@node Float Basics
@section Floating Point Basics
+@cindex @acronym{IEEE} floating point
Floating point numbers are useful for representing numbers that are
not integral. The precise range of floating point numbers is
machine-specific; it is the same as the range of the C data type
-@code{double} on the machine you are using.
+@code{double} on the machine you are using. Emacs uses the
+@acronym{IEEE} floating point standard where possible (the standard is
+supported by most modern computers).
- The read-syntax for floating point numbers requires either a decimal
+ The read syntax for floating point numbers requires either a decimal
point (with at least one digit following), an exponent, or both. For
example, @samp{1500.0}, @samp{15e2}, @samp{15.0e2}, @samp{1.5e3}, and
@samp{.15e4} are five ways of writing a floating point number whose
-value is 1500. They are all equivalent. You can also use a minus sign
-to write negative floating point numbers, as in @samp{-1.0}.
+value is 1500. They are all equivalent. You can also use a minus
+sign to write negative floating point numbers, as in @samp{-1.0}.
+
+ Emacs Lisp treats @code{-0.0} as equal to ordinary zero (with
+respect to @code{equal} and @code{=}), even though the two are
+distinguishable in the @acronym{IEEE} floating point standard.
-@cindex @acronym{IEEE} floating point
@cindex positive infinity
@cindex negative infinity
@cindex infinity
@cindex NaN
- Most modern computers support the @acronym{IEEE} floating point standard,
-which provides for positive infinity and negative infinity as floating point
-values. It also 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. For practical purposes, there's no significant difference between
-different NaN values in Emacs Lisp, and there's no rule for precisely
-which NaN value should be used in a particular case, so Emacs Lisp
-doesn't try to distinguish them (but it does report the sign, if you
-print it). Here are the read syntaxes for these special floating
-point values:
+ The @acronym{IEEE} floating point standard supports positive
+infinity and negative infinity as floating point values. It also
+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. (NaN
+values can also carry a sign, but for practical purposes there's no
+significant difference between different NaN values in Emacs Lisp.)
+Here are the read syntaxes for these special floating point values:
@table @asis
@item positive infinity
@samp{0.0e+NaN} or @samp{-0.0e+NaN}.
@end table
- To test whether a floating point value is a NaN, compare it with
-itself using @code{=}. That returns @code{nil} for a NaN, and
-@code{t} for any other floating point value.
+@defun isnan number
+This predicate tests whether its argument is NaN, and returns @code{t}
+if so, @code{nil} otherwise. The argument must be a number.
+@end defun
+
+ The following functions are specialized for handling floating point
+numbers:
+
+@defun frexp x
+This function returns a cons cell @code{(@var{sig} . @var{exp})},
+where @var{sig} and @var{exp} are respectively the significand and
+exponent of the floating point number @var{x}:
+
+@smallexample
+@var{x} = @var{sig} * 2^@var{exp}
+@end smallexample
+
+@var{sig} is a floating point number between 0.5 (inclusive) and 1.0
+(exclusive). If @var{x} is zero, the return value is @code{(0 . 0)}.
+@end defun
- The value @code{-0.0} is distinguishable from ordinary zero in
-@acronym{IEEE} floating point, but Emacs Lisp @code{equal} and
-@code{=} consider them equal values.
+@defun ldexp sig &optional exp
+This function returns a floating point number corresponding to the
+significand @var{sig} and exponent @var{exp}.
+@end defun
- You can use @code{logb} to extract the binary exponent of a floating
-point number (or estimate the logarithm of an integer):
+@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
+numbers.
+@end defun
@defun logb number
This function returns the binary exponent of @var{number}. More
@end example
@end defun
-@defvar float-e
-The mathematical constant @math{e} (2.71828@dots{}).
-@end defvar
-
-@defvar float-pi
-The mathematical constant @math{pi} (3.14159@dots{}).
-@end defvar
-
@node Predicates on Numbers
@section Type Predicates for Numbers
@cindex predicates for numbers
@end defun
@defun exp arg
-This is the exponential function; it returns
-@tex
-@math{e}
-@end tex
-@ifnottex
-@i{e}
-@end ifnottex
-to the power @var{arg}.
-@tex
-@math{e}
-@end tex
-@ifnottex
-@i{e}
-@end ifnottex
-is a fundamental mathematical constant also called the base of natural
-logarithms.
+This is the exponential function; it returns @math{e} to the power
+@var{arg}.
@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 base
-@tex
-@math{e}
-@end tex
-@ifnottex
-@i{e}
-@end ifnottex
-is used. If @var{arg} is negative, it signals a @code{domain-error}
-error.
+This function returns the logarithm of @var{arg}, with base
+@var{base}. If you don't specify @var{base}, the natural base
+@math{e} is used. If @var{arg} is negative, it signals a
+@code{domain-error} error.
@end defun
@ignore
it signals a @code{domain-error} error.
@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
+
@node Random Numbers
@section Random Numbers
@cindex random numbers
If @var{limit} is @code{t}, it means to choose a new seed based on the
current time of day and on Emacs's process @acronym{ID} number.
-@c "Emacs'" is incorrect usage!
On some machines, any integer representable in Lisp may be the result
of @code{random}. On other machines, the result can never be larger
@ifnottex
2**26
@end ifnottex
-bit as well as the code for the corresponding non-control
-character. Ordinary terminals have no way of generating non-@acronym{ASCII}
-control characters, but you can generate them straightforwardly using X
-and other window systems.
+bit as well as the code for the corresponding non-control character.
+Ordinary text terminals have no way of generating non-@acronym{ASCII}
+control characters, but you can generate them straightforwardly using
+X and other window systems.
For historical reasons, Emacs treats the @key{DEL} character as
the control equivalent of @kbd{?}:
@end ifnottex
bit to indicate that the shift key was used in typing a control
character. This distinction is possible only when you use X terminals
-or other special terminals; ordinary terminals do not report the
-distinction to the computer in any way. The Lisp syntax for
-the shift bit is @samp{\S-}; thus, @samp{?\C-\S-o} or @samp{?\C-\S-O}
-represents the shifted-control-o character.
+or other special terminals; ordinary text terminals do not report the
+distinction. The Lisp syntax for the shift bit is @samp{\S-}; thus,
+@samp{?\C-\S-o} or @samp{?\C-\S-O} represents the shifted-control-o
+character.
@cindex hyper characters
@cindex super characters
independently.
A symbol whose name starts with a colon (@samp{:}) is called a
-@dfn{keyword symbol}. These symbols automatically act as constants, and
-are normally used only by comparing an unknown symbol with a few
-specific alternatives.
+@dfn{keyword symbol}. These symbols automatically act as constants,
+and are normally used only by comparing an unknown symbol with a few
+specific alternatives. @xref{Constant Variables}.
@cindex @samp{\} in symbols
@cindex backslash in symbols
@subsection Sequence Types
A @dfn{sequence} is a Lisp object that represents an ordered set of
-elements. There are two kinds of sequence in Emacs Lisp, lists and
-arrays. Thus, an object of type list or of type array is also
-considered a sequence.
-
- Arrays are further subdivided into strings, vectors, char-tables and
-bool-vectors. Vectors can hold elements of any type, but string
-elements must be characters, and bool-vector elements must be @code{t}
-or @code{nil}. Char-tables are like vectors except that they are
-indexed by any valid character code. The characters in a string can
-have text properties like characters in a buffer (@pxref{Text
-Properties}), but vectors do not support text properties, even when
-their elements happen to be characters.
-
- Lists, strings and the other array types are different, but they have
-important similarities. For example, all have a length @var{l}, and all
-have elements which can be indexed from zero to @var{l} minus one.
-Several functions, called sequence functions, accept any kind of
-sequence. For example, the function @code{elt} can be used to extract
-an element of a sequence, given its index. @xref{Sequences Arrays
-Vectors}.
+elements. There are two kinds of sequence in Emacs Lisp: @dfn{lists}
+and @dfn{arrays}.
+
+ Lists are the most commonly-used sequences. A list can hold
+elements of any type, and its length can be easily changed by adding
+or removing elements. See the next subsection for more about lists.
+
+ Arrays are fixed-length sequences. They are further subdivided into
+strings, vectors, char-tables and bool-vectors. Vectors can hold
+elements of any type, whereas string elements must be characters, and
+bool-vector elements must be @code{t} or @code{nil}. Char-tables are
+like vectors except that they are indexed by any valid character code.
+The characters in a string can have text properties like characters in
+a buffer (@pxref{Text Properties}), but vectors do not support text
+properties, even when their elements happen to be characters.
+
+ Lists, strings and the other array types also share important
+similarities. For example, all have a length @var{l}, and all have
+elements which can be indexed from zero to @var{l} minus one. Several
+functions, called sequence functions, accept any kind of sequence.
+For example, the function @code{length} reports the length of any kind
+of sequence. @xref{Sequences Arrays Vectors}.
It is generally impossible to read the same sequence twice, since
sequences are always created anew upon reading. If you read the read
@cindex decrement field of register
@cindex pointers
- A @dfn{cons cell} is an object that consists of two slots, called the
-@sc{car} slot and the @sc{cdr} slot. Each slot can @dfn{hold} or
-@dfn{refer to} any Lisp object. We also say that ``the @sc{car} of
-this cons cell is'' whatever object its @sc{car} slot currently holds,
-and likewise for the @sc{cdr}.
-
-@quotation
-A note to C programmers: in Lisp, we do not distinguish between
-``holding'' a value and ``pointing to'' the value, because pointers in
-Lisp are implicit.
-@end quotation
+ A @dfn{cons cell} is an object that consists of two slots, called
+the @sc{car} slot and the @sc{cdr} slot. Each slot can @dfn{hold} any
+Lisp object. We also say that ``the @sc{car} of this cons cell is''
+whatever object its @sc{car} slot currently holds, and likewise for
+the @sc{cdr}.
+@cindex list structure
A @dfn{list} is a series of cons cells, linked together so that the
@sc{cdr} slot of each cons cell holds either the next cons cell or the
empty list. The empty list is actually the symbol @code{nil}.
-@xref{Lists}, for functions that work on lists. Because most cons
-cells are used as part of lists, the phrase @dfn{list structure} has
-come to refer to any structure made out of cons cells.
+@xref{Lists}, for details. Because most cons cells are used as part
+of lists, we refer to any structure made out of cons cells as a
+@dfn{list structure}.
+
+@cindex linked list
+@quotation
+A note to C programmers: a Lisp list thus works as a @dfn{linked list}
+built up of cons cells. Because pointers in Lisp are implicit, we do
+not distinguish between a cons cell slot ``holding'' a value versus
+``pointing to'' the value.
+@end quotation
@cindex atoms
Because cons cells are so central to Lisp, we also have a word for
@node Non-ASCII in Strings
@subsubsection Non-@acronym{ASCII} Characters in Strings
- You can include a non-@acronym{ASCII} international character in a string
-constant by writing it literally. There are two text representations
-for non-@acronym{ASCII} characters in Emacs strings (and in buffers): unibyte
-and multibyte. If the string constant is read from a multibyte source,
-such as a multibyte buffer or string, or a file that would be visited as
-multibyte, then the character is read as a multibyte character, and that
-makes the string multibyte. If the string constant is read from a
-unibyte source, then the character is read as unibyte and that makes the
-string unibyte.
-
- You can also represent a multibyte non-@acronym{ASCII} character with its
-character code: use a hex escape, @samp{\x@var{nnnnnnn}}, with as many
-digits as necessary. (Multibyte non-@acronym{ASCII} character codes are all
-greater than 256.) Any character which is not a valid hex digit
-terminates this construct. If the next character in the string could be
-interpreted as a hex digit, write @w{@samp{\ }} (backslash and space) to
-terminate the hex escape---for example, @w{@samp{\xe0\ }} represents
-one character, @samp{a} with grave accent. @w{@samp{\ }} in a string
-constant is just like backslash-newline; it does not contribute any
-character to the string, but it does terminate the preceding hex escape.
+ You can include a non-@acronym{ASCII} international character in a
+string constant by writing it literally. There are two text
+representations for non-@acronym{ASCII} characters in Emacs strings
+(and in buffers): unibyte and multibyte (@pxref{Text
+Representations}). If the string constant is read from a multibyte
+source, such as a multibyte buffer or string, or a file that would be
+visited as multibyte, then Emacs reads the non-@acronym{ASCII}
+character as a multibyte character and automatically makes the string
+a multibyte string. If the string constant is read from a unibyte
+source, then Emacs reads the non-@acronym{ASCII} character as unibyte,
+and makes the string unibyte.
+
+ Instead of writing a non-@acronym{ASCII} character literally into a
+multibyte string, you can write it as its character code using a hex
+escape, @samp{\x@var{nnnnnnn}}, with as many digits as necessary.
+(Multibyte non-@acronym{ASCII} character codes are all greater than
+256.) You can also specify a character in a multibyte string using
+the @samp{\u} or @samp{\U} Unicode escape syntax (@pxref{General
+Escape Syntax}). In either case, any character which is not a valid
+hex digit terminates the construct. If the next character in the
+string could be interpreted as a hex digit, write @w{@samp{\ }}
+(backslash and space) to terminate the hex escape---for example,
+@w{@samp{\xe0\ }} represents one character, @samp{a} with grave
+accent. @w{@samp{\ }} in a string constant is just like
+backslash-newline; it does not contribute any character to the string,
+but it does terminate the preceding hex escape. Using any hex escape
+in a string (even for an @acronym{ASCII} character) automatically
+forces the string to be multibyte.
You can represent a unibyte non-@acronym{ASCII} character with its
character code, which must be in the range from 128 (0200 octal) to
255 (0377 octal). If you write all such character codes in octal and
the string contains no other characters forcing it to be multibyte,
-this produces a unibyte string. However, using any hex escape in a
-string (even for an @acronym{ASCII} character) forces the string to be
-multibyte.
-
- You can also specify characters in a string by their numeric values
-in Unicode, using @samp{\u} and @samp{\U} (@pxref{Character Type}).
-
- @xref{Text Representations}, for more information about the two
-text representations.
+this produces a unibyte string.
@node Nonprinting Characters
@subsubsection Nonprinting Characters in Strings
@section Equality Predicates
@cindex equality
- Here we describe functions that test for equality between any two
-objects. Other functions test equality of contents between objects of specific
-types, e.g., strings. For these predicates, see the appropriate chapter
-describing the data type.
+ Here we describe functions that test for equality between two
+objects. Other functions test equality of contents between objects of
+specific types, e.g.@: strings. For these predicates, see the
+appropriate chapter describing the data type.
@defun eq object1 object2
This function returns @code{t} if @var{object1} and @var{object2} are
-the same object, @code{nil} otherwise.
-
-@code{eq} returns @code{t} if @var{object1} and @var{object2} are
-integers with the same value. Also, since symbol names are normally
-unique, if the arguments are symbols with the same name, they are
-@code{eq}. For other types (e.g., lists, vectors, strings), two
-arguments with the same contents or elements are not necessarily
-@code{eq} to each other: they are @code{eq} only if they are the same
-object, meaning that a change in the contents of one will be reflected
-by the same change in the contents of the other.
+the same object, and @code{nil} otherwise.
+
+If @var{object1} and @var{object2} are integers with the same value,
+they are considered to be the same object (i.e.@: @code{eq} returns
+@code{t}). If @var{object1} and @var{object2} are symbols with the
+same name, they are normally the same object---but see @ref{Creating
+Symbols} for exceptions. For other types (e.g.@: lists, vectors,
+strings), two arguments with the same contents or elements are not
+necessarily @code{eq} to each other: they are @code{eq} only if they
+are the same object, meaning that a change in the contents of one will
+be reflected by the same change in the contents of the other.
@example
@group
@end group
@end example
+@noindent
The @code{make-symbol} function returns an uninterned symbol, distinct
from the symbol that is used if you write the name in a Lisp expression.
Distinct symbols with the same name are not @code{eq}. @xref{Creating
@defun equal object1 object2
This function returns @code{t} if @var{object1} and @var{object2} have
-equal components, @code{nil} otherwise. Whereas @code{eq} tests if its
-arguments are the same object, @code{equal} looks inside nonidentical
-arguments to see if their elements or contents are the same. So, if two
-objects are @code{eq}, they are @code{equal}, but the converse is not
-always true.
+equal components, and @code{nil} otherwise. Whereas @code{eq} tests
+if its arguments are the same object, @code{equal} looks inside
+nonidentical arguments to see if their elements or contents are the
+same. So, if two objects are @code{eq}, they are @code{equal}, but
+the converse is not always true.
@example
@group
@end example
Comparison of strings is case-sensitive, but does not take account of
-text properties---it compares only the characters in the strings. Use
-@code{equal-including-properties} to also compare text properties. For
-technical reasons, a unibyte string and a multibyte string are
-@code{equal} if and only if they contain the same sequence of
-character codes and all these codes are either in the range 0 through
-127 (@acronym{ASCII}) or 160 through 255 (@code{eight-bit-graphic}).
-(@pxref{Text Representations}).
+text properties---it compares only the characters in the strings.
+@xref{Text Properties}. Use @code{equal-including-properties} to also
+compare text properties. For technical reasons, a unibyte string and
+a multibyte string are @code{equal} if and only if they contain the
+same sequence of character codes and all these codes are either in the
+range 0 through 127 (@acronym{ASCII}) or 160 through 255
+(@code{eight-bit-graphic}). (@pxref{Text Representations}).
@example
@group
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