Move Minor Modes node of Emacs manual next to the Major Modes node

[gnu-emacs] / doc / lispref / numbers.texi

diff --git a/doc/lispref/numbers.texi b/doc/lispref/numbers.texi
index 91945967f22c46a44358d6db76aa67e650bf60cf..65921f444e0d94666f4d238b67baebd56fdfafbf 100644 (file)
--- a/doc/lispref/numbers.texi
+++ b/doc/lispref/numbers.texi
@@ -1,7 +1,7 @@
 @c -*-texinfo-*-
 @c This is part of the GNU Emacs Lisp Reference Manual.
 @c -*-texinfo-*-
 @c This is part of the GNU Emacs Lisp Reference Manual.

-@c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999, 2001,
-@c   2002, 2003, 2004, 2005, 2006, 2007  Free Software Foundation, Inc.
+@c Copyright (C) 1990-1995, 1998-1999, 2001-2011
+@c   Free Software Foundation, Inc.

 @c See the file elisp.texi for copying conditions.
 @setfilename ../../info/numbers
 @node Numbers, Strings and Characters, Lisp Data Types, Top
 @c See the file elisp.texi for copying conditions.
 @setfilename ../../info/numbers
 @node Numbers, Strings and Characters, Lisp Data Types, Top


@@ -20,10 +20,10 @@ exact; they have a fixed, limited amount of precision.
 
 @menu
 * Integer Basics::            Representation and range of integers.
 
 @menu
 * Integer Basics::            Representation and range of integers.

-* Float Basics::             Representation and range of floating point.
+* Float Basics::              Representation and range of floating point.

 * Predicates on Numbers::     Testing for numbers.
 * Comparison of Numbers::     Equality and inequality predicates.
 * Predicates on Numbers::     Testing for numbers.
 * Comparison of Numbers::     Equality and inequality predicates.

-* Numeric Conversions::              Converting float to integer and vice versa.
+* Numeric Conversions::       Converting float to integer and vice versa.

 * Arithmetic Operations::     How to add, subtract, multiply and divide.
 * Rounding Operations::       Explicitly rounding floating point numbers.
 * Bitwise Operations::        Logical and, or, not, shifting.
 * Arithmetic Operations::     How to add, subtract, multiply and divide.
 * Rounding Operations::       Explicitly rounding floating point numbers.
 * Bitwise Operations::        Logical and, or, not, shifting.


@@ -36,33 +36,35 @@ exact; they have a fixed, limited amount of precision.
 @section Integer Basics
 
   The range of values for an integer depends on the machine.  The
 @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.,
+minimum range is @minus{}536870912 to 536870911 (30 bits; i.e.,

 @ifnottex
 @ifnottex

--2**28
+-2**29

 @end ifnottex
 @tex
 @end ifnottex
 @tex

-@math{-2^{28}}
+@math{-2^{29}}

 @end tex
 to
 @ifnottex
 @end tex
 to
 @ifnottex

-2**28 - 1),
+2**29 - 1),

 @end ifnottex
 @tex
 @end ifnottex
 @tex

-@math{2^{28}-1}),
+@math{2^{29}-1}),

 @end tex
 @end tex

-but some machines may provide a wider range.  Many examples in this
-chapter assume an integer has 29 bits.
+but some machines provide a wider range.  Many examples in this
+chapter assume that an integer has 30 bits and that floating point
+numbers are IEEE double precision.

 @cindex overflow
 
   The Lisp reader reads an integer as a sequence of digits with optional
 @cindex overflow
 
   The Lisp reader reads an integer as a sequence of digits with optional

-initial sign and optional final period.
+initial sign and optional final period.  An integer that is out of the
+Emacs range is treated as a floating-point number.

 
 @example
  1               ; @r{The integer 1.}
  1.              ; @r{The integer 1.}
 +1               ; @r{Also the integer 1.}
 -1               ; @r{The integer @minus{}1.}
 
 @example
  1               ; @r{The integer 1.}
  1.              ; @r{The integer 1.}
 +1               ; @r{Also the integer 1.}
 -1               ; @r{The integer @minus{}1.}

- 536870913       ; @r{Also the integer 1, due to overflow.}
+ 1073741825      ; @r{The floating point number 1073741825.0.}

  0               ; @r{The integer 0.}
 -0               ; @r{The integer 0.}
 @end example
  0               ; @r{The integer 0.}
 -0               ; @r{The integer 0.}
 @end example


@@ -93,25 +95,26 @@ from 2 to 36.  For example:
 bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
 view the numbers in their binary form.
 
 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:
+  In 30-bit binary, the decimal integer 5 looks like this:

 
 @example
 
 @example

-0 0000  0000 0000  0000 0000  0000 0101
+0000...000101 (30 bits total)

 @end example
 
 @noindent
 @end example
 
 @noindent

-(We have inserted spaces between groups of 4 bits, and two spaces
-between groups of 8 bits, to make the binary integer easier to read.)
+(The @samp{...} stands for enough bits to fill out a 30-bit word; in
+this case, @samp{...} stands for twenty 0 bits.  Later examples also
+use the @samp{...} notation to make binary integers easier to read.)

 
   The integer @minus{}1 looks like this:
 
 @example
 
   The integer @minus{}1 looks like this:
 
 @example

-1 1111  1111 1111  1111 1111  1111 1111
+1111...111111 (30 bits total)

 @end example
 
 @noindent
 @cindex two's complement
 @end example
 
 @noindent
 @cindex two's complement

-@minus{}1 is represented as 29 ones.  (This is called @dfn{two's
+@minus{}1 is represented as 30 ones.  (This is called @dfn{two's

 complement} notation.)
 
   The negative integer, @minus{}5, is creating by subtracting 4 from
 complement} notation.)
 
   The negative integer, @minus{}5, is creating by subtracting 4 from


@@ -119,24 +122,24 @@ complement} notation.)
 @minus{}5 looks like this:
 
 @example
 @minus{}5 looks like this:
 
 @example

-1 1111  1111 1111  1111 1111  1111 1011
+1111...111011 (30 bits total)

 @end example
 
 @end example
 

-  In this implementation, the largest 29-bit binary integer value is
-268,435,455 in decimal.  In binary, it looks like this:
+  In this implementation, the largest 30-bit binary integer value is
+536,870,911 in decimal.  In binary, it looks like this:

 
 @example
 
 @example

-0 1111  1111 1111  1111 1111  1111 1111
+0111...111111 (30 bits total)

 @end example
 
   Since the arithmetic functions do not check whether integers go
 @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:
+outside their range, when you add 1 to 536,870,911, the value is the
+negative integer @minus{}536,870,912:

 
 @example
 
 @example

-(+ 1 268435455)
-     @result{} -268435456
-     @result{} 1 0000  0000 0000  0000 0000  0000 0000
+(+ 1 536870911)
+     @result{} -536870912
+     @result{} 1000...000000 (30 bits total)

 @end example
 
   Many of the functions described in this chapter accept markers for
 @end example
 
   Many of the functions described in this chapter accept markers for


@@ -155,6 +158,9 @@ The value of this variable is the smallest integer that Emacs Lisp can
 handle.  It is negative.
 @end defvar
 
 handle.  It is negative.
 @end defvar
 

+  @xref{Character Codes, max-char}, for the maximum value of a valid
+character codepoint.
+

 @node Float Basics
 @section Floating Point Basics
 
 @node Float Basics
 @section Floating Point Basics
 


@@ -192,7 +198,7 @@ point values:
 @samp{1.0e+INF}
 @item negative infinity
 @samp{-1.0e+INF}
 @samp{1.0e+INF}
 @item negative infinity
 @samp{-1.0e+INF}

-@item Not-a-number 
+@item Not-a-number

 @samp{0.0e+NaN} or @samp{-0.0e+NaN}.
 @end table
 
 @samp{0.0e+NaN} or @samp{-0.0e+NaN}.
 @end table
 


@@ -220,6 +226,14 @@ down to an integer.
 @end example
 @end defun
 
 @end example
 @end defun
 

+@defvar float-e
+The mathematical constant @math{e} (2.71828@dots{}).
+@end defvar
+
+@defvar float-pi
+The mathematical constant @math{pi} (3.14159@dots{}).
+@end defvar
+

 @node Predicates on Numbers
 @section Type Predicates for Numbers
 @cindex predicates for numbers
 @node Predicates on Numbers
 @section Type Predicates for Numbers
 @cindex predicates for numbers


@@ -496,8 +510,8 @@ commonly used.
 if any argument is floating.
 
   It is important to note that in Emacs Lisp, arithmetic functions
 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.
+do not check for overflow.  Thus @code{(1+ 536870911)} may evaluate to
+@minus{}536870912, depending on your hardware.

 
 @defun 1+ number-or-marker
 This function returns @var{number-or-marker} plus 1.
 
 @defun 1+ number-or-marker
 This function returns @var{number-or-marker} plus 1.


@@ -817,19 +831,19 @@ 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
 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:
+536,870,911 produces @minus{}2 in the 30-bit implementation:

 
 @example
 
 @example

-(lsh 268435455 1)          ; @r{left shift}
+(lsh 536870911 1)          ; @r{left shift}

      @result{} -2
 @end example
 
      @result{} -2
 @end example
 

-In binary, in the 29-bit implementation, the argument looks like this:
+In binary, the argument looks like this:

 
 @example
 @group
 
 @example
 @group

-;; @r{Decimal 268,435,455}
-0 1111  1111 1111  1111 1111  1111 1111
+;; @r{Decimal 536,870,911}
+0111...111111 (30 bits total)

 @end group
 @end example
 
 @end group
 @end example
 


@@ -839,7 +853,7 @@ which becomes the following when left shifted:
 @example
 @group
 ;; @r{Decimal @minus{}2}
 @example
 @group
 ;; @r{Decimal @minus{}2}

-1 1111  1111 1111  1111 1111  1111 1110
+1111...111110 (30 bits total)

 @end group
 @end example
 @end defun
 @end group
 @end example
 @end defun


@@ -862,9 +876,9 @@ looks like this:
 @group
 (ash -6 -1) @result{} -3
 ;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
 @group
 (ash -6 -1) @result{} -3
 ;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}

-1 1111  1111 1111  1111 1111  1111 1010
+1111...111010 (30 bits total)

      @result{}
      @result{}

-1 1111  1111 1111  1111 1111  1111 1101
+1111...111101 (30 bits total)

 @end group
 @end example
 
 @end group
 @end example
 


@@ -873,11 +887,11 @@ In contrast, shifting the pattern of bits one place to the right with
 
 @example
 @group
 
 @example
 @group

-(lsh -6 -1) @result{} 268435453
-;; @r{Decimal @minus{}6 becomes decimal 268,435,453.}
-1 1111  1111 1111  1111 1111  1111 1010
+(lsh -6 -1) @result{} 536870909
+;; @r{Decimal @minus{}6 becomes decimal 536,870,909.}
+1111...111010 (30 bits total)

      @result{}
      @result{}

-0 1111  1111 1111  1111 1111  1111 1101
+0111...111101 (30 bits total)

 @end group
 @end example
 
 @end group
 @end example
 


@@ -887,34 +901,35 @@ Here are other examples:
 @c     with smallbook but not with regular book! --rjc 16mar92
 @smallexample
 @group
 @c     with smallbook but not with regular book! --rjc 16mar92
 @smallexample
 @group

-                   ;  @r{             29-bit binary values}
+                   ;  @r{       30-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}
+(lsh 5 2)          ;   5  =  @r{0000...000101}
+     @result{} 20         ;      =  @r{0000...010100}

 @end group
 @group
 (ash 5 2)
      @result{} 20
 @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}
+(lsh -5 2)         ;  -5  =  @r{1111...111011}
+     @result{} -20        ;      =  @r{1111...101100}

 (ash -5 2)
      @result{} -20
 @end group
 @group
 (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}
+(lsh 5 -2)         ;   5  =  @r{0000...000101}
+     @result{} 1          ;      =  @r{0000...000001}

 @end group
 @group
 (ash 5 -2)
      @result{} 1
 @end group
 @group
 @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}
+(lsh -5 -2)        ;  -5  =  @r{1111...111011}
+     @result{} 268435454
+                   ;      =  @r{0011...111110}

 @end group
 @group
 @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}
+(ash -5 -2)        ;  -5  =  @r{1111...111011}
+     @result{} -2         ;      =  @r{1111...111110}

 @end group
 @end smallexample
 @end defun
 @end group
 @end smallexample
 @end defun


@@ -949,23 +964,23 @@ because its binary representation consists entirely of ones.  If
 
 @smallexample
 @group
 
 @smallexample
 @group

-                   ; @r{               29-bit binary values}
+                   ; @r{       30-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}
+(logand 14 13)     ; 14  =  @r{0000...001110}
+                   ; 13  =  @r{0000...001101}
+     @result{} 12         ; 12  =  @r{0000...001100}

 @end group
 
 @group
 @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}
+(logand 14 13 4)   ; 14  =  @r{0000...001110}
+                   ; 13  =  @r{0000...001101}
+                   ;  4  =  @r{0000...000100}
+     @result{} 4          ;  4  =  @r{0000...000100}

 @end group
 
 @group
 (logand)
 @end group
 
 @group
 (logand)

-     @result{} -1         ; -1  =  @r{1 1111  1111 1111  1111 1111  1111 1111}
+     @result{} -1         ; -1  =  @r{1111...111111}

 @end group
 @end smallexample
 @end defun
 @end group
 @end smallexample
 @end defun


@@ -979,18 +994,18 @@ passed just one argument, it returns that argument.
 
 @smallexample
 @group
 
 @smallexample
 @group

-                   ; @r{              29-bit binary values}
+                   ; @r{       30-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}
+(logior 12 5)      ; 12  =  @r{0000...001100}
+                   ;  5  =  @r{0000...000101}
+     @result{} 13         ; 13  =  @r{0000...001101}

 @end group
 
 @group
 @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}
+(logior 12 5 7)    ; 12  =  @r{0000...001100}
+                   ;  5  =  @r{0000...000101}
+                   ;  7  =  @r{0000...000111}
+     @result{} 15         ; 15  =  @r{0000...001111}

 @end group
 @end smallexample
 @end defun
 @end group
 @end smallexample
 @end defun


@@ -1004,18 +1019,18 @@ result is 0, which is an identity element for this operation.  If
 
 @smallexample
 @group
 
 @smallexample
 @group

-                   ; @r{              29-bit binary values}
+                   ; @r{       30-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}
+(logxor 12 5)      ; 12  =  @r{0000...001100}
+                   ;  5  =  @r{0000...000101}
+     @result{} 9          ;  9  =  @r{0000...001001}

 @end group
 
 @group
 @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}
+(logxor 12 5 7)    ; 12  =  @r{0000...001100}
+                   ;  5  =  @r{0000...000101}
+                   ;  7  =  @r{0000...000111}
+     @result{} 14         ; 14  =  @r{0000...001110}

 @end group
 @end smallexample
 @end defun
 @end group
 @end smallexample
 @end defun


@@ -1028,9 +1043,9 @@ bit is one in the result if, and only if, the @var{n}th bit is zero in
 @example
 (lognot 5)
      @result{} -6
 @example
 (lognot 5)
      @result{} -6

-;;  5  =  @r{0 0000  0000 0000  0000 0000  0000 0101}
+;;  5  =  @r{0000...000101} (30 bits total)

 ;; @r{becomes}
 ;; @r{becomes}

-;; -6  =  @r{1 1111  1111 1111  1111 1111  1111 1010}
+;; -6  =  @r{1111...111010} (30 bits total)

 @end example
 @end defun
 
 @end example
 @end defun
 


@@ -1205,7 +1220,3 @@ On some machines, any integer representable in Lisp may be the result
 of @code{random}.  On other machines, the result can never be larger
 than a certain maximum or less than a certain (negative) minimum.
 @end defun
 of @code{random}.  On other machines, the result can never be larger
 than a certain maximum or less than a certain (negative) minimum.
 @end defun

-
-@ignore
-   arch-tag: 574e8dd2-d513-4616-9844-c9a27869782e
-@end ignore