64-bit integer arithmetics v2

[John W. Eaton]

On  5-Oct-2008, Jaroslav Hajek wrote:

| this is an improved version of the previous attempt at implementing
| 64-bit arithmetics.
| The mixed precision operators and relations should now work robustly
| in all cases (and in case you have long double, they will even be fast
| :)
| These expressions should now work as expected:
| uint64(2^64), int64(2^63)...
| a = 1.9*2^61; b = uint64(a); b++; b > a
| a = 1.9*2^61; b = int64(a); b++; b > a
| (note that these two may already work in current tip and/or 3.0.x
| because of the CPU using long double behind the scene, but it will
| probably depend on optimization level) and maybe more ... (tests yet
| to be written).

OK.

| also, the mixed (u)int64-double binary operations avoid precision loss
| (using long double if possible).
| 
| OK to push?

Yes, but before doing that, will you please fix the following?

| +#include <math.h>

Octave C++ files should not include standard C headers directly.
Instead of <math.h>, we should be including <cmath>.

| +#if (SIZEOF_LONG_DOUBLE >= 10) && defined (HAVE_ROUNDL)
| +inline long double xround (long double x) { return roundl (x); }
| +#define OCTAVE_INT_USE_LONG_DOUBLE
| +#endif

The test for SIZEOF_LONG_DOUBLE probably works in practice, but the
overall size doesn't guarantee the precision, does it?  So it would
probably be better to have a test that checks whether a 64-bit integer
can be exactly represented by the long double type.

How about changing the macro to something like
OCTAVE_INT64_FITS_IN_LONG_DOUBLE (I'm not sure of the best name) and
then defining that in config.h if SIZEOF_LONG_DOUBLE is >= 10, and
also inserting a comment in configure.in saying that it would be
better to have a proper test for this rather than just checking the
size?

Also, it would be good to avoid these warnings:

  /home/jwe/src/octave/liboctave/oct-inttypes.h: In static member function 
'static T octave_int_base<T>::convert_real(const S&) [with S = long double, T = 
long int]':
  /home/jwe/src/octave/liboctave/oct-inttypes.h:768:   instantiated from 
'octave_int<T>::octave_int(long double) [with T = long int]'
  /home/jwe/src/octave/liboctave/oct-inttypes.h:1022:   instantiated from here
  /home/jwe/src/octave/liboctave/oct-inttypes.h:287: warning: unused variable 
'thmin'
  /home/jwe/src/octave/liboctave/oct-inttypes.h:288: warning: unused variable 
'thmax'

Since oct-inttypes.h is included in many files, these are repeated
many times.

Thanks,

jwe