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.

2 files changed, 35 insertions, 13 deletions

diff --git a/doc/lispref/ChangeLog b/doc/lispref/ChangeLog
index ceb199dae88..ce99c81a912 100644
--- a/doc/lispref/ChangeLog
+++ b/doc/lispref/ChangeLog
@@ -1,3 +1,16 @@
+2012-09-11  Paul Eggert  <eggert@cs.ucla.edu>
+
+        Simplify, document, and port floating-point (Bug#12381).
+        * 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.
+
 2012-09-09  Chong Yidong  <cyd@gnu.org>
 
         * lists.texi (Sets And Lists): Explain that the return value for
diff --git a/doc/lispref/numbers.texi b/doc/lispref/numbers.texi
index 17f3ee099bd..7c9672a38c0 100644
--- a/doc/lispref/numbers.texi
+++ b/doc/lispref/numbers.texi
@@ -196,6 +196,14 @@ 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.)
+
+When a function is documented to return a NaN, it returns an
+implementation-defined value when Emacs is running on one of the
+now-rare platforms that do not use @acronym{IEEE} floating point.  For
+example, @code{(log -1.0)} typically returns a NaN, but on
+non-@acronym{IEEE} platforms it returns an implementation-defined
+value.
+
 Here are the read syntaxes for these special floating point values:
 
 @table @asis
@@ -241,7 +249,7 @@ numbers.
 
 @defun logb number
 This function returns the binary exponent of @var{number}.  More
-precisely, the value is the logarithm of @var{number} base 2, rounded
+precisely, the value is the logarithm of |@var{number}| base 2, rounded
 down to an integer.
 
 @example
@@ -694,7 +702,8 @@ arguments.  It also permits floating point arguments; it rounds the
 quotient downward (towards minus infinity) to an integer, and uses that
 quotient to compute the remainder.
 
-An @code{arith-error} results if @var{divisor} is 0.
+If @var{divisor} is zero, @code{mod} signals an @code{arith-error}
+error if both arguments are integers, and returns a NaN otherwise.
 
 @example
 @group
@@ -1096,8 +1105,8 @@ pi/2
 @tex
 @math{\pi/2}
 @end tex
-(inclusive) whose sine is @var{arg}; if, however, @var{arg} is out of
-range (outside [@minus{}1, 1]), it signals a @code{domain-error} error.
+(inclusive) whose sine is @var{arg}.  If @var{arg} is out of range
+(outside [@minus{}1, 1]), @code{asin} returns a NaN.
 @end defun
 
 @defun acos arg
@@ -1108,8 +1117,8 @@ pi
 @tex
 @math{\pi}
 @end tex
-(inclusive) whose cosine is @var{arg}; if, however, @var{arg} is out
-of range (outside [@minus{}1, 1]), it signals a @code{domain-error} error.
+(inclusive) whose cosine is @var{arg}.  If @var{arg} is out of range
+(outside [@minus{}1, 1]), @code{acos} returns a NaN.
 @end defun
 
 @defun atan y &optional x
@@ -1141,8 +1150,8 @@ This is the exponential function; it returns @math{e} to the power
 @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
-@math{e} is used.  If @var{arg} is negative, it signals a
-@code{domain-error} error.
+@math{e} is used.  If @var{arg} or @var{base} is negative, @code{log}
+returns a NaN.
 @end defun
 
 @ignore
@@ -1160,21 +1169,21 @@ lose accuracy.
 @end ignore
 
 @defun log10 arg
-This function returns the logarithm of @var{arg}, with base 10.  If
-@var{arg} is negative, it signals a @code{domain-error} error.
-@code{(log10 @var{x})} @equiv{} @code{(log @var{x} 10)}, at least
-approximately.
+This function returns the logarithm of @var{arg}, with base 10:
+@code{(log10 @var{x})} @equiv{} @code{(log @var{x} 10)}.
 @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.
+If @var{x} is a finite negative number and @var{y} is a finite
+non-integer, @code{expt} returns a NaN.
 @end defun
 
 @defun sqrt arg
 This returns the square root of @var{arg}.  If @var{arg} is negative,
-it signals a @code{domain-error} error.
+@code{sqrt} returns a NaN.
 @end defun
 
 In addition, Emacs defines the following common mathematical