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emacs/doc/lispref/numbers.texi

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@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
@c Copyright (C) 1990-1995, 1998-1999, 2001-2016 Free Software
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@c Foundation, Inc.
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@c See the file elisp.texi for copying conditions.
@node Numbers
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@chapter Numbers
@cindex integers
@cindex numbers
GNU Emacs supports two numeric data types: @dfn{integers} and
@dfn{floating-point numbers}. Integers are whole numbers such as
@minus{}3, 0, 7, 13, and 511. Floating-point numbers are numbers with
fractional parts, such as @minus{}4.5, 0.0, and 2.71828. They can
also be expressed in exponential notation: @samp{1.5e2} is the same as
@samp{150.0}; here, @samp{e2} stands for ten to the second power, and
that is multiplied by 1.5. Integer computations are exact, though
they may overflow. Floating-point computations often involve rounding
errors, as the numbers have a fixed amount of precision.
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@menu
* Integer Basics:: Representation and range of integers.
* Float Basics:: Representation and range of floating point.
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* Predicates on Numbers:: Testing for numbers.
* Comparison of Numbers:: Equality and inequality predicates.
* Numeric Conversions:: Converting float to integer and vice versa.
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* Arithmetic Operations:: How to add, subtract, multiply and divide.
* Rounding Operations:: Explicitly rounding floating-point numbers.
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* Bitwise Operations:: Logical and, or, not, shifting.
* Math Functions:: Trig, exponential and logarithmic functions.
* Random Numbers:: Obtaining random integers, predictable or not.
@end menu
@node Integer Basics
@section Integer Basics
The range of values for an integer depends on the machine. The
minimum range is @minus{}536,870,912 to 536,870,911 (30 bits; i.e.,
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@ifnottex
@minus{}2**29
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@end ifnottex
@tex
@math{-2^{29}}
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@end tex
to
@ifnottex
2**29 @minus{} 1),
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@end ifnottex
@tex
@math{2^{29}-1}),
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@end tex
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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but many machines provide a wider range. Many examples in this
chapter assume the minimum integer width of 30 bits.
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@cindex overflow
The Lisp reader reads an integer as a sequence of digits with optional
initial sign and optional final period. An integer that is out of the
Emacs range is treated as a floating-point number.
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@example
1 ; @r{The integer 1.}
1. ; @r{The integer 1.}
+1 ; @r{Also the integer 1.}
-1 ; @r{The integer @minus{}1.}
9000000000000000000
; @r{The floating-point number 9e18.}
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0 ; @r{The integer 0.}
-0 ; @r{The integer 0.}
@end example
@cindex integers in specific radix
@cindex radix for reading an integer
@cindex base for reading an integer
@cindex hex numbers
@cindex octal numbers
@cindex reading numbers in hex, octal, and binary
The syntax for integers in bases other than 10 uses @samp{#}
followed by a letter that specifies the radix: @samp{b} for binary,
@samp{o} for octal, @samp{x} for hex, or @samp{@var{radix}r} to
specify radix @var{radix}. Case is not significant for the letter
that specifies the radix. Thus, @samp{#b@var{integer}} reads
@var{integer} in binary, and @samp{#@var{radix}r@var{integer}} reads
@var{integer} in radix @var{radix}. Allowed values of @var{radix} run
from 2 to 36. For example:
@example
#b101100 @result{} 44
#o54 @result{} 44
#x2c @result{} 44
#24r1k @result{} 44
@end example
To understand how various functions work on integers, especially the
bitwise operators (@pxref{Bitwise Operations}), it is often helpful to
view the numbers in their binary form.
In 30-bit binary, the decimal integer 5 looks like this:
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@example
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0000...000101 (30 bits total)
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@end example
@noindent
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(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.)
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The integer @minus{}1 looks like this:
@example
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1111...111111 (30 bits total)
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@end example
@noindent
@cindex two's complement
@minus{}1 is represented as 30 ones. (This is called @dfn{two's
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complement} notation.)
Subtracting 4 from @minus{}1 returns the negative integer @minus{}5.
In binary, the decimal integer 4 is 100. Consequently,
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@minus{}5 looks like this:
@example
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1111...111011 (30 bits total)
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@end example
In this implementation, the largest 30-bit binary integer is
536,870,911 in decimal. In binary, it looks like this:
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@example
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0111...111111 (30 bits total)
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@end example
Since the arithmetic functions do not check whether integers go
outside their range, when you add 1 to 536,870,911, the value is the
negative integer @minus{}536,870,912:
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@example
(+ 1 536870911)
@result{} -536870912
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@result{} 1000...000000 (30 bits total)
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@end example
Many of the functions described in this chapter accept markers for
arguments in place of numbers. (@xref{Markers}.) Since the actual
arguments to such functions may be either numbers or markers, we often
give these arguments the name @var{number-or-marker}. When the argument
value is a marker, its position value is used and its buffer is ignored.
@cindex largest Lisp integer
@cindex maximum Lisp integer
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@defvar most-positive-fixnum
The value of this variable is the largest integer that Emacs Lisp can
handle. Typical values are
@ifnottex
2**29 @minus{} 1
@end ifnottex
@tex
@math{2^{29}-1}
@end tex
on 32-bit and
@ifnottex
2**61 @minus{} 1
@end ifnottex
@tex
@math{2^{61}-1}
@end tex
on 64-bit platforms.
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@end defvar
@cindex smallest Lisp integer
@cindex minimum Lisp integer
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@defvar most-negative-fixnum
The value of this variable is the smallest integer that Emacs Lisp can
handle. It is negative. Typical values are
@ifnottex
@minus{}2**29
@end ifnottex
@tex
@math{-2^{29}}
@end tex
on 32-bit and
@ifnottex
@minus{}2**61
@end ifnottex
@tex
@math{-2^{61}}
@end tex
on 64-bit platforms.
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@end defvar
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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In Emacs Lisp, text characters are represented by integers. Any
integer between zero and the value of @code{(max-char)}, inclusive, is
considered to be valid as a character. @xref{Character Codes}.
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@node Float Basics
@section Floating-Point Basics
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@cindex @acronym{IEEE} floating point
Floating-point numbers are useful for representing numbers that are
not integral. The range of floating-point numbers is
the same as the range of the C data type @code{double} on the machine
you are using. On all computers currently supported by Emacs, this is
double-precision @acronym{IEEE} floating point.
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The read syntax for floating-point numbers requires either a decimal
point, an exponent, or both. Optional signs (@samp{+} or @samp{-})
precede the number and its exponent. For example, @samp{1500.0},
@samp{+15e2}, @samp{15.0e+2}, @samp{+1500000e-3}, and @samp{.15e4} are
five ways of writing a floating-point number whose value is 1500.
They are all equivalent. Like Common Lisp, Emacs Lisp requires at
least one digit after any decimal point in a floating-point number;
@samp{1500.} is an integer, not a floating-point number.
Emacs Lisp treats @code{-0.0} as numerically equal to ordinary zero
with respect to @code{equal} and @code{=}. This follows the
@acronym{IEEE} floating-point standard, which says @code{-0.0} and
@code{0.0} are numerically equal even though other operations can
distinguish them.
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@cindex positive infinity
@cindex negative infinity
@cindex infinity
@cindex NaN
The @acronym{IEEE} floating-point standard supports positive
infinity and negative infinity as floating-point values. It also
Restore some of the quoting in the manuals * doc/lispref/windows.texi (Coordinates and Windows) (Coordinates and Windows): * doc/lispref/variables.texi (Lexical Binding) (File Local Variables): * doc/lispref/text.texi (Format Properties): * doc/lispref/symbols.texi (Symbol Components): * doc/lispref/strings.texi (Creating Strings): * doc/lispref/sequences.texi (Sequence Functions): * doc/lispref/searching.texi (Regexp Special, Regexp Search) (Search and Replace): * doc/lispref/processes.texi (Bindat Spec): * doc/lispref/os.texi (Idle Timers): * doc/lispref/objects.texi (Basic Char Syntax): * doc/lispref/numbers.texi (Float Basics, Random Numbers): * doc/lispref/nonascii.texi (Character Properties): * doc/lispref/modes.texi (Major Mode Conventions, Mode Hooks) (Mode Line Variables): * doc/lispref/minibuf.texi (Text from Minibuffer): * doc/lispref/loading.texi (Autoload): * doc/lispref/keymaps.texi (Controlling Active Maps): * doc/lispref/frames.texi (Frame Layout, Size and Position) (Size Parameters, Implied Frame Resizing): * doc/lispref/files.texi (Changing Files, Magic File Names): * doc/lispref/eval.texi (Self-Evaluating Forms): * doc/lispref/display.texi (Progress, Abstract Display) (Abstract Display Example, Bidirectional Display): * doc/lispref/commands.texi (Event Mod): * doc/emacs/windows.texi (Displaying Buffers): * doc/emacs/trouble.texi (Bug Criteria, Checklist): * doc/emacs/text.texi (Enriched Text): * doc/emacs/programs.texi (MixedCase Words): * doc/emacs/picture-xtra.texi (Insert in Picture) (Tabs in Picture): * doc/emacs/misc.texi (Emacs Server, Printing): * doc/emacs/mini.texi (Minibuffer History): * doc/emacs/maintaining.texi (Old Revisions, VC Change Log) (Pulling / Pushing): * doc/emacs/killing.texi (Yanking, Cut and Paste, Clipboard): * doc/emacs/help.texi (Help, Help Echo): * doc/emacs/glossary.texi (Glossary): * doc/emacs/frames.texi (Mouse Commands, Creating Frames) (Frame Commands): * doc/emacs/files.texi (Reverting, Saving, Directories): * doc/emacs/entering.texi (Exiting): * doc/emacs/emacs.texi (Top): * doc/emacs/cmdargs.texi (Window Size X, Icons X): * doc/emacs/anti.texi (Antinews): Restore quoting of text where appropriate or replace quoting with @dfn. * doc/misc/ediff.texi (Window and Frame Configuration): * doc/lispref/processes.texi (Network Feature Testing): * doc/lispref/display.texi (Display Margins): Quote the phrase after "a.k.a." where appropriate.
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provides for a class of values called NaN, or ``not a number'';
numerical functions return such values in cases where there is no
correct answer. For example, @code{(/ 0.0 0.0)} returns a NaN@.
Although NaN values carry a sign, for practical purposes there is no other
significant difference between different NaN values in Emacs Lisp.
Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
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Here are read syntaxes for these special floating-point values:
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@table @asis
@item infinity
@samp{1.0e+INF} and @samp{-1.0e+INF}
@item not-a-number
@samp{0.0e+NaN} and @samp{-0.0e+NaN}
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@end table
The following functions are specialized for handling floating-point
numbers:
@defun isnan x
This predicate returns @code{t} if its floating-point argument is a NaN,
@code{nil} otherwise.
@end defun
@defun frexp x
This function returns a cons cell @code{(@var{s} . @var{e})},
where @var{s} and @var{e} are respectively the significand and
exponent of the floating-point number @var{x}.
If @var{x} is finite, then @var{s} is a floating-point number between 0.5
(inclusive) and 1.0 (exclusive), @var{e} is an integer, and
@ifnottex
@var{x} = @var{s} * 2**@var{e}.
@end ifnottex
@tex
@math{x = s 2^e}.
@end tex
If @var{x} is zero or infinity, then @var{s} is the same as @var{x}.
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If @var{x} is a NaN, then @var{s} is also a NaN@.
If @var{x} is zero, then @var{e} is 0.
@end defun
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@defun ldexp s e
Given a numeric significand @var{s} and an integer exponent @var{e},
this function returns the floating point number
@ifnottex
@var{s} * 2**@var{e}.
@end ifnottex
@tex
@math{s 2^e}.
@end tex
@end defun
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@defun copysign x1 x2
This function copies the sign of @var{x2} to the value of @var{x1},
and returns the result. @var{x1} and @var{x2} must be floating point.
@end defun
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@defun logb x
This function returns the binary exponent of @var{x}. More
precisely, the value is the logarithm base 2 of @math{|x|}, rounded
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down to an integer.
@example
(logb 10)
@result{} 3
(logb 10.0e20)
@result{} 69
@end example
@end defun
@node Predicates on Numbers
@section Type Predicates for Numbers
@cindex predicates for numbers
The functions in this section test for numbers, or for a specific
type of number. The functions @code{integerp} and @code{floatp} can
take any type of Lisp object as argument (they would not be of much
use otherwise), but the @code{zerop} predicate requires a number as
its argument. See also @code{integer-or-marker-p} and
@code{number-or-marker-p}, in @ref{Predicates on Markers}.
@defun floatp object
This predicate tests whether its argument is floating point
and returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun integerp object
This predicate tests whether its argument is an integer, and returns
@code{t} if so, @code{nil} otherwise.
@end defun
@defun numberp object
This predicate tests whether its argument is a number (either integer or
floating point), and returns @code{t} if so, @code{nil} otherwise.
@end defun
@defun natnump object
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@cindex natural numbers
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This predicate (whose name comes from the phrase ``natural number'')
tests to see whether its argument is a nonnegative integer, and
returns @code{t} if so, @code{nil} otherwise. 0 is considered
non-negative.
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@findex wholenump
@code{wholenump} is a synonym for @code{natnump}.
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@end defun
@defun zerop number
This predicate tests whether its argument is zero, and returns @code{t}
if so, @code{nil} otherwise. The argument must be a number.
@code{(zerop x)} is equivalent to @code{(= x 0)}.
@end defun
@node Comparison of Numbers
@section Comparison of Numbers
@cindex number comparison
@cindex comparing numbers
To test numbers for numerical equality, you should normally use
@code{=}, not @code{eq}. There can be many distinct floating-point
objects with the same numeric value. If you use @code{eq} to
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compare them, then you test whether two values are the same
@emph{object}. By contrast, @code{=} compares only the numeric values
of the objects.
In Emacs Lisp, each integer is a unique Lisp object.
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Therefore, @code{eq} is equivalent to @code{=} where integers are
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
concerned. It is sometimes convenient to use @code{eq} for comparing
an unknown value with an integer, because @code{eq} does not report an
error if the unknown value is not a number---it accepts arguments of
any type. By contrast, @code{=} signals an error if the arguments are
not numbers or markers. However, it is better programming practice to
use @code{=} if you can, even for comparing integers.
Sometimes it is useful to compare numbers with @code{equal}, which
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treats two numbers as equal if they have the same data type (both
integers, or both floating point) and the same value. By contrast,
@code{=} can treat an integer and a floating-point number as equal.
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@xref{Equality Predicates}.
There is another wrinkle: because floating-point arithmetic is not
exact, it is often a bad idea to check for equality of floating-point
values. Usually it is better to test for approximate equality.
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Here's a function to do this:
@example
(defvar fuzz-factor 1.0e-6)
(defun approx-equal (x y)
(or (= x y)
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(< (/ (abs (- x y))
(max (abs x) (abs y)))
fuzz-factor)))
@end example
@cindex CL note---integers vrs @code{eq}
@quotation
@b{Common Lisp note:} Comparing numbers in Common Lisp always requires
@code{=} because Common Lisp implements multi-word integers, and two
distinct integer objects can have the same numeric value. Emacs Lisp
can have just one integer object for any given value because it has a
limited range of integers.
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@end quotation
@defun = number-or-marker &rest number-or-markers
This function tests whether all its arguments are numerically equal,
and returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun eql value1 value2
This function acts like @code{eq} except when both arguments are
numbers. It compares numbers by type and numeric value, so that
@code{(eql 1.0 1)} returns @code{nil}, but @code{(eql 1.0 1.0)} and
@code{(eql 1 1)} both return @code{t}.
@end defun
@defun /= number-or-marker1 number-or-marker2
This function tests whether its arguments are numerically equal, and
returns @code{t} if they are not, and @code{nil} if they are.
@end defun
@defun < number-or-marker &rest number-or-markers
This function tests whether each argument is strictly less than the
following argument. It returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun <= number-or-marker &rest number-or-markers
This function tests whether each argument is less than or equal to
the following argument. It returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun > number-or-marker &rest number-or-markers
This function tests whether each argument is strictly greater than
the following argument. It returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun >= number-or-marker &rest number-or-markers
This function tests whether each argument is greater than or equal to
the following argument. It returns @code{t} if so, @code{nil} otherwise.
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@end defun
@defun max number-or-marker &rest numbers-or-markers
This function returns the largest of its arguments.
If any of the arguments is floating point, the value is returned
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as floating point, even if it was given as an integer.
@example
(max 20)
@result{} 20
(max 1 2.5)
@result{} 2.5
(max 1 3 2.5)
@result{} 3.0
@end example
@end defun
@defun min number-or-marker &rest numbers-or-markers
This function returns the smallest of its arguments.
If any of the arguments is floating point, the value is returned
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as floating point, even if it was given as an integer.
@example
(min -4 1)
@result{} -4
@end example
@end defun
@defun abs number
This function returns the absolute value of @var{number}.
@end defun
@node Numeric Conversions
@section Numeric Conversions
@cindex rounding in conversions
@cindex number conversions
@cindex converting numbers
To convert an integer to floating point, use the function @code{float}.
@defun float number
This returns @var{number} converted to floating point.
If @var{number} is already floating point, @code{float} returns
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it unchanged.
@end defun
There are four functions to convert floating-point numbers to
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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integers; they differ in how they round. All accept an argument
@var{number} and an optional argument @var{divisor}. Both arguments
may be integers or floating-point numbers. @var{divisor} may also be
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@code{nil}. If @var{divisor} is @code{nil} or omitted, these
functions convert @var{number} to an integer, or return it unchanged
if it already is an integer. If @var{divisor} is non-@code{nil}, they
divide @var{number} by @var{divisor} and convert the result to an
integer. If @var{divisor} is zero (whether integer or
floating point), Emacs signals an @code{arith-error} error.
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@defun truncate number &optional divisor
This returns @var{number}, converted to an integer by rounding towards
zero.
@example
(truncate 1.2)
@result{} 1
(truncate 1.7)
@result{} 1
(truncate -1.2)
@result{} -1
(truncate -1.7)
@result{} -1
@end example
@end defun
@defun floor number &optional divisor
This returns @var{number}, converted to an integer by rounding downward
(towards negative infinity).
If @var{divisor} is specified, this uses the kind of division
operation that corresponds to @code{mod}, rounding downward.
@example
(floor 1.2)
@result{} 1
(floor 1.7)
@result{} 1
(floor -1.2)
@result{} -2
(floor -1.7)
@result{} -2
(floor 5.99 3)
@result{} 1
@end example
@end defun
@defun ceiling number &optional divisor
This returns @var{number}, converted to an integer by rounding upward
(towards positive infinity).
@example
(ceiling 1.2)
@result{} 2
(ceiling 1.7)
@result{} 2
(ceiling -1.2)
@result{} -1
(ceiling -1.7)
@result{} -1
@end example
@end defun
@defun round number &optional divisor
This returns @var{number}, converted to an integer by rounding towards the
nearest integer. Rounding a value equidistant between two integers
returns the even integer.
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@example
(round 1.2)
@result{} 1
(round 1.7)
@result{} 2
(round -1.2)
@result{} -1
(round -1.7)
@result{} -2
@end example
@end defun
@node Arithmetic Operations
@section Arithmetic Operations
@cindex arithmetic operations
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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Emacs Lisp provides the traditional four arithmetic operations
(addition, subtraction, multiplication, and division), as well as
remainder and modulus functions, and functions to add or subtract 1.
Except for @code{%}, each of these functions accepts both integer and
floating-point arguments, and returns a floating-point number if any
argument is floating point.
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Emacs Lisp arithmetic functions do not check for integer overflow.
Thus @code{(1+ 536870911)} may evaluate to
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@minus{}536870912, depending on your hardware.
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@defun 1+ number-or-marker
This function returns @var{number-or-marker} plus 1.
For example,
@example
(setq foo 4)
@result{} 4
(1+ foo)
@result{} 5
@end example
This function is not analogous to the C operator @code{++}---it does not
increment a variable. It just computes a sum. Thus, if we continue,
@example
foo
@result{} 4
@end example
If you want to increment the variable, you must use @code{setq},
like this:
@example
(setq foo (1+ foo))
@result{} 5
@end example
@end defun
@defun 1- number-or-marker
This function returns @var{number-or-marker} minus 1.
@end defun
@defun + &rest numbers-or-markers
This function adds its arguments together. When given no arguments,
@code{+} returns 0.
@example
(+)
@result{} 0
(+ 1)
@result{} 1
(+ 1 2 3 4)
@result{} 10
@end example
@end defun
@defun - &optional number-or-marker &rest more-numbers-or-markers
The @code{-} function serves two purposes: negation and subtraction.
When @code{-} has a single argument, the value is the negative of the
argument. When there are multiple arguments, @code{-} subtracts each of
the @var{more-numbers-or-markers} from @var{number-or-marker},
cumulatively. If there are no arguments, the result is 0.
@example
(- 10 1 2 3 4)
@result{} 0
(- 10)
@result{} -10
(-)
@result{} 0
@end example
@end defun
@defun * &rest numbers-or-markers
This function multiplies its arguments together, and returns the
product. When given no arguments, @code{*} returns 1.
@example
(*)
@result{} 1
(* 1)
@result{} 1
(* 1 2 3 4)
@result{} 24
@end example
@end defun
@defun / number &rest divisors
With one or more @var{divisors}, this function divides @var{number}
by each divisor in @var{divisors} in turn, and returns the quotient.
With no @var{divisors}, this function returns 1/@var{number}, i.e.,
the multiplicative inverse of @var{number}. Each argument may be a
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number or a marker.
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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If all the arguments are integers, the result is an integer, obtained
by rounding the quotient towards zero after each division.
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@example
@group
(/ 6 2)
@result{} 3
@end group
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@group
2007-09-06 04:25:08 +00:00
(/ 5 2)
@result{} 2
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@end group
@group
2007-09-06 04:25:08 +00:00
(/ 5.0 2)
@result{} 2.5
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@end group
@group
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(/ 5 2.0)
@result{} 2.5
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@end group
@group
2007-09-06 04:25:08 +00:00
(/ 5.0 2.0)
@result{} 2.5
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@end group
@group
(/ 4.0)
@result{} 0.25
@end group
@group
(/ 4)
@result{} 0
@end group
@group
2007-09-06 04:25:08 +00:00
(/ 25 3 2)
@result{} 4
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@end group
2007-09-06 04:25:08 +00:00
@group
(/ -17 6)
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@result{} -2
2007-09-06 04:25:08 +00:00
@end group
@end example
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@cindex @code{arith-error} in division
If you divide an integer by the integer 0, Emacs signals an
@code{arith-error} error (@pxref{Errors}). Floating-point division of
a nonzero number by zero yields either positive or negative infinity
(@pxref{Float Basics}).
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@end defun
@defun % dividend divisor
@cindex remainder
This function returns the integer remainder after division of @var{dividend}
by @var{divisor}. The arguments must be integers or markers.
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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For any two integers @var{dividend} and @var{divisor},
@example
@group
(+ (% @var{dividend} @var{divisor})
(* (/ @var{dividend} @var{divisor}) @var{divisor}))
@end group
@end example
2007-09-06 04:25:08 +00:00
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
@noindent
always equals @var{dividend} if @var{divisor} is nonzero.
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@example
(% 9 4)
@result{} 1
(% -9 4)
@result{} -1
(% 9 -4)
@result{} 1
(% -9 -4)
@result{} -1
@end example
@end defun
@defun mod dividend divisor
@cindex modulus
This function returns the value of @var{dividend} modulo @var{divisor};
in other words, the remainder after division of @var{dividend}
by @var{divisor}, but with the same sign as @var{divisor}.
The arguments must be numbers or markers.
Unlike @code{%}, @code{mod} permits floating-point arguments; it
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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rounds the quotient downward (towards minus infinity) to an integer,
and uses that quotient to compute the remainder.
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Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
2012-09-11 02:28:27 +00:00
If @var{divisor} is zero, @code{mod} signals an @code{arith-error}
error if both arguments are integers, and returns a NaN otherwise.
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@example
@group
(mod 9 4)
@result{} 1
@end group
@group
(mod -9 4)
@result{} 3
@end group
@group
(mod 9 -4)
@result{} -3
@end group
@group
(mod -9 -4)
@result{} -1
@end group
@group
(mod 5.5 2.5)
@result{} .5
@end group
@end example
For any two numbers @var{dividend} and @var{divisor},
@example
@group
(+ (mod @var{dividend} @var{divisor})
(* (floor @var{dividend} @var{divisor}) @var{divisor}))
@end group
@end example
@noindent
always equals @var{dividend}, subject to rounding error if either
argument is floating point and to an @code{arith-error} if @var{dividend} is an
integer and @var{divisor} is 0. For @code{floor}, see @ref{Numeric
2007-09-06 04:25:08 +00:00
Conversions}.
@end defun
@node Rounding Operations
@section Rounding Operations
@cindex rounding without conversion
The functions @code{ffloor}, @code{fceiling}, @code{fround}, and
@code{ftruncate} take a floating-point argument and return a floating-point
result whose value is a nearby integer. @code{ffloor} returns the
2007-09-06 04:25:08 +00:00
nearest integer below; @code{fceiling}, the nearest integer above;
@code{ftruncate}, the nearest integer in the direction towards zero;
@code{fround}, the nearest integer.
@defun ffloor float
This function rounds @var{float} to the next lower integral value, and
returns that value as a floating-point number.
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@end defun
@defun fceiling float
This function rounds @var{float} to the next higher integral value, and
returns that value as a floating-point number.
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@end defun
@defun ftruncate float
This function rounds @var{float} towards zero to an integral value, and
returns that value as a floating-point number.
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@end defun
@defun fround float
This function rounds @var{float} to the nearest integral value,
and returns that value as a floating-point number.
Rounding a value equidistant between two integers returns the even integer.
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@end defun
@node Bitwise Operations
@section Bitwise Operations on Integers
@cindex bitwise arithmetic
@cindex logical arithmetic
In a computer, an integer is represented as a binary number, a
sequence of @dfn{bits} (digits which are either zero or one). A bitwise
operation acts on the individual bits of such a sequence. For example,
@dfn{shifting} moves the whole sequence left or right one or more places,
reproducing the same pattern moved over.
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The bitwise operations in Emacs Lisp apply only to integers.
@defun lsh integer1 count
@cindex logical shift
@code{lsh}, which is an abbreviation for @dfn{logical shift}, shifts the
bits in @var{integer1} to the left @var{count} places, or to the right
if @var{count} is negative, bringing zeros into the vacated bits. If
@var{count} is negative, @code{lsh} shifts zeros into the leftmost
(most-significant) bit, producing a positive result even if
@var{integer1} is negative. Contrast this with @code{ash}, below.
Here are two examples of @code{lsh}, shifting a pattern of bits one
place to the left. We show only the low-order eight bits of the binary
pattern; the rest are all zero.
@example
@group
(lsh 5 1)
@result{} 10
;; @r{Decimal 5 becomes decimal 10.}
00000101 @result{} 00001010
(lsh 7 1)
@result{} 14
;; @r{Decimal 7 becomes decimal 14.}
00000111 @result{} 00001110
@end group
@end example
@noindent
As the examples illustrate, shifting the pattern of bits one place to
the left produces a number that is twice the value of the previous
number.
Shifting a pattern of bits two places to the left produces results
like this (with 8-bit binary numbers):
@example
@group
(lsh 3 2)
@result{} 12
;; @r{Decimal 3 becomes decimal 12.}
00000011 @result{} 00001100
@end group
@end example
On the other hand, shifting one place to the right looks like this:
@example
@group
(lsh 6 -1)
@result{} 3
;; @r{Decimal 6 becomes decimal 3.}
00000110 @result{} 00000011
@end group
@group
(lsh 5 -1)
@result{} 2
;; @r{Decimal 5 becomes decimal 2.}
00000101 @result{} 00000010
@end group
@end example
@noindent
As the example illustrates, shifting one place to the right divides the
value of a positive integer by two, rounding downward.
The function @code{lsh}, like all Emacs Lisp arithmetic functions, does
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not check for overflow, so shifting left can discard significant bits
and change the sign of the number. For example, left shifting
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536,870,911 produces @minus{}2 in the 30-bit implementation:
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@example
(lsh 536870911 1) ; @r{left shift}
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@result{} -2
@end example
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In binary, the argument looks like this:
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@example
@group
;; @r{Decimal 536,870,911}
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0111...111111 (30 bits total)
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@end group
@end example
@noindent
which becomes the following when left shifted:
@example
@group
;; @r{Decimal @minus{}2}
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1111...111110 (30 bits total)
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@end group
@end example
@end defun
@defun ash integer1 count
@cindex arithmetic shift
@code{ash} (@dfn{arithmetic shift}) shifts the bits in @var{integer1}
to the left @var{count} places, or to the right if @var{count}
is negative.
@code{ash} gives the same results as @code{lsh} except when
@var{integer1} and @var{count} are both negative. In that case,
@code{ash} puts ones in the empty bit positions on the left, while
@code{lsh} puts zeros in those bit positions.
Thus, with @code{ash}, shifting the pattern of bits one place to the right
looks like this:
@example
@group
(ash -6 -1) @result{} -3
;; @r{Decimal @minus{}6 becomes decimal @minus{}3.}
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1111...111010 (30 bits total)
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@result{}
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1111...111101 (30 bits total)
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@end group
@end example
In contrast, shifting the pattern of bits one place to the right with
@code{lsh} looks like this:
@example
@group
(lsh -6 -1) @result{} 536870909
;; @r{Decimal @minus{}6 becomes decimal 536,870,909.}
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1111...111010 (30 bits total)
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@result{}
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0111...111101 (30 bits total)
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@end group
@end example
Here are other examples:
@c !!! Check if lined up in smallbook format! XDVI shows problem
@c with smallbook but not with regular book! --rjc 16mar92
@smallexample
@group
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; @r{ 30-bit binary values}
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(lsh 5 2) ; 5 = @r{0000...000101}
@result{} 20 ; = @r{0000...010100}
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@end group
@group
(ash 5 2)
@result{} 20
(lsh -5 2) ; -5 = @r{1111...111011}
@result{} -20 ; = @r{1111...101100}
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(ash -5 2)
@result{} -20
@end group
@group
(lsh 5 -2) ; 5 = @r{0000...000101}
@result{} 1 ; = @r{0000...000001}
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@end group
@group
(ash 5 -2)
@result{} 1
@end group
@group
(lsh -5 -2) ; -5 = @r{1111...111011}
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@result{} 268435454
; = @r{0011...111110}
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@end group
@group
(ash -5 -2) ; -5 = @r{1111...111011}
@result{} -2 ; = @r{1111...111110}
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@end group
@end smallexample
@end defun
@defun logand &rest ints-or-markers
This function returns the bitwise AND of the arguments: the @var{n}th
bit is 1 in the result if, and only if, the @var{n}th bit is 1 in all
the arguments.
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For example, using 4-bit binary numbers, the bitwise AND of 13 and
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12 is 12: 1101 combined with 1100 produces 1100.
In both the binary numbers, the leftmost two bits are both 1
so the leftmost two bits of the returned value are both 1.
However, for the rightmost two bits, each is 0 in at least one of
the arguments, so the rightmost two bits of the returned value are both 0.
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@noindent
Therefore,
@example
@group
(logand 13 12)
@result{} 12
@end group
@end example
If @code{logand} is not passed any argument, it returns a value of
@minus{}1. This number is an identity element for @code{logand}
because its binary representation consists entirely of ones. If
@code{logand} is passed just one argument, it returns that argument.
@smallexample
@group
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; @r{ 30-bit binary values}
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(logand 14 13) ; 14 = @r{0000...001110}
; 13 = @r{0000...001101}
@result{} 12 ; 12 = @r{0000...001100}
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@end group
@group
(logand 14 13 4) ; 14 = @r{0000...001110}
; 13 = @r{0000...001101}
; 4 = @r{0000...000100}
@result{} 4 ; 4 = @r{0000...000100}
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@end group
@group
(logand)
@result{} -1 ; -1 = @r{1111...111111}
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@end group
@end smallexample
@end defun
@defun logior &rest ints-or-markers
This function returns the bitwise inclusive OR of its arguments: the @var{n}th
bit is 1 in the result if, and only if, the @var{n}th bit is 1 in at
least one of the arguments. If there are no arguments, the result is 0,
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which is an identity element for this operation. If @code{logior} is
passed just one argument, it returns that argument.
@smallexample
@group
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; @r{ 30-bit binary values}
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(logior 12 5) ; 12 = @r{0000...001100}
; 5 = @r{0000...000101}
@result{} 13 ; 13 = @r{0000...001101}
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@end group
@group
(logior 12 5 7) ; 12 = @r{0000...001100}
; 5 = @r{0000...000101}
; 7 = @r{0000...000111}
@result{} 15 ; 15 = @r{0000...001111}
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@end group
@end smallexample
@end defun
@defun logxor &rest ints-or-markers
This function returns the bitwise exclusive OR of its arguments: the
@var{n}th bit is 1 in the result if, and only if, the @var{n}th bit is
1 in an odd number of the arguments. If there are no arguments, the
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result is 0, which is an identity element for this operation. If
@code{logxor} is passed just one argument, it returns that argument.
@smallexample
@group
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; @r{ 30-bit binary values}
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(logxor 12 5) ; 12 = @r{0000...001100}
; 5 = @r{0000...000101}
@result{} 9 ; 9 = @r{0000...001001}
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@end group
@group
(logxor 12 5 7) ; 12 = @r{0000...001100}
; 5 = @r{0000...000101}
; 7 = @r{0000...000111}
@result{} 14 ; 14 = @r{0000...001110}
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@end group
@end smallexample
@end defun
@defun lognot integer
This function returns the bitwise complement of its argument: the @var{n}th
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bit is one in the result if, and only if, the @var{n}th bit is zero in
@var{integer}, and vice-versa.
@example
(lognot 5)
@result{} -6
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;; 5 = @r{0000...000101} (30 bits total)
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;; @r{becomes}
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;; -6 = @r{1111...111010} (30 bits total)
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@end example
@end defun
@node Math Functions
@section Standard Mathematical Functions
@cindex transcendental functions
@cindex mathematical functions
@cindex floating-point functions
These mathematical functions allow integers as well as floating-point
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numbers as arguments.
@defun sin arg
@defunx cos arg
@defunx tan arg
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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These are the basic trigonometric functions, with argument @var{arg}
measured in radians.
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@end defun
@defun asin arg
The value of @code{(asin @var{arg})} is a number between
@ifnottex
@minus{}pi/2
@end ifnottex
@tex
@math{-\pi/2}
@end tex
and
@ifnottex
pi/2
@end ifnottex
@tex
@math{\pi/2}
@end tex
Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
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(inclusive) whose sine is @var{arg}. If @var{arg} is out of range
(outside [@minus{}1, 1]), @code{asin} returns a NaN.
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@end defun
@defun acos arg
The value of @code{(acos @var{arg})} is a number between 0 and
@ifnottex
pi
@end ifnottex
@tex
@math{\pi}
@end tex
Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
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(inclusive) whose cosine is @var{arg}. If @var{arg} is out of range
(outside [@minus{}1, 1]), @code{acos} returns a NaN.
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@end defun
@defun atan y &optional x
The value of @code{(atan @var{y})} is a number between
@ifnottex
@minus{}pi/2
@end ifnottex
@tex
@math{-\pi/2}
@end tex
and
@ifnottex
pi/2
@end ifnottex
@tex
@math{\pi/2}
@end tex
(exclusive) whose tangent is @var{y}. If the optional second
argument @var{x} is given, the value of @code{(atan y x)} is the
angle in radians between the vector @code{[@var{x}, @var{y}]} and the
@code{X} axis.
@end defun
@defun exp arg
This is the exponential function; it returns @math{e} to the power
@var{arg}.
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@end defun
@defun log arg &optional base
This function returns the logarithm of @var{arg}, with base
@var{base}. If you don't specify @var{base}, the natural base
Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
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@math{e} is used. If @var{arg} or @var{base} is negative, @code{log}
returns a NaN.
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@end defun
@defun expt x 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, overflow causes truncation, so watch out.
Simplify, document, and port floating-point. The porting part of this patch fixes bugs on non-IEEE platforms with frexp, ldexp, logb. * admin/CPP-DEFINES (HAVE_CBRT, HAVE_LOGB, logb): Remove. * configure.ac (logb, cbrt): Do not check for these functions, as they are not being used. * doc/lispref/numbers.texi (Float Basics, Arithmetic Operations, Math Functions): Document that / and mod (with floating point arguments), along with asin, acos, log, log10, expt and sqrt, return special values instead of signaling exceptions. (Float Basics): Document that logb operates on the absolute value of its argument. (Math Functions): Document that (log ARG BASE) also returns NaN if BASE is negative. Document that (expt X Y) returns NaN if X is a finite negative number and Y a finite non-integer. * etc/NEWS: Document NaNs versus signaling-error change. * src/data.c, src/lisp.h (Qdomain_error, Qsingularity_error, Qunderflow_error): Now static. * src/floatfns.c: Simplify discussion of functions that Emacs doesn't support, by removing commented-out code and briefly listing the C89 functions excluded. The commented-out stuff was confusing maintenance, e.g., we thought we needed cbrt but it was commented out. (logb): Remove decl; no longer needed. (isfinite): New macro, if not already supplied. (isnan): Don't replace any existing macro. (Ffrexp, Fldexp): Define even if !HAVE_COPYSIGN, as frexp and ldexp are present on all C89 platforms. (Ffrexp): Do not special-case zero, as frexp does the right thing for that case. (Flogb): Do not use logb, as it doesn't have the desired meaning on hosts that use non-base-2 floating point. Instead, stick with frexp, which is C89 anyway. Do not pass an infinity or a NaN to frexp, to avoid getting an unspecified result.
2012-09-11 02:28:27 +00:00
If @var{x} is a finite negative number and @var{y} is a finite
non-integer, @code{expt} returns a NaN.
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@end defun
@defun sqrt arg
This returns the square root of @var{arg}. If @var{arg} is finite
and less than zero, @code{sqrt} returns a NaN.
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@end defun
In addition, Emacs defines the following common mathematical
constants:
@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
2007-09-06 04:25:08 +00:00
@node Random Numbers
@section Random Numbers
@cindex random numbers
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
2012-09-30 09:18:38 +00:00
A deterministic computer program cannot generate true random
numbers. For most purposes, @dfn{pseudo-random numbers} suffice. A
series of pseudo-random numbers is generated in a deterministic
fashion. The numbers are not truly random, but they have certain
properties that mimic a random series. For example, all possible
values occur equally often in a pseudo-random series.
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Restore some of the quoting in the manuals * doc/lispref/windows.texi (Coordinates and Windows) (Coordinates and Windows): * doc/lispref/variables.texi (Lexical Binding) (File Local Variables): * doc/lispref/text.texi (Format Properties): * doc/lispref/symbols.texi (Symbol Components): * doc/lispref/strings.texi (Creating Strings): * doc/lispref/sequences.texi (Sequence Functions): * doc/lispref/searching.texi (Regexp Special, Regexp Search) (Search and Replace): * doc/lispref/processes.texi (Bindat Spec): * doc/lispref/os.texi (Idle Timers): * doc/lispref/objects.texi (Basic Char Syntax): * doc/lispref/numbers.texi (Float Basics, Random Numbers): * doc/lispref/nonascii.texi (Character Properties): * doc/lispref/modes.texi (Major Mode Conventions, Mode Hooks) (Mode Line Variables): * doc/lispref/minibuf.texi (Text from Minibuffer): * doc/lispref/loading.texi (Autoload): * doc/lispref/keymaps.texi (Controlling Active Maps): * doc/lispref/frames.texi (Frame Layout, Size and Position) (Size Parameters, Implied Frame Resizing): * doc/lispref/files.texi (Changing Files, Magic File Names): * doc/lispref/eval.texi (Self-Evaluating Forms): * doc/lispref/display.texi (Progress, Abstract Display) (Abstract Display Example, Bidirectional Display): * doc/lispref/commands.texi (Event Mod): * doc/emacs/windows.texi (Displaying Buffers): * doc/emacs/trouble.texi (Bug Criteria, Checklist): * doc/emacs/text.texi (Enriched Text): * doc/emacs/programs.texi (MixedCase Words): * doc/emacs/picture-xtra.texi (Insert in Picture) (Tabs in Picture): * doc/emacs/misc.texi (Emacs Server, Printing): * doc/emacs/mini.texi (Minibuffer History): * doc/emacs/maintaining.texi (Old Revisions, VC Change Log) (Pulling / Pushing): * doc/emacs/killing.texi (Yanking, Cut and Paste, Clipboard): * doc/emacs/help.texi (Help, Help Echo): * doc/emacs/glossary.texi (Glossary): * doc/emacs/frames.texi (Mouse Commands, Creating Frames) (Frame Commands): * doc/emacs/files.texi (Reverting, Saving, Directories): * doc/emacs/entering.texi (Exiting): * doc/emacs/emacs.texi (Top): * doc/emacs/cmdargs.texi (Window Size X, Icons X): * doc/emacs/anti.texi (Antinews): Restore quoting of text where appropriate or replace quoting with @dfn. * doc/misc/ediff.texi (Window and Frame Configuration): * doc/lispref/processes.texi (Network Feature Testing): * doc/lispref/display.texi (Display Margins): Quote the phrase after "a.k.a." where appropriate.
2015-09-16 09:56:45 +00:00
@cindex seed, for random number generation
Pseudo-random numbers are generated from a @dfn{seed value}. Starting from
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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any given seed, the @code{random} function always generates the same
sequence of numbers. By default, Emacs initializes the random seed at
startup, in such a way that the sequence of values of @code{random}
(with overwhelming likelihood) differs in each Emacs run.
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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Sometimes you want the random number sequence to be repeatable. For
example, when debugging a program whose behavior depends on the random
number sequence, it is helpful to get the same behavior in each
program run. To make the sequence repeat, execute @code{(random "")}.
This sets the seed to a constant value for your particular Emacs
executable (though it may differ for other Emacs builds). You can use
other strings to choose various seed values.
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@defun random &optional limit
This function returns a pseudo-random integer. Repeated calls return a
series of pseudo-random integers.
If @var{limit} is a positive integer, the value is chosen to be
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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nonnegative and less than @var{limit}. Otherwise, the value might be
any integer representable in Lisp, i.e., an integer between
Update docs for a bunch of 24.3 changes. * doc/emacs/killing.texi (Rectangles): Document copy-rectangle-as-kill. * doc/emacs/search.texi (Special Isearch): Document the lax space search feature and M-s SPC. (Regexp Search): Move main search-whitespace-regexp description to Special Isearch. (Replace): Document replace-lax-whitespace. * doc/emacs/basic.texi (Position Info): Document C-u M-=. (Moving Point): Document move-to-column. * doc/emacs/display.texi (Useless Whitespace): Add delete-trailing-lines. * doc/emacs/misc.texi (emacsclient Options): Document the effect of initial-buffer-choice on client frames. Document server-auth-dir. Do not document server-host, which is bad security practice. * doc/emacs/building.texi (Lisp Libraries): Docstring lookups can trigger autoloading. Document help-enable-auto-load. * doc/emacs/mini.texi (Yes or No Prompts): New node. * doc/emacs/ack.texi (Acknowledgments): Remove obsolete packages. * doc/lispref/commands.texi (Click Events): Define "mouse position list". Remove mention of unimplemented horizontal scroll bars. (Drag Events, Motion Events): Refer to "mouse position list". (Accessing Mouse): Document posnp. * doc/lispref/errors.texi (Standard Errors): Tweak arith-error description. Tweak markup. Remove domain-error and friends, which seem to be unused after the floating-point code revamp. * doc/lispref/functions.texi (Obsolete Functions): Obsolescence also affects documentation commands. Various clarifications. (Declare Form): New node. * doc/lispref/loading.texi (Autoload): * doc/lispref/help.texi (Documentation Basics): The special sequences can trigger autoloading. * doc/lispref/macros.texi (Defining Macros): Move description of `declare' to Declare Form node. * doc/lispref/numbers.texi (Integer Basics): Copyedits. (Float Basics): Consider IEEE floating point always available. (Random Numbers): Document actual limits. (Arithmetic Operations): Clarify division by zero. Don't mention the machine-independence of negative division since it does not happen in practice. * doc/lispref/os.texi (Idle Timers): Minor clarifications. (User Identification): Add system-users and system-groups. * doc/lispref/strings.texi (String Basics): Copyedits. * lisp/minibuffer.el (minibuffer-local-filename-syntax): Doc fix. * lisp/server.el (server-host): Document the security implications. (server-auth-key): Doc fix. * lisp/startup.el (initial-buffer-choice): Doc fix. * src/fns.c (Frandom): Doc fix.
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@code{most-negative-fixnum} and @code{most-positive-fixnum}
(@pxref{Integer Basics}).
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If @var{limit} is @code{t}, it means to choose a new seed as if Emacs
were restarting, typically from the system entropy. On systems
lacking entropy pools, choose the seed from less-random volatile data
such as the current time.
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If @var{limit} is a string, it means to choose a new seed based on the
string's contents.
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@end defun