@end example
732 731
@@ -735,11 +734,11 @@ In contrast, shifting the pattern of bits one place to the right with
735 734
736@example 735@example
737@group 736@group
738(lsh -6 -1) @result{} 8388605 737(lsh -6 -1) @result{} 134217725
739;; @r{Decimal @minus{}6 becomes decimal 8,388,605.} 738;; @r{Decimal @minus{}6 becomes decimal 134,217,725.}
7401111 1111 1111 1111 1111 1010 7391111 1111 1111 1111 1111 1111 1010
741 @result{} 740 @result{}
7420111 1111 1111 1111 1111 1101 7410111 1111 1111 1111 1111 1111 1101
743@end group 742@end group
744@end example 743@end example
745 744
@@ -749,34 +748,34 @@ Here are other examples:
749@c with smallbook but not with regular book! --rjc 16mar92 748@c with smallbook but not with regular book! --rjc 16mar92
750@smallexample 749@smallexample
751@group 750@group
752 ; @r{ 24-bit binary values} 751 ; @r{ 28-bit binary values}
753 752
754(lsh 5 2) ; 5 = @r{0000 0000 0000 0000 0000 0101} 753(lsh 5 2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
755 @result{} 20 ; = @r{0000 0000 0000 0000 0001 0100} 754 @result{} 20 ; = @r{0000 0000 0000 0000 0000 0001 0100}
756@end group 755@end group
757@group 756@group
758(ash 5 2) 757(ash 5 2)
759 @result{} 20 758 @result{} 20
760(lsh -5 2) ; -5 = @r{1111 1111 1111 1111 1111 1011} 759(lsh -5 2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011}
761 @result{} -20 ; = @r{1111 1111 1111 1111 1110 1100} 760 @result{} -20 ; = @r{1111 1111 1111 1111 1111 1110 1100}
762(ash -5 2) 761(ash -5 2)
763 @result{} -20 762 @result{} -20
764@end group 763@end group
765@group 764@group
766(lsh 5 -2) ; 5 = @r{0000 0000 0000 0000 0000 0101} 765(lsh 5 -2) ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
767 @result{} 1 ; = @r{0000 0000 0000 0000 0000 0001} 766 @result{} 1 ; = @r{0000 0000 0000 0000 0000 0000 0001}
768@end group 767@end group
769@group 768@group
770(ash 5 -2) 769(ash 5 -2)
771 @result{} 1 770 @result{} 1
772@end group 771@end group
773@group 772@group
774(lsh -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1011} 773(lsh -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011}
775 @result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1110} 774 @result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1111 1110}
776@end group 775@end group
777@group 776@group
778(ash -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1011} 777(ash -5 -2) ; -5 = @r{1111 1111 1111 1111 1111 1111 1011}
779 @result{} -2 ; = @r{1111 1111 1111 1111 1111 1110} 778 @result{} -2 ; = @r{1111 1111 1111 1111 1111 1111 1110}
780@end group 779@end group
781@end smallexample 780@end smallexample
782@end defun 781@end defun
@@ -813,23 +812,23 @@ because its binary representation consists entirely of ones. If
813 812
814@smallexample 813@smallexample
815@group 814@group
816 ; @r{ 24-bit binary values} 815 ; @r{ 28-bit binary values}
817 816
818(logand 14 13) ; 14 = @r{0000 0000 0000 0000 0000 1110} 817(logand 14 13) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
819 ; 13 = @r{0000 0000 0000 0000 0000 1101} 818 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
820 @result{} 12 ; 12 = @r{0000 0000 0000 0000 0000 1100} 819 @result{} 12 ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
821@end group 820@end group
822 821
823@group 822@group
824(logand 14 13 4) ; 14 = @r{0000 0000 0000 0000 0000 1110} 823(logand 14 13 4) ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
825 ; 13 = @r{0000 0000 0000 0000 0000 1101} 824 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
826 ; 4 = @r{0000 0000 0000 0000 0000 0100} 825 ; 4 = @r{0000 0000 0000 0000 0000 0000 0100}
827 @result{} 4 ; 4 = @r{0000 0000 0000 0000 0000 0100} 826 @result{} 4 ; 4 = @r{0000 0000 0000 0000 0000 0000 0100}
828@end group 827@end group
829 828
830@group 829@group
831(logand) 830(logand)
832 @result{} -1 ; -1 = @r{1111 1111 1111 1111 1111 1111} 831 @result{} -1 ; -1 = @r{1111 1111 1111 1111 1111 1111 1111}
833@end group 832@end group
834@end smallexample 833@end smallexample
835@end defun 834@end defun
@@ -845,18 +844,18 @@ passed just one argument, it returns that argument.
845 844
846@smallexample 845@smallexample
847@group 846@group
848 ; @r{ 24-bit binary values} 847 ; @r{ 28-bit binary values}
849 848
850(logior 12 5) ; 12 = @r{0000 0000 0000 0000 0000 1100} 849(logior 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
851 ; 5 = @r{0000 0000 0000 0000 0000 0101} 850 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
852 @result{} 13 ; 13 = @r{0000 0000 0000 0000 0000 1101} 851 @result{} 13 ; 13 = @r{0000 0000 0000 0000 0000 0000 1101}
853@end group 852@end group
854 853
855@group 854@group
856(logior 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 1100} 855(logior 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
857 ; 5 = @r{0000 0000 0000 0000 0000 0101} 856 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
858 ; 7 = @r{0000 0000 0000 0000 0000 0111} 857 ; 7 = @r{0000 0000 0000 0000 0000 0000 0111}
859 @result{} 15 ; 15 = @r{0000 0000 0000 0000 0000 1111} 858 @result{} 15 ; 15 = @r{0000 0000 0000 0000 0000 0000 1111}
860@end group 859@end group
861@end smallexample 860@end smallexample
862@end defun 861@end defun
@@ -872,18 +871,18 @@ result is 0, which is an identity element for this operation. If
872 871
873@smallexample 872@smallexample
874@group 873@group
875 ; @r{ 24-bit binary values} 874 ; @r{ 28-bit binary values}
876 875
877(logxor 12 5) ; 12 = @r{0000 0000 0000 0000 0000 1100} 876(logxor 12 5) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
878 ; 5 = @r{0000 0000 0000 0000 0000 0101} 877 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
879 @result{} 9 ; 9 = @r{0000 0000 0000 0000 0000 1001} 878 @result{} 9 ; 9 = @r{0000 0000 0000 0000 0000 0000 1001}
880@end group 879@end group
881 880
882@group 881@group
883(logxor 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 1100} 882(logxor 12 5 7) ; 12 = @r{0000 0000 0000 0000 0000 0000 1100}
884 ; 5 = @r{0000 0000 0000 0000 0000 0101} 883 ; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
885 ; 7 = @r{0000 0000 0000 0000 0000 0111} 884 ; 7 = @r{0000 0000 0000 0000 0000 0000 0111}
886 @result{} 14 ; 14 = @r{0000 0000 0000 0000 0000 1110} 885 @result{} 14 ; 14 = @r{0000 0000 0000 0000 0000 0000 1110}
887@end group 886@end group
888@end smallexample 887@end smallexample
889@end defun 888@end defun
@@ -898,9 +897,9 @@ bit is one in the result if, and only if, the @var{n}th bit is zero in
898@example 897@example
899(lognot 5) 898(lognot 5)
900 @result{} -6 899 @result{} -6
901;; 5 = @r{0000 0000 0000 0000 0000 0101} 900;; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
902;; @r{becomes} 901;; @r{becomes}
903;; -6 = @r{1111 1111 1111 1111 1111 1010} 902;; -6 = @r{1111 1111 1111 1111 1111 1111 1010}
904@end example 903@end example
905@end defun 904@end defun
906 905
@@ -970,7 +969,10 @@ This function returns the logarithm of @var{arg}, with base 10. If
970@end defun 969@end defun
971 970
972@defun expt x y 971@defun expt x y
973This function returns @var{x} raised to power @var{y}. 972This function returns @var{x} raised to power @var{y}. If both
973arguments are integers and @var{y} is positive, the result is an
974integer; in this case, it is truncated to fit the range of possible
975integer values.
974@end defun 976@end defun
975 977
976@defun sqrt arg 978@defun sqrt arg
generated by cgit v1.2.1 (git 2.18.0) at 2026-02-15 17:00:46 +0000