(Integer Basics): Clarify radix explanation.

(Predicates on Numbers): Minor clarification.
(Comparison of Numbers): Minor clarification.  Clarify eql.
Typos in min, max.
(Math Functions): Clarify overflow in expt.

1 files changed, 34 insertions, 28 deletions

diff --git a/lispref/numbers.texi b/lispref/numbers.texi
index 53435da081b..776251e4933 100644
--- a/lispref/numbers.texi
+++ b/lispref/numbers.texi
@@ -73,14 +73,21 @@ initial sign and optional final period.
 @cindex hex numbers
 @cindex octal numbers
 @cindex reading numbers in hex, octal, and binary
-  In addition, the Lisp reader recognizes a syntax for integers in
-bases other than 10: @samp{#B@var{integer}} reads @var{integer} in
-binary (radix 2), @samp{#O@var{integer}} reads @var{integer} in octal
-(radix 8), @samp{#X@var{integer}} reads @var{integer} in hexadecimal
-(radix 16), and @samp{#@var{radix}r@var{integer}} reads @var{integer}
-in radix @var{radix} (where @var{radix} is between 2 and 36,
-inclusively).  Case is not significant for the letter after @samp{#}
-(@samp{B}, @samp{O}, etc.) that denotes the radix.
+  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
@@ -211,13 +218,12 @@ down to an integer.
 @node Predicates on Numbers
 @section Type Predicates for Numbers
 
-  The functions in this section test whether the argument is a number or
-whether it is a certain sort of number.  The functions @code{integerp}
-and @code{floatp} can take any type of Lisp object as argument (the
-predicates 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}.
+  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 a floating point
@@ -251,7 +257,7 @@ considered non-negative.
 This predicate tests whether its argument is zero, and returns @code{t}
 if so, @code{nil} otherwise.  The argument must be a number.
 
-These two forms are equivalent: @code{(zerop x)} @equiv{} @code{(= x 0)}.
+@code{(zerop x)} is equivalent to @code{(= x 0)}.
 @end defun
 
 @node Comparison of Numbers
@@ -275,10 +281,11 @@ numbers or markers.  However, it is a good idea to use @code{=} if you
 can, even for comparing integers, just in case we change the
 representation of integers in a future Emacs version.
 
-  Sometimes it is useful to compare numbers with @code{equal}; it 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.
+  Sometimes it is useful to compare numbers with @code{equal}; it
+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.
+@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 two floating
@@ -309,10 +316,10 @@ returns @code{t} if so, @code{nil} otherwise.
 @end defun
 
 @defun eql value1 value2
-This function compares two floating point numbers like @code{=}, and
-compares two integers like @code{=}, and acts like @code{eq} in all
-other cases.  Thus, @code{(eql 1.0 1)} returns @code{nil}, but
-@code{(eql 1.0 1.0)} and @code{(eql 1 1)} both return @code{t}.
+This function acts like @code{eq} except when both arguments are
+numbers.  It compares numbers by type and numberic 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
@@ -345,7 +352,7 @@ otherwise.
 
 @defun max number-or-marker &rest numbers-or-markers
 This function returns the largest of its arguments.
-If any of the argument is floating-point, the value is returned
+If any of the arguments is floating-point, the value is returned
 as floating point, even if it was given as an integer.
 
 @example
@@ -360,7 +367,7 @@ as floating point, even if it was given as an integer.
 
 @defun min number-or-marker &rest numbers-or-markers
 This function returns the smallest of its arguments.
-If any of the argument is floating-point, the value is returned
+If any of the arguments is floating-point, the value is returned
 as floating point, even if it was given as an integer.
 
 @example
@@ -1147,8 +1154,7 @@ approximately.
 @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, it is truncated to fit the range of possible
-integer values.
+integer; in this case, overflow causes truncation, so watch out.
 @end defun
 
 @defun sqrt arg