Hello,

Current byte compiler has potential problems in arithmetic operations.
Examples are all on Intel 32-bit. Result may occur in other
environments.

1. Operations are all compiled to binary operations. It may cause
overflows or truncations in floating point data operations.

   Examples.
      (upper result is by interpreter, lower is by code after compile)

    (let ((a most-positive-fixnum) (b 1) (c 1.0))  (+ a b c))
         --> 268435457.0
         --> -268435455.0

    (let ((a most-positive-fixnum) (b -2) (c 1.0)) (- a b c))
         --> 268435456.0
         --> -268435456.0

    (let ((a most-positive-fixnum) (b 2) (c 1.0))  (* a b c))
         --> 536870910.0
         --> -2.0

    (let ((a 3) (b 2) (c 1.0)) (/ a b c))
         --> 1.5
         --> 1.0


2. Most integer constants are moved to the end of expressions and
pre-calculated at compile time. Changing of order may cause different
result from original expressions.
(In other words, `byte-optimize-delay-constants-math' should not be called)

   Examples.

      (let ((a (+ 1 (expt 2 -52))) (b (expt 2 -53))) (+ a -1 b))
         --> 3.3306690738754696e-016
         --> 4.440892098500626e-016

      (let ((a (expt 2 -1074)) (b 0.25)) (* a 4 b))
         --> 5e-324
         --> 0.0


3. Mulitiplication/Division optimization sometimes don't consider
floating point operators.

   Examples.

      (let ((a 1.0)) (* a 0))
         --> 0.0
         --> 0

      (let ((a 1.0)) (* a 2.0 0))
         --> 0.0
         --> 0

      (let ((a 1.0)) (/ 0 a))
         --> 0.0
         --> 0

      (let ((a 1.0)) (/ 3 a 2))
         --> 1.5
         --> 1.0


4. In division, optimizing -1 twice and cause erroneous results.

   Examples.

      (/ 3 -1)
         --> -3
         --> 3


Attached files are rewrittren version and too much changed, so it is
possibly just for references (At least, alias functions are not
treated well, and not comprehensively tested).

   bytecomp-patch.el -- contain only new and modified symbols/functions.
   byte-opt-test.el  -- test function that shows interpreter/original/revised
                        results.
   test.log          -- test result using above files.
   byte-opt.el bytecomp.el -- changed files to replace.

Regards,
Shigeru