Commit 8be5e0fc authored by Richard M. Stallman's avatar Richard M. Stallman
Browse files

Integers now at least 28 bits.

parent 32ce36ad
......@@ -39,23 +39,22 @@ where Emacs does not support them.
@section Integer Basics
The range of values for an integer depends on the machine. The
range is @minus{}8388608 to 8388607 (24 bits; i.e.,
range is @minus{}8388608 to 8388607 (28 bits; i.e.,
@ifinfo
-2**23
-2**27
@end ifinfo
@tex
$-2^{23}$
$-2^{27}$
@end tex
to
@ifinfo
2**23 - 1)
2**27 - 1)
@end ifinfo
@tex
$2^{23}-1$)
$2^{27}-1$)
@end tex
on most machines, but on others it is @minus{}16777216 to 16777215 (25
bits), or @minus{}33554432 to 33554431 (26 bits). Many examples in this
chapter assume an integer has 24 bits.
on most machines, but some machines may have 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
......@@ -66,7 +65,7 @@ initial sign and optional final period.
1. ; @r{The integer 1.}
+1 ; @r{Also the integer 1.}
-1 ; @r{The integer @minus{}1.}
16777217 ; @r{Also the integer 1, due to overflow.}
268435457 ; @r{Also the integer 1, due to overflow.}
0 ; @r{The integer 0.}
-0 ; @r{The integer 0.}
@end example
......@@ -75,10 +74,10 @@ initial sign and optional final period.
bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
view the numbers in their binary form.
In 24-bit binary, the decimal integer 5 looks like this:
In 28-bit binary, the decimal integer 5 looks like this:
@example
0000 0000 0000 0000 0000 0101
0000 0000 0000 0000 0000 0000 0101
@end example
@noindent
......@@ -88,12 +87,12 @@ 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 1111 1111 1111 1111 1111 1111
@end example
@noindent
@cindex two's complement
@minus{}1 is represented as 24 ones. (This is called @dfn{two's
@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
......@@ -101,24 +100,24 @@ complement} notation.)
@minus{}5 looks like this:
@example
1111 1111 1111 1111 1111 1011
1111 1111 1111 1111 1111 1111 1011
@end example
In this implementation, the largest 24-bit binary integer is the
decimal integer 8,388,607. In binary, it looks like this:
decimal integer 134,217,727. In binary, it looks like this:
@example
0111 1111 1111 1111 1111 1111
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 8,388,607, the value is the
negative integer @minus{}8,388,608:
outside their range, when you add 1 to 134,217,727, the value is the
negative integer @minus{}134,217,728:
@example
(+ 1 8388607)
@result{} -8388608
@result{} 1000 0000 0000 0000 0000 0000
(+ 1 134217727)
@result{} -134217728
@result{} 1000 0000 0000 0000 0000 0000 0000
@end example
Many of the following functions accept markers for arguments as well
......@@ -651,12 +650,12 @@ produces @minus{}2 on a 24-bit machine:
@result{} -2
@end example
In binary, in the 24-bit implementation, the argument looks like this:
In binary, in the 28-bit implementation, the argument looks like this:
@example
@group
;; @r{Decimal 8,388,607}
0111 1111 1111 1111 1111 1111
;; @r{Decimal 134.217,727}
0111 1111 1111 1111 1111 1111 1111
@end group
@end example
......@@ -666,7 +665,7 @@ which becomes the following when left shifted:
@example
@group
;; @r{Decimal @minus{}2}
1111 1111 1111 1111 1111 1110
1111 1111 1111 1111 1111 1111 1110
@end group
@end example
......@@ -724,9 +723,9 @@ looks like this:
@group
(ash -6 -1) @result{} -3
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
1111 1111 1111 1111 1111 1010
1111 1111 1111 1111 1111 1111 1010
@result{}
1111 1111 1111 1111 1111 1101
1111 1111 1111 1111 1111 1111 1101
@end group
@end example
......@@ -735,11 +734,11 @@ In contrast, shifting the pattern of bits one place to the right with
@example
@group
(lsh -6 -1) @result{} 8388605
;; @r{Decimal @minus{}6 becomes decimal 8,388,605.}
1111 1111 1111 1111 1111 1010
(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 1101
0111 1111 1111 1111 1111 1111 1101
@end group
@end example
......@@ -749,34 +748,34 @@ Here are other examples:
@c with smallbook but not with regular book! --rjc 16mar92
@smallexample
@group
; @r{ 24-bit binary values}
; @r{ 28-bit binary values}
(lsh 5 2) ; 5 = @r{0000 0000 0000 0000 0000 0101}
@result{} 20 ; = @r{0000 0000 0000 0000 0001 0100}
(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 1011}
@result{} -20 ; = @r{1111 1111 1111 1111 1110 1100}
(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 0101}
@result{} 1 ; = @r{0000 0000 0000 0000 0000 0001}
(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 1011}
@result{} 4194302 ; = @r{0011 1111 1111 1111 1111 1110}
(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 1011}
@result{} -2 ; = @r{1111 1111 1111 1111 1111 1110}
(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
......@@ -813,23 +812,23 @@ because its binary representation consists entirely of ones. If
@smallexample
@group
; @r{ 24-bit binary values}
; @r{ 28-bit binary values}
(logand 14 13) ; 14 = @r{0000 0000 0000 0000 0000 1110}
; 13 = @r{0000 0000 0000 0000 0000 1101}
@result{} 12 ; 12 = @r{0000 0000 0000 0000 0000 1100}
(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 1110}
; 13 = @r{0000 0000 0000 0000 0000 1101}
; 4 = @r{0000 0000 0000 0000 0000 0100}
@result{} 4 ; 4 = @r{0000 0000 0000 0000 0000 0100}
(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}
@result{} -1 ; -1 = @r{1111 1111 1111 1111 1111 1111 1111}
@end group
@end smallexample
@end defun
......@@ -845,18 +844,18 @@ passed just one argument, it returns that argument.
@smallexample
@group
; @r{ 24-bit binary values}
; @r{ 28-bit binary values}
(logior 12 5) ; 12 = @r{0000 0000 0000 0000 0000 1100}
; 5 = @r{0000 0000 0000 0000 0000 0101}
@result{} 13 ; 13 = @r{0000 0000 0000 0000 0000 1101}
(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 1100}
; 5 = @r{0000 0000 0000 0000 0000 0101}
; 7 = @r{0000 0000 0000 0000 0000 0111}
@result{} 15 ; 15 = @r{0000 0000 0000 0000 0000 1111}
(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
......@@ -872,18 +871,18 @@ result is 0, which is an identity element for this operation. If
@smallexample
@group
; @r{ 24-bit binary values}
; @r{ 28-bit binary values}
(logxor 12 5) ; 12 = @r{0000 0000 0000 0000 0000 1100}
; 5 = @r{0000 0000 0000 0000 0000 0101}
@result{} 9 ; 9 = @r{0000 0000 0000 0000 0000 1001}
(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 1100}
; 5 = @r{0000 0000 0000 0000 0000 0101}
; 7 = @r{0000 0000 0000 0000 0000 0111}
@result{} 14 ; 14 = @r{0000 0000 0000 0000 0000 1110}
(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
......@@ -898,9 +897,9 @@ 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 0101}
;; 5 = @r{0000 0000 0000 0000 0000 0000 0101}
;; @r{becomes}
;; -6 = @r{1111 1111 1111 1111 1111 1010}
;; -6 = @r{1111 1111 1111 1111 1111 1111 1010}
@end example
@end defun
......@@ -970,7 +969,10 @@ This function returns the logarithm of @var{arg}, with base 10. If
@end defun
@defun expt x y
This function returns @var{x} raised to power @var{y}.
This function returns @var{x} raised to power @var{y}. If both
arguments are integers and @var{y} is positive, the result is an
integer; in this case, it is truncated to fit the range of possible
integer values.
@end defun
@defun sqrt arg
......
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