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Reorder discussion of integer basics

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* doc/lispref/numbers.texi (Integer Basics): Put the fixnum/bignum
discussion at the end of the section, not at the start (Bug#39557).
This commit is contained in:
Paul Eggert 2020-02-17 13:36:50 -08:00
parent f765aad28b
commit 4e5ac4b0c6
1 changed files with 40 additions and 37 deletions
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doc/lispref/numbers.texi
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@ -34,39 +34,6 @@ numbers have a fixed amount of precision.
@node Integer Basics
@section Integer Basics
Integers in Emacs Lisp are not limited to the machine word size.
Under the hood, though, there are two kinds of integers: smaller
ones, called @dfn{fixnums}, and larger ones, called @dfn{bignums}.
Some functions in Emacs accept only fixnums. Also, while fixnums can
be compared for numeric equality with @code{eq}, bignums require
more-heavyweight equality predicates like @code{eql} and @code{=}.
The range of values for bignums is limited by the amount of main
memory, by machine characteristics such as the size of the word used
to represent a bignum's exponent, and by the @code{integer-width}
variable. These limits are typically much more generous than the
limits for fixnums. A bignum is never numerically equal to a fixnum;
if Emacs computes an integer in fixnum range, it represents the
integer as a fixnum, not a bignum.
The range of values for a fixnum depends on the machine. The
minimum range is @minus{}536,870,912 to 536,870,911 (30 bits; i.e.,
@ifnottex
@minus{}2**29
@end ifnottex
@tex
@math{-2^{29}}
@end tex
to
@ifnottex
2**29 @minus{} 1),
@end ifnottex
@tex
@math{2^{29}-1}),
@end tex
but many machines provide a wider range.
The Lisp reader reads an integer as a nonempty sequence
of decimal digits with optional initial sign and optional
final period.
@ -145,6 +112,46 @@ 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.
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}.
Integers in Emacs Lisp are not limited to the machine word size.
Under the hood, though, there are two kinds of integers: smaller ones,
called @dfn{fixnums}, and larger ones, called @dfn{bignums}. Although
Emacs Lisp code ordinarily should not depend on whether an integer is
a fixnum or a bignum, older Emacs versions support only fixnums, some
functions in Emacs still accept only fixnums, and older Emacs Lisp
code may have trouble when given bignums. For example, while older
Emacs Lisp code could safely compare integers for numeric equality
with @code{eq}, the presence of bignums means that equality predicates
like @code{eql} and @code{=} should now be used to compare integers.
The range of values for bignums is limited by the amount of main
memory, by machine characteristics such as the size of the word used
to represent a bignum's exponent, and by the @code{integer-width}
variable. These limits are typically much more generous than the
limits for fixnums. A bignum is never numerically equal to a fixnum;
if Emacs computes an integer in fixnum range, it represents the
integer as a fixnum, not a bignum.
The range of values for a fixnum depends on the machine. The
minimum range is @minus{}536,870,912 to 536,870,911 (30 bits; i.e.,
@ifnottex
@minus{}2**29
@end ifnottex
@tex
@math{-2^{29}}
@end tex
to
@ifnottex
2**29 @minus{} 1),
@end ifnottex
@tex
@math{2^{29}-1}),
@end tex
but many machines provide a wider range.
@cindex largest fixnum
@cindex maximum fixnum
@defvar most-positive-fixnum
@ -207,10 +214,6 @@ Setting this variable to a large number can be costly if a computation
creates huge integers.
@end defvar
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}.
@node Float Basics
@section Floating-Point Basics